Compressible Dns Within Pecos
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COMPRESSIBLE DNS WITHIN PECOS Kalen Braman, Rhys Ulerich Predictive Engineering and Computational Science
Motivation
DNS’ role in the turbulence model validation cycle
PECOS calibration and validation requirements: • UQ-driven approach requires significant amounts of calibration and validation data • To succeed at QoI prediction, turbulence modeling effort needs high quality data for effective calibration
Prior on Parameters
Parameters become Priors
Prior Parameters Calibration Process
Impact of turbulent boundary layer physics on reentry problem QoI: • Turbulence enhances transport of heat and chemical species to thermal protection system surface • Location of turbulence onset significantly affects total heat load • Uncertainty in transition location causes large uncertainties in reentry problem QoI • Injection of ablation products at surface can trigger or enhance turbulence in the boundary layer [Par84] • Enhanced diffusion due to turbulence carries radiation absorbing products away from the surface, which reduces gas absorption of radiation, and thus increases radiation reaching the ablator surface [MOSS05]
Validation Process
Math Model Data from DNS
QoI
Experimental data
QoI Data from DNS
Inadequate Data
Decision
Too Much Uncertainty
experimental data
Invalid Model
Not invalid
• DNS aids calibration and validation efforts by augmenting experimental data
Goals
• DNS provides data with measurement uncertainties only limited by available compute resources • DNS samples portions of the turbulence parameter space not explored in physical laboratories • DNS supports turbulence model improvement efforts by being the highest fidelity “model”
• Support PECOS calibration and validation process • Advance understanding of ablation product/turbulent boundary layer interaction • Improve understanding of turbulence transition phenomena for transpired compressible flows,
especially characterization of what ablative conditions may sustain turbulence
Spectral code details
Finite volume code details
Existing code base: • Legacy compressible DNS code using spectral methods in two homogeneous directions • Uses B-splines in the wall normal direction for their flexibility and resolution properties [KMJ01] • Reduces computational domain via compressible slow growth terms [Spa88] [Gua98] • Proven transpired boundary layer capabilities [VMN08] • Temporal discretization done with explicit, low storage third-order Runge-Kutta [SMR91] • Originally designed to simulate compressible shear flows without strong shocks
• Compressible extension of a finite volume DNS code • MPI-based exhibiting favorable scalability • Formulated with approximately energy conserving convective terms to capture turbulent energy
dynamics • Uses hyperviscosity shock capturing method of Cook and Cabot [CC04] • Suitable for problems on non-periodic domains • Able to handle wall blowing and jets (models for ablation product injection and reaction thruster firing, respectively) • Currently undergoing verification effort for compressible wall-bounded flows
Near term plans: • Increase scenario parameters capabilities (e.g. boundary conditions) to aid use as VV data source • Improve scalability by incorporating petascale FFT techniques [Pek08] • Update code base to comply with PECOS software standards
Density gradient growth in a M∞ = 2.5 boundary layer
Turbulent kinetic energy in a transpiration-driven channel [VMN08] 6
20
(a)
(b)
4
10
2
0
δ
0 -10 -2 0
0.1
y/δ
-20 0
0.2
0.1
y/δ
Simulated density gradient for a perfect gas flow over an adiabatic plate: M∞ = 2.5, T∞ = 273K. Figure courtesy of Heeseok Koo.
0.2
Terms in the turbulent kinetic energy equation for the (a) transpiration-driven and (b) non-transpired channel, normalized by the average production of turbulent kinetic energy. Transpired data taken 40 half channel widths (δ ) downstream from a closed channel head with = 0.025. Convection of turbulent kinetic energy ( ), production ( ), turbulent diffusion ( ), pressure diffusion ( ), pressure dilatation ( ), viscous diffusion ( ), dissipation ( ♦ ), contribution from slow growth terms (×), compressibility terms due to Favre averaging (∗). Obtained from the Reynolds stress tensor’s time evolution, the turbulent kinetic energy equation is
1 ∂ρu00i u00i =− 2 ∂t
1 ∂ u˜2ρu00i u00i |2 ∂x2 {z }
convection of turbulent kinetic energy
− ρu1u00i
∂ui ∂u0i + ∂xs ∂xs
|
∂ 1 ∂ 00 00 00 00 00 − ρui ui u2 − ρui u2 u˜i |2 ∂x2 {z } | {z∂x2 } turbulent diffusion
!
production
1 ∂ρu1 00 00 1 00 00 0 ∂ρ ∂u1 0 − ui ui − ui ui u1 +ρ 2 ∂xs 2 ∂xs ∂xs {z
viscous diffusion
dissipation
Andrew Cook and William Cabot. A high-wavenumber viscosity for high-resolution numerical methods. Journal of Computational Physics, 195:594–601, 2004.
[Gua98]
S. Guarini. Direct Numerical Simulation of Supersonic Turbulent Boundary Layers. PhD thesis, Stanford University, 1998.
[KMJ01]
´ Wai Y. Kwok, Robert D. Moser, and Javier Jimenez. A critical evaluation of the resolution properties of b-spline and compact finite difference methods. Journal of Computational Physics, 174(2):510–551, December 2001.
0 ∂u1 + u1 +ρ ∂xs ∂xs
contribution from slow growth terms
pressure dilation
[CC04]
∂ρ0
}
00 0 u00 00 ∂u ∂τ ∂u ∂p0u002 1 1 ∂p ∂p 1 00 ∂τ i2 i i2 i i 0 00 00 0 − + p + − τik − u1 − u2 + ui . ∂x}i ∂x2 } |Re {z∂xk} | ∂xs ∂x |∂x {z2} |Re {z {z2 Re ∂x2} | {z pressure diffusion
References
compressibility terms due to Favre averaging
The parameter is the ratio of mass injection flux to the streamwise mass flux. The model problem is constructed so that = 1/x. Additional assumptions are required to model the slow derivatives used in this study’s homogenized equations.
[MOSS05] Shingo Matsuyama, Naofumi Ohnishi, Akihiro Sasoh, and Keisuke Sawada. Numerical simulation of galileo probe entry flowfield with radiation and ablation. Journal of Thermophysics and Heat Transfer, 19:28–35, 2005. [Par84]
Chul Park. Injection-induced turbulence in stagnation point boundary layers. AIAA Journal, 36:219–225, 1984.
[Pek08]
Dmitry Pekurovsky. Parallel Three-Dimensional Fast Fourier Transforms (P3DFFT). San Diego Supercomputer Center, 2008.
[SMR91] Philippe R. Spalart, Robert D. Moser, and Michael M. Rogers. Spectral methods for the navier-stokes equations with one infinite and two periodic directions. J. Comput. Phys., 96(2):297–324, 1991. [Spa88]
Philippe R. Spalart. Direct simulation of a turbulent boundary layer up to re = 1410. Journal of Fluid Mechanics, 187:61–98, 1988.
[VMN08] Prem Venugopal, Robert D. Moser, and Fady M. Najjar. Direct numerical simulation of turbulence in injection-driven plane channel flows. Physics of Fluids, 20(10), 2008.
Institute for Computational Engineering and Sciences (ICES)
[email protected], [email protected]
http://pecos.ices.utexas.edu
Motivation
DNS’ role in the turbulence model validation cycle
PECOS calibration and validation requirements: • UQ-driven approach requires significant amounts of calibration and validation data • To succeed at QoI prediction, turbulence modeling effort needs high quality data for effective calibration
Prior on Parameters
Parameters become Priors
Prior Parameters Calibration Process
Impact of turbulent boundary layer physics on reentry problem QoI: • Turbulence enhances transport of heat and chemical species to thermal protection system surface • Location of turbulence onset significantly affects total heat load • Uncertainty in transition location causes large uncertainties in reentry problem QoI • Injection of ablation products at surface can trigger or enhance turbulence in the boundary layer [Par84] • Enhanced diffusion due to turbulence carries radiation absorbing products away from the surface, which reduces gas absorption of radiation, and thus increases radiation reaching the ablator surface [MOSS05]
Validation Process
Math Model Data from DNS
QoI
Experimental data
QoI Data from DNS
Inadequate Data
Decision
Too Much Uncertainty
experimental data
Invalid Model
Not invalid
• DNS aids calibration and validation efforts by augmenting experimental data
Goals
• DNS provides data with measurement uncertainties only limited by available compute resources • DNS samples portions of the turbulence parameter space not explored in physical laboratories • DNS supports turbulence model improvement efforts by being the highest fidelity “model”
• Support PECOS calibration and validation process • Advance understanding of ablation product/turbulent boundary layer interaction • Improve understanding of turbulence transition phenomena for transpired compressible flows,
especially characterization of what ablative conditions may sustain turbulence
Spectral code details
Finite volume code details
Existing code base: • Legacy compressible DNS code using spectral methods in two homogeneous directions • Uses B-splines in the wall normal direction for their flexibility and resolution properties [KMJ01] • Reduces computational domain via compressible slow growth terms [Spa88] [Gua98] • Proven transpired boundary layer capabilities [VMN08] • Temporal discretization done with explicit, low storage third-order Runge-Kutta [SMR91] • Originally designed to simulate compressible shear flows without strong shocks
• Compressible extension of a finite volume DNS code • MPI-based exhibiting favorable scalability • Formulated with approximately energy conserving convective terms to capture turbulent energy
dynamics • Uses hyperviscosity shock capturing method of Cook and Cabot [CC04] • Suitable for problems on non-periodic domains • Able to handle wall blowing and jets (models for ablation product injection and reaction thruster firing, respectively) • Currently undergoing verification effort for compressible wall-bounded flows
Near term plans: • Increase scenario parameters capabilities (e.g. boundary conditions) to aid use as VV data source • Improve scalability by incorporating petascale FFT techniques [Pek08] • Update code base to comply with PECOS software standards
Density gradient growth in a M∞ = 2.5 boundary layer
Turbulent kinetic energy in a transpiration-driven channel [VMN08] 6
20
(a)
(b)
4
10
2
0
δ
0 -10 -2 0
0.1
y/δ
-20 0
0.2
0.1
y/δ
Simulated density gradient for a perfect gas flow over an adiabatic plate: M∞ = 2.5, T∞ = 273K. Figure courtesy of Heeseok Koo.
0.2
Terms in the turbulent kinetic energy equation for the (a) transpiration-driven and (b) non-transpired channel, normalized by the average production of turbulent kinetic energy. Transpired data taken 40 half channel widths (δ ) downstream from a closed channel head with = 0.025. Convection of turbulent kinetic energy ( ), production ( ), turbulent diffusion ( ), pressure diffusion ( ), pressure dilatation ( ), viscous diffusion ( ), dissipation ( ♦ ), contribution from slow growth terms (×), compressibility terms due to Favre averaging (∗). Obtained from the Reynolds stress tensor’s time evolution, the turbulent kinetic energy equation is
1 ∂ρu00i u00i =− 2 ∂t
1 ∂ u˜2ρu00i u00i |2 ∂x2 {z }
convection of turbulent kinetic energy
− ρu1u00i
∂ui ∂u0i + ∂xs ∂xs
|
∂ 1 ∂ 00 00 00 00 00 − ρui ui u2 − ρui u2 u˜i |2 ∂x2 {z } | {z∂x2 } turbulent diffusion
!
production
1 ∂ρu1 00 00 1 00 00 0 ∂ρ ∂u1 0 − ui ui − ui ui u1 +ρ 2 ∂xs 2 ∂xs ∂xs {z
viscous diffusion
dissipation
Andrew Cook and William Cabot. A high-wavenumber viscosity for high-resolution numerical methods. Journal of Computational Physics, 195:594–601, 2004.
[Gua98]
S. Guarini. Direct Numerical Simulation of Supersonic Turbulent Boundary Layers. PhD thesis, Stanford University, 1998.
[KMJ01]
´ Wai Y. Kwok, Robert D. Moser, and Javier Jimenez. A critical evaluation of the resolution properties of b-spline and compact finite difference methods. Journal of Computational Physics, 174(2):510–551, December 2001.
0 ∂u1 + u1 +ρ ∂xs ∂xs
contribution from slow growth terms
pressure dilation
[CC04]
∂ρ0
}
00 0 u00 00 ∂u ∂τ ∂u ∂p0u002 1 1 ∂p ∂p 1 00 ∂τ i2 i i2 i i 0 00 00 0 − + p + − τik − u1 − u2 + ui . ∂x}i ∂x2 } |Re {z∂xk} | ∂xs ∂x |∂x {z2} |Re {z {z2 Re ∂x2} | {z pressure diffusion
References
compressibility terms due to Favre averaging
The parameter is the ratio of mass injection flux to the streamwise mass flux. The model problem is constructed so that = 1/x. Additional assumptions are required to model the slow derivatives used in this study’s homogenized equations.
[MOSS05] Shingo Matsuyama, Naofumi Ohnishi, Akihiro Sasoh, and Keisuke Sawada. Numerical simulation of galileo probe entry flowfield with radiation and ablation. Journal of Thermophysics and Heat Transfer, 19:28–35, 2005. [Par84]
Chul Park. Injection-induced turbulence in stagnation point boundary layers. AIAA Journal, 36:219–225, 1984.
[Pek08]
Dmitry Pekurovsky. Parallel Three-Dimensional Fast Fourier Transforms (P3DFFT). San Diego Supercomputer Center, 2008.
[SMR91] Philippe R. Spalart, Robert D. Moser, and Michael M. Rogers. Spectral methods for the navier-stokes equations with one infinite and two periodic directions. J. Comput. Phys., 96(2):297–324, 1991. [Spa88]
Philippe R. Spalart. Direct simulation of a turbulent boundary layer up to re = 1410. Journal of Fluid Mechanics, 187:61–98, 1988.
[VMN08] Prem Venugopal, Robert D. Moser, and Fady M. Najjar. Direct numerical simulation of turbulence in injection-driven plane channel flows. Physics of Fluids, 20(10), 2008.
Institute for Computational Engineering and Sciences (ICES)
[email protected], [email protected]
http://pecos.ices.utexas.edu
