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NASA NTRS2014

Turbulence Modeling Verification and Validation

Computational fluid dynamics (CFD) software that solves the Reynolds-averaged Navier-Stokes (RANS) equations has been in routine use for more than a quarter of a century. It is currently employed not only for basic research in fluid dynamics, but also for the analysis and design processes in many industries worldwide, including aerospace, automotive, power generation, chemical manufacturing, polymer processing, and petroleum exploration. A key feature of RANS CFD is the turbulence model. Because the RANS equations are unclosed, a model is necessary to describe the effects of the turbulence on the mean flow, through the Reynolds stress terms. The turbulence model is one of the largest sources of uncertainty in RANS CFD, and most models are known to be flawed in one way or another. Alternative methods such as direct numerical simulations (DNS) and large eddy simulations (LES) rely less on modeling and hence include more physics than RANS. In DNS all turbulent scales are resolved, and in LES the large scales are resolved and the effects of the smallest turbulence scales are modeled. However, both DNS and LES are too expensive for most routine industrial usage on today's computers. Hybrid RANS-LES, which blends RANS near walls with LES away from walls, helps to moderate the cost while still retaining some of the scale-resolving capability of LES, but for some applications it can still be too expensive. Even considering its associated uncertainties, RANS turbulence modeling has proved to be very useful for a wide variety of applications. For example, in the aerospace field, many RANS models are considered to be reliable for computing attached flows. However, existing turbulence models are known to be inaccurate for many flows involving separation. Research has been ongoing for decades in an attempt to improve turbulence models for separated and other nonequilibrium flows. When developing or improving turbulence models, both verification and validation are important steps in the process. Verification insures that the CFD code is solving the equations as intended (no errors in the implementation). This is typically done either through the method of manufactured solutions (MMS) or through careful step-by-step comparisons with other verified codes. After the verification step is concluded, validation is performed to document the ability of the turbulence model to represent different types of flow physics. Validation can involve a large number of test case comparisons with experiments, theory, or DNS. Organized workshops have proved to be valuable resources for the turbulence modeling community in its pursuit of turbulence modeling verification and validation. Workshop contributors using different CFD codes run the same cases, often according to strict guidelines, and compare results. Through these comparisons, it is often possible to (1) identify codes that have likely implementation errors, and (2) gain insight into the capabilities and shortcomings of different turbulence models to predict the flow physics associated with particular types of flows. These are valuable lessons because they help bring consistency to CFD codes by encouraging the correction of faulty programming and facilitating the adoption of better models. They also sometimes point to specific areas needed for improvement in the models. In this paper, several recent workshops are summarized primarily from the point of view of turbulence modeling verification and validation. Furthermore, the NASA Langley Turbulence Modeling Resource website is described. The purpose of this site is to provide a central location where RANS turbulence models are documented, and test cases, grids, and data are provided. The goal of this paper is to provide an abbreviated survey of turbulence modeling verification and validation efforts, summarize some of the outcomes, and give some ideas for future endeavors in this area.

Rumsey, Christopher L.↗
NASA NTRS2021

Overview of Dragonfly Entry Aerosciences Measurements (DrEAM)

NASA Ames Research Center (ARC) leads the Dragonfly Entry Aerosciences Measurements (DrEAM) project, which is an aeroshell instrumentation suite on the Dragonfly mission that fulfills the Engineering Science Investigation requirement for the New Frontiers mission. NASA ARC is partnering with NASA Langley Research Center (LaRC) and the German Aerospace Center (DLR) to provide a comprehensive sensor suite, including a DLR-provided Data Acquisition System (DAS). DrEAM will provide key aerothermodynamic data and performance analysis for Dragonfly’s forebody and backshell Thermal Protection System (TPS). Titan’s atmosphere predominantly consists of ni-trogen (~98% by mole) with small amounts of me-thane (~2% by mole) and other trace gases. CN is a strong radiator, and is found in nonequilibrium con-centrations for Titan entry. The accurate modeling of nonequilibrium CN radiation has proven to be a diffi-cult task. Prompted by the Huygens mission, many experimental campaigns and analyses were performed to better understand the aerothermal environments experienced by the probe during Titan entry [1]. How-ever, the Huygens probe carried no heatshield instru-mentation. Therefore, the DrEAM sensor suite will sig-nificantly advance the state-of-the-art not only by documenting the environment and performance of Dragonfly’s entry system but also by making key in situ measurements in Titan’s atmosphere for the first time. Aerothermal environments and TPS response will be measured using sensors whose flight heritage is tak-en from the Mars Entry, Descent, and Landing In-strumentation 2 (MEDLI2) thermocouple plugs and the COMbined Aerothermal and Radiometer Sensor (COMARS) suite [2], with the latter supplied by DLR. The MEDLI2 project used embedded thermocouples to directly measure the in-depth TPS temperature-time history at several locations on the heat shield and backshell of the Mars 2020 entry vehicle. These tem-perature measurements, in turn, can be used to infer surface environments via an inverse analysis proce-dure analogous to that used for MEDLI. For DrEAM, the thermocouple plug subsystem will be known as Dragonfly Sensors for Aero-Thermal Reconstruction (DragSTR). On Schiaparelli, the COMARS suite in-cluded three total surface-mounted heat flux sensors, three pressure sensors, and one radiometer. For DrEAM, the COMARS package will be known as the COmbined Sensor System for Titan Atmosphere (COSSTA). Since the methane concentration in the Titan atmos-phere is directly proportional to the radiative heat flux, the COSSTA measurements will be used to reduce the current uncertainty in the methane volume fraction. Atmospheric density measurements and capsule aero-dynamic data will be obtained through the onboard Inertial Measurement Unit (IMU), supplemented by pressure transducers similar to those used by the MEDLI and MEDLI2 projects. The DrEAM pressure sensors will be known as the Dragonfly Atmospheric Flight Transducers. (DrAFT). The pressure measure-ments, when combined with data from the on-board IMU, will allow for reconstruction of such quantities as vehicle Mach number, freestream density, and atmos-pheric winds. DrAFT measurements will enhance Dragonfly trajectory reconstruction and enable a sepa-ration of the aerodynamics from the atmosphere, as was done for MEDLI [3] and is currently in process for the MEDLI2 flight data set.

EDL↗
NASA NTRS2013

Comparative Study on High-Order Positivity-preserving WENO Schemes

In gas dynamics and magnetohydrodynamics flows, physically, the density and the pressure p should both be positive. In a standard conservative numerical scheme, however, the computed internal energy is obtained by subtracting the kinetic energy from the total energy, resulting in a computed p that may be negative. Examples are problems in which the dominant energy is kinetic. Negative may often emerge in computing blast waves. In such situations the computed eigenvalues of the Jacobian will become imaginary. Consequently, the initial value problem for the linearized system will be ill posed. This explains why failure of preserving positivity of density or pressure may cause blow-ups of the numerical algorithm. The adhoc methods in numerical strategy which modify the computed negative density and/or the computed negative pressure to be positive are neither a conservative cure nor a stable solution. Conservative positivity-preserving schemes are more appropriate for such flow problems. The ideas of Zhang & Shu (2012) and Hu et al. (2012) precisely address the aforementioned issue. Zhang & Shu constructed a new conservative positivity-preserving procedure to preserve positive density and pressure for high-order WENO schemes by the Lax-Friedrichs flux (WENO/LLF). In general, WENO/LLF is too dissipative for flows such as turbulence with strong shocks computed in direct numerical simulations (DNS) and large eddy simulations (LES). The new conservative positivity-preserving procedure proposed in Hu et al. (2012) can be used with any high-order shock-capturing scheme, including high-order WENO schemes using the Roe's flux (WENO/Roe). The goal of this study is to compare the results obtained by non-positivity-preserving methods with the recently developed positivity-preserving schemes for representative test cases. In particular the more difficult 3D Noh and Sedov problems are considered. These test cases are chosen because of the negative pressure/density most often exhibited by standard high-order shock-capturing schemes. The simulation of a hypersonic nonequilibrium viscous shock tube that is related to the NASA Electric Arc Shock Tube (EAST) is also included. EAST is a high-temperature and high Mach number viscous nonequilibrium flow consisting of 13 species. In addition, as most common shock-capturing schemes have been developed for problems without source terms, when applied to problems with nonlinear and/or sti source terms these methods can result in spurious solutions, even when solving a conservative system of equations with a conservative scheme. This kind of behavior can be observed even for a scalar case (LeVeque & Yee 1990) as well as for the case consisting of two species and one reaction (Wang et al. 2012). For further information concerning this issue see (LeVeque & Yee 1990; Griffiths et al. 1992; Lafon & Yee 1996; Yee et al. 2012). This EAST example indicated that standard high-order shock-capturing methods exhibit instability of density/pressure in addition to grid-dependent discontinuity locations with insufficient grid points. The evaluation of these test cases is based on the stability of the numerical schemes together with the accuracy of the obtained solutions.

WENO↗
NASA NTRS2014

Comparitive Study of High-Order Positivity-Preserving WENO Schemes

In gas dynamics and magnetohydrodynamics flows, physically, the density ρ and the pressure p should both be positive. In a standard conservative numerical scheme, however, the computed internal energy is The ideas of Zhang & Shu (2012) and Hu et al. (2012) precisely address the aforementioned issue. Zhang & Shu constructed a new conservative positivity-preserving procedure to preserve positive density and pressure for high-order Weighted Essentially Non-Oscillatory (WENO) schemes by the Lax-Friedrichs flux (WENO/LLF). In general, WENO/LLF is obtained by subtracting the kinetic energy from the total energy, resulting in a computed p that may be negative. Examples are problems in which the dominant energy is kinetic. Negative ρ may often emerge in computing blast waves. In such situations the computed eigenvalues of the Jacobian will become imaginary. Consequently, the initial value problem for the linearized system will be ill posed. This explains why failure of preserving positivity of density or pressure may cause blow-ups of the numerical algorithm. The adhoc methods in numerical strategy which modify the computed negative density and/or the computed negative pressure to be positive are neither a conservative cure nor a stable solution. Conservative positivity-preserving schemes are more appropriate for such flow problems. too dissipative for flows such as turbulence with strong shocks computed in direct numerical simulations (DNS) and large eddy simulations (LES). The new conservative positivity-preserving procedure proposed in Hu et al. (2012) can be used with any high-order shock-capturing scheme, including high-order WENO schemes using the Roe's flux (WENO/Roe). The goal of this study is to compare the results obtained by non-positivity-preserving methods with the recently developed positivity-preserving schemes for representative test cases. In particular the more di cult 3D Noh and Sedov problems are considered. These test cases are chosen because of the negative pressure/density most often exhibited by standard high-order shock-capturing schemes. The simulation of a hypersonic nonequilibrium viscous shock tube that is related to the NASA Electric Arc Shock Tube (EAST) is also included. EAST is a high-temperature and high Mach number viscous nonequilibrium ow consisting of 13 species. In addition, as most common shock-capturing schemes have been developed for problems without source terms, when applied to problems with nonlinear and/or sti source terms these methods can result in spurious solutions, even when solving a conservative system of equations with a conservative scheme. This kind of behavior can be observed even for a scalar case as well as for the case consisting of two species and one reaction.. This EAST example indicated that standard high-order shock-capturing methods exhibit instability of density/pressure in addition to grid-dependent discontinuity locations with insufficient grid points. The evaluation of these test cases is based on the stability of the numerical schemes together with the accuracy of the obtained solutions.

Schemes↗
NASA NTRS2016

Investigation of Non-Equilibrium Radiation for Earth Entry

For Earth re-entry at velocities between 8 and 11.5 km/s, the accuracy of NASA's computational uid dynamic and radiative simulations of non-equilibrium shock layer radiation is assessed through comparisons with measurements. These measurements were obtained in the NASA Ames Research Center's Electric Arc Shock Tube (EAST) facility. The experiments were aimed at measuring the spatially and spectrally resolved radiance at relevant entry conditions for both an approximate Earth atmosphere (79% N2 : 21% O2 by mole) as well as a more accurate composition featuring the trace species Ar and CO2 (78.08% N2 : 20.95% O2 : 0.04% CO2 : 0.93% Ar by mole). The experiments were configured to target a wide range of conditions, of which shots from 8 to 11.5 km/s at 0.2 Torr (26.7 Pa) are examined in this paper. The non-equilibrium component was chosen to be the focus of this study as it can account for a significant percentage of the emitted radiation for Earth re-entry, and more importantly, non-equilibrium has traditionally been assigned a large uncertainty for vehicle design. The main goals of this study are to present the shock tube data in the form of a non-equilibrium metric, evaluate the level of agreement between the experiment and simulations, identify key discrepancies and to examine critical aspects of modeling non-equilibrium radiating flows. Radiance pro les integrated over discreet wavelength regions, ranging from the Vacuum Ultra Violet (VUV) through to the Near Infra-Red (NIR), were compared in order to maximize both the spectral coverage and the number of experiments that could be used in the analysis. A previously defined non-equilibrium metric has been used to allow comparisons with several shots and reveal trends in the data. Overall, LAURA/HARA is shown to under-predict EAST by as much as 40% and over-predict by as much as 12% depending on the shock speed. DPLR/NEQAIR is shown to under-predict EAST by as much as 50% and over-predict by as much as 20% depending on the shock speed. The one standard deviation scatter in the EAST results was calculated to be 31%. An estimate for the upper bound of the absolute error in wall-directed heat flux was calculated. Below 9 km/s, where the relative difference is large, the absolute error in radiative heat flux due to non-equilibrium models is estimated to be less then 1 W/sq cm. At the highest shock speed of 11 km/s, the error in non-equilibrium is estimated to be less than 20 W/sq cm.

Shock Tube↗