Guillaume Blanquart

An 11-species thermochemical model for H$_2$/ He mixtures with state-specific kinetics for atomic H is developed and used to simulate 1-D shocks at conditions relevant for ice and gas giant entry flows. To implement this kinetic model, a literature review of the state-specific excitation and ionization rate constants of atomic H is first performed. While electron-impact rate constants from various sources are found to be in good agreement, large discrepancies are found in the limited data available on heavy-particle-impact rate constants. To validate the kinetic model, 1-D steady shocks are simulated using a space-marching code that explicitly accounts for shock tube boundary layer effects. The resulting radiance profiles are compared to experimental data from the NASA Ames Electric Arc Shock Tube (EAST) facility, and are found to reproduce the measured values reasonably accurately while capturing the distinct induction zone behavior observed in the experiments. A sensitivity analysis of the kinetic rates and boundary layer treatment reveals avenues for further improvement of the model. Finally, a comparison to alternate models from the literature underscores the improved accuracy of the present model in predicting ionization and radiation profiles.

An 11-species thermochemical model for H$_2$/ He mixtures with state-specific kinetics for atomic H is developed and used to simulate 1-D shocks at conditions relevant for ice and gas giant entry flows. To implement this kinetic model, a literature review of the state-specific excitation and ionization rate constants of atomic H is first performed. While electron-impact rate constants from various sources are found to be in good agreement, large discrepancies are found in the limited data available on heavy-particle-impact rate constants. To validate the kinetic model, 1-D steady shocks are simulated using a space-marching code that explicitly accounts for shock tube boundary layer effects. The resulting radiance profiles are compared to experimental data from the NASA Ames Electric Arc Shock Tube (EAST) facility, and are found to reproduce the measured values reasonably accurately while capturing the distinct induction zone behavior observed in the experiments. A sensitivity analysis of the kinetic rates and boundary layer treatment reveals avenues for further improvement of the model. Finally, a comparison to alternate models from the literature underscores the improved accuracy of the present model in predicting ionization and radiation profiles.

The dynamics of turbulent Rayleigh–Taylor (RT) mixing layers is investigated across a broad range of Atwood and Reynolds numbers using the statistically stationary RT flow configuration – a computational framework that enables simulation of a minimal flow unit for RT flows at reduced cost. Normalizations are developed for all dominant non-transport terms in the continuity, mixed mass and turbulent kinetic energy budgets in terms of the input parameters: the mixing layer height $h$ , gravitational acceleration $g$ and fluid densities $\rho _H$ and $\rho _L$ . Most normalized quantities collapse well across the parameter space. In some cases, variations in the Atwood number $A$ (or the density ratio $R$ ) lead to consistent integral magnitudes but spatially shifted profiles. These shifts are primarily related to a division by density and are similarly observed in the analytical solution of the one-dimensional variable-density diffusion problem. The analysis introduces a reference density for the mixed mass, examines trends in Favre-averaged statistics and derives a scaling law for the growth rate of the mixing layer. For height definitions encompassing the full extent of the layer, the conventional growth parameter, $\alpha =\dot {h}^2/4Agh$ , varies with Atwood number. Our analysis leads to an alternative formulation using an effective Atwood number, $A^*= (\ln R)/2$ , that is consistent with the scaling proposed by Belen’kii & Fradkin (1965 Trudy FIAN 29, 207–238). Applying this $A^*$ scaling to existing RT data, the corresponding growth parameter, $\alpha ^*=\dot {h}^2/4A^*gh$ , remains nearly constant across all Atwood numbers considered, offering a unified scaling for variable-density RT flows.

The dynamics of turbulent Rayleigh–Taylor (RT) mixing layers is investigated across a broad range of Atwood and Reynolds numbers using the statistically stationary RT flow configuration – a computational framework that enables simulation of a minimal flow unit for RT flows at reduced cost. Normalizations are developed for all dominant non-transport terms in the continuity, mixed mass and turbulent kinetic energy budgets in terms of the input parameters: the mixing layer height $h$ , gravitational acceleration $g$ and fluid densities $\rho _H$ and $\rho _L$ . Most normalized quantities collapse well across the parameter space. In some cases, variations in the Atwood number $A$ (or the density ratio $R$ ) lead to consistent integral magnitudes but spatially shifted profiles. These shifts are primarily related to a division by density and are similarly observed in the analytical solution of the one-dimensional variable-density diffusion problem. The analysis introduces a reference density for the mixed mass, examines trends in Favre-averaged statistics and derives a scaling law for the growth rate of the mixing layer. For height definitions encompassing the full extent of the layer, the conventional growth parameter, $\alpha =\dot {h}^2/4Agh$ , varies with Atwood number. Our analysis leads to an alternative formulation using an effective Atwood number, $A^*= (\ln R)/2$ , that is consistent with the scaling proposed by Belen’kii & Fradkin (1965 Trudy FIAN 29, 207–238). Applying this $A^*$ scaling to existing RT data, the corresponding growth parameter, $\alpha ^*=\dot {h}^2/4A^*gh$ , remains nearly constant across all Atwood numbers considered, offering a unified scaling for variable-density RT flows.

In an early theoretical work published in 1965, Belen'kii & Fradkin proposed a turbulent diffusivity model for Rayleigh--Taylor (RT) mixing. We review its derivation and present alternative arguments leading to the same final similarity equation. The original work then introduced an approximation that led to a simplified ordinary differential equation (ODE), which was used primarily to derive the important scaling result, $h \sim (\ln R)gt^2$. Here, we extend the analysis by examining the solutions to both the full similarity ODE and the simplified ODE in detail. It is shown that the full similarity equation captures many now well-known features of non-Boussinesq RT flows, including asymmetric spike and bubble growth and a systematic shift of velocity statistics toward the light-fluid side. Comparisons of the theoretical model with numerical and experimental studies show reasonable agreement in both spatial profiles and growth trends of mixing layer heights. We further show that a global mass correction applied to the simplified solution closely approximates the full solution, highlighting that, to leading order, RT mixing is governed by the competing dynamics between diffusion of $\ln \barρ$ and mass conservation.

In an early theoretical work published in 1965, Belen'kii & Fradkin proposed a turbulent diffusivity model for Rayleigh--Taylor (RT) mixing. We review its derivation and present alternative arguments leading to the same final similarity equation. The original work then introduced an approximation that led to a simplified ordinary differential equation (ODE), which was used primarily to derive the important scaling result, $h \sim (\ln R)gt^2$. Here, we extend the analysis by examining the solutions to both the full similarity ODE and the simplified ODE in detail. It is shown that the full similarity equation captures many now well-known features of non-Boussinesq RT flows, including asymmetric spike and bubble growth and a systematic shift of velocity statistics toward the light-fluid side. Comparisons of the theoretical model with numerical and experimental studies show reasonable agreement in both spatial profiles and growth trends of mixing layer heights. We further show that a global mass correction applied to the simplified solution closely approximates the full solution, highlighting that, to leading order, RT mixing is governed by the competing dynamics between diffusion of $\ln \barρ$ and mass conservation.

This work presents a detailed description of the thermochemical nonequilibrium dissociation of diatomic molecules and applies this theory to the case of [Formula: see text] dissociation. In particular, the rovibrational state-specific master equations are analyzed in three key limits/regimes of dissociation-dominated flows: the thermal equilibrium limit, the quasi-steady-state (QSS) regime, and the pre-QSS regime. Under several simplifying assumptions, the macroscopic chemical source term and rovibrational energy expressions that hold in all of these regimes and are ultimately only a function of the translational temperature, [Formula: see text], and the degree of dissociation, [Formula: see text], are proposed. These expressions have two nonequilibrium input parameters: the QSS value in the absence of recombination, i.e., [Formula: see text] for the dissociation rate constant and [Formula: see text] for the rovibrational energy, and a pre-QSS correction factor, [Formula: see text]. Despite their simple functional forms, the proposed expressions are able to reproduce the majority of master equation results for a 0-D isothermal and isochoric reactor for the case of [Formula: see text] dissociation with the third bodies [Formula: see text], H, and He.

We propose a computational framework for simulating the self-similar regime of turbulent Rayleigh–Taylor (RT) mixing layers in a statistically stationary manner. By leveraging the anticipated self-similar behaviour of RT mixing layers, a transformation of the vertical coordinate and velocities is applied to the Navier–Stokes equations (NSE), yielding modified equations that resemble the original NSE but include two sets of additional terms. Solving these equations, a statistically stationary RT (SRT) flow is achieved. Unlike temporally growing Rayleigh–Taylor (TRT) flow, SRT flow is independent of initial conditions and can be simulated over infinite simulation time without escalating resolution requirements, hence guaranteeing statistical convergence. Direct numerical simulations (DNS) are performed at an Atwood number of 0.5 and unity Schmidt number. By varying the ratio of the mixing layer height to the domain width, a minimal flow unit of aspect ratio 1.5 is found to approximate TRT turbulence in the self-similar mode-coupling regime. The SRT minimal flow unit has one-sixteenth the number of grid points required by the equivalent TRT simulation of the same Reynolds number and grid resolution. The resultant flow corresponds to a theoretical limit where self-similarity is observed in all fields and across the entire spatial domain – a late-time state that existing experiments and DNS of TRT flow have difficulties attaining. Simulations of the SRT minimal flow unit span TRT-equivalent Reynolds numbers (based on mixing layer height) ranging from 500 to 10 800. The SRT results are validated against TRT data from this study as well as from Cabot & Cook ( Nat. Phys. , vol. 2, 2006, pp. 562–568).

This work presents a detailed description of the thermochemical non-equilibrium dissociation of diatomic molecules, and applies this theory to the case of $\rm H_2$ dissociation. The master equations are used to derive corresponding aggregate rate constant expressions that hold for any degree of thermochemical non-equilibrium. These general expressions are analyzed in three key limits/ regimes: the thermal equilibrium limit, the quasi-steady-state (QSS) regime, and the pre-QSS regime. Under several simplifying assumptions, an analytical source term expression that holds in all of these regimes, and is only a function of the translational temperature, $T_{\rm t}$, and the fraction of dissociation, $ϕ_{\rm A}$, is proposed. This expression has two input parameters: the QSS dissociation rate constant in the absence of recombination, $k_{\rm d,nr}(T_{\rm t})$, and a pre-QSS correction factor, $η(T_{\rm t})$. The value of $η(T_{\rm t})$ is evaluated by comparing the predictions of the proposed expression against existing master equation simulations of a 0-D isothermal and isochoric reactor for the case of $\rm H_2$ dissociation with the third-bodies $\rm H_2$, $\rm H$, and $\rm He$. Despite its simple functional form, the proposed expression is able to reproduce the master equation results for the majority of the tested conditions. The best fit of $k_{\rm d,nr}(T_{\rm t})$ is then evaluated by conducting a detailed literature review. Data from a wide range of experimental and computational studies are considered for the third-bodies $\rm H_2$, $\rm H$, and inert gases, and fits that are valid from 200 to 20,000 K are proposed. From this review, the uncertainty of the proposed fits are estimated to be less than a factor of two.

Lean turbulent premixed hydrogen/air flames have substantially increased flame speeds, commonly attributed to differential diffusion effects. In this work, the effect of turbulence on lean hydrogen combustion is studied through Direct Numerical Simulation using detailed chemistry and detailed transport. Simulations are conducted at six Karlovitz numbers and three integral length scales. A general expression for the burning efficiency is proposed which depends on the conditional mean chemical source term and gradient of a progress variable. At a fixed Karlovitz number, the normalized turbulent flame speed and area both increase linearly with the integral length scale ratio. The effect on the mean source term profile is minimal, indicating that the increase in flame speed can solely be attributed to the increase in flame area. At a fixed integral length scale, both the flame speed and area first increase with Karlovitz number before decreasing. At higher Karlovitz numbers, the diffusivity is enhanced due to penetration of turbulence into the reaction zone, significantly dampening differential diffusion effects.

A 23-species State-to-State (StS) thermochemical model for H2/He mixtures is developed and used to simulate 1-D shocks at conditions relevant for ice and gas giant entry flows. To implement this StS model, a literature review of the state-specific excitation and ionization rates of atomic H is first performed. While electron impact rates from various sources are found to be in relatively good agreement, large discrepancies are found in the limited data available on heavy particle impact rates. To investigate the impact of these discrepancies on the predicted shock and radiance profiles, simulations are performed for three different versions of the kinetic model, each with a different set of heavy particle impact rates from the literature. Of these three models, two are found to over-predict and one is found to under-predict the radiance values seen in corresponding experimental data from the NASA Ames Electric Arc Shock Tube (EAST) facility. A sensitivity analysis to the electron and heavy particle impact rates is then performed, from which an improved kinetic model with modified rates is proposed. This modified kinetic model is found to reproduce the total integrated radiance from one of the EAST shot conditions reasonably accurately. However, some discrepancies are still found in the relative contributions to the total radiance from different spectral features, suggesting that additional improvements to the kinetic model still need to be made.

Lean turbulent premixed hydrogen/air flames have substantially increased flame speeds, commonly attributed to differential diffusion effects. In this work, the effect of turbulence on lean hydrogen combustion is studied through Direct Numerical Simulation using detailed chemistry and detailed transport. Simulations are conducted at six Karlovitz numbers and three integral length scales. A general expression for the burning efficiency is proposed which depends on the conditional mean chemical source term and gradient of a progress variable. At a fixed Karlovitz number, the normalized turbulent flame speed and area both increase linearly with the integral length scale ratio. The effect on the mean source term profile is minimal, indicating that the increase in flame speed can solely be attributed to the increase in flame area. At a fixed integral length scale, both the flame speed and area first increase with Karlovitz number before decreasing. At higher Karlovitz numbers, the diffusivity is enhanced due to penetration of turbulence into the reaction zone, significantly dampening differential diffusion effects.

View Video Presentation: https://doi.org/10.2514/6.2023-3728.vid Several different thermochemical models for H2/He mixtures are used to simulate a 1-D shock in a viscous CFD code at conditions relevant for hypersonic entry into the ice and gas giants. These models range from a 6-species, 1-temperature (1-T) model, to more complex 17 and 25-species state-to-state (StS) models. Corresponding radiance profiles for each of these models are then computed using a radiation code, and results are compared to experimental data from the NASA Ames Electric Arc Shock Tube (EAST) facility. Overall, the 6-species model with a quasi-steady state (QSS) solver for atomic H and modified ionization rates, along with both the 17 and 25-species StS models, are found to reproduce the magnitude of the radiance seen in the EAST experiments reasonably accurately. Two additional changes to the modeling of species diffusion fluxes are also investigated: the exclusion of a gradient of mixture molecular weight term, as well as the inclusion of Soret/ Dufour effects. It is determined that these changes to the transport modeling have a negligible impact on the flowfield and therefore the radiance predictions for the H2/He shock conditions considered in this study.