Peter C. Ma

An entropy-stable hybrid scheme for simulations of transcritical real-fluid flows

Abstract A finite-volume method is developed for simulating the mixing of turbulent flows at transcritical conditions. Spurious pressure oscillations associated with fully conservative formulations are addressed by extending a double-flux model to real-fluid equations of state. An entropy-stable formulation that combines high-order non-dissipative and low-order dissipative finite-volume schemes is proposed to preserve the physical realizability of numerical solutions across large density gradients. Convexity conditions and constraints on the application of the cubic state equation to transcritical flows are investigated, and conservation properties relevant to the double-flux model are examined. The resulting method is applied to a series of test cases to demonstrate the capability in simulations of problems that are relevant for multi-species transcritical real-fluid flows.

Large Eddy Simulation of Shear Coaxial Rocket Injector: Real Fluid Effects

The implementation and verification of real-fluid effects towards the high-fidelity large eddy simulation of rocket combustors is reported. The non-ideal fluid behavior is modeled using a cubic Peng-Robinson equation of state; a thermodynamically consistent approach is used to convert conserved into primitive variables. The viscosity is estimated by Chung et al.’s method in the supercritical gas phase. In the transcritical liquid phase, a simple, accurate and efficient method to estimate the viscosity as a function of temperature and pressure is proposed. The highly non-linear coupling of the primitive thermodynamic variables requires special consideration in regions of high-density gradients to avoid spurious numerical oscillations. The characterization of the non-linearity of the equation of state identifies the regions of high sensitivity. In these regions, small relative changes in the pressure lead to significant changes in density and/or temperature, therefore, numerical instabilities tend to be amplified in these regions. To avoid non-physical oscillations, a first-order and second-order essentially non-oscillatory (ENO) schemes are locally applied to the flux computation on the faces identified with a dual-threshold relative density sensor. The evaluation of the sensor and capabilities of the non-oscillatory schemes on canonical test cases are presented. Finally, these schemes are used to model two canonical cases.

Sub- or Supercritical? A flamelet analysis of high pressure rocket propellant injection

It remains an open problem as to whether droplets exist during the injection of liquid oxygen in a rocket combustion chamber at pressures higher than the oxygen critical pressure. While surface tension and thus droplets vanish in a pure fluid, a mixture state may exhibit a higher critical pressure, possibly reintroducing surface tension. In this paper, we address this problem by analyzing the non-premixed flamelet representation of combustion under liquid propellant rocket engine (LRE) conditions. The turbulent flames in a LRE can be thought of as being composed of elementary 1D laminar counterflow diffusion flames. The physically possible configurations for a given rocket operating condition, corresponding to the boundary conditions of the 1D flamelet problem, are captured by variation of the strain rate. For an exemplary supercritical operating condition (p = 7 MPa, Tin,LOX = 120 K, Tin,H2 = 295 K) we show that, despite local mixing, the fluid never reaches a multiphase state from equilibrium combustion to quenching. The transition from supercritical liquid oxygen to an ideal gas state is found to occur in what is essentially a pure fluid process; real fluid mixing only occurs among LOX and water with a water mass fraction < 3% before the ideal gas transition. Representing the mixing trajectories of each flamelet in a reduced pressure – reduced temperature diagram allows to capture all physical mixture states of a configuration in a single plot. This approach furthermore allows to intuitively assess changes in operating conditions with respect to critical-state conditions.

MVP-Workshop Contribution: Modeling of Volvo bluff body flame experiment

The Volvo burner features the canonical configuration of a bluff-body stabilized premixed flame. This configuration was studied experimentally under the Volvo Flygmotor AB program. Two cases are considered in this study: a non-reacting case with an inlet flow speed of 16.6 m/s and a reacting case with equilibrium ratio of 0.65 and inflow speed of 17.3 m/s. The characteristic vortex shedding in the wake behind the bluff body is present in the non-reacting case, while two oscillation modes are intermittently present in the reacting case. A series of large-eddy simulations are performed on this configuration using two solvers, one using a high-resolution finite-volume (FV) scheme and the other featuring a high-order discontinuousGalerkin (DG) discretization. The FV calculations are conducted on hexahedral meshes with three different resolution (4mm, 2mm, and 1mm). The DG calculations are performed using two different polynomial orders on the same tetrahedral mesh. For the non-reacting cases, good agreement with respect to the experimental data is achieved by both solvers at high numerical resolution. The reacting cases are calculated using a two-step global mechanism in combination with the thickened-flame model. Reasonable agreement with experiments is obtained by both solvers at higher resolution. Models for combustion-turbulence interaction are necessary for the reacting case as it contains the length scale of the flame, which is smaller than the grid resolution in all calculations. The impact of such models on the flame stability and flow/flame dynamics is the subject of future research. ∗Corresponding Author: mihme@stanford.edu ar X iv :1 70 7. 05 80 5v 2 [ ph ys ic s. co m pph ] 2 9 A ug 2 01 7

Non-equilibrium wall-modeling for internal combustion engine simulations with wall heat transfer:

Heat transfer affects the performance and phasing of internal combustion engines. Correlations and equilibrium wall-function models are typically employed in engine simulations to predict heat transfer. However, many studies have shown that significant errors are expected, owing to the failure of fundamental assumptions in deriving equilibrium wall-function models. Non-equilibrium wall models provide a more accurate way of describing the near-wall region of in-cylinder flows. In this study, simultaneous high-speed high-resolution particle image velocimetry and heat-flux measurements are conducted in an optically accessible engine. The experiments are performed under both motored and fired conditions at two different engine speeds. The experimental data are utilized to assess the performance of different models in predicting the thermoviscous boundary layer. These models include commonly used heat transfer correlations, equilibrium and modified wall-function models, and a recently developed non-equilibrium wall model. It is found that the equilibrium wall-function model significantly underpredicts the heat flux under both motored and fired conditions. By considering heat release effects in the boundary layer, the non-equilibrium wall model is shown to be able to adequately capture the structure and dynamics of both momentum and thermal boundary layers in comparison with experimental measurements, demonstrating its improved performance over previously employed correlation functions and the equilibrium model.

Numerical framework for transcritical real-fluid reacting flow simulations using the flamelet progress variable approach

An extension to the classical FPV model is developed for transcritical real-fluid combustion simulations in the context of finite volume, fully compressible, explicit solvers. A double-flux model is developed for transcritical flows to eliminate the spurious pressure oscillations. A hybrid scheme with entropy-stable flux correction is formulated to robustly represent large density ratios. The thermodynamics for ideal-gas values is modeled by a linearized specific heat ratio model. Parameters needed for the cubic EoS are pre-tabulated for the evaluation of departure functions and a quadratic expression is used to recover the attraction parameter. The novelty of the proposed approach lies in the ability to account for pressure and temperature variations from the baseline table. Cryogenic LOX/GH2 mixing and reacting cases are performed to demonstrate the capability of the proposed approach in multidimensional simulations. The proposed combustion model and numerical schemes are directly applicable for LES simulations of real applications under transcritical conditions.

Seven questions about supercritical fluids - towards a new fluid state diagram

In this paper, we discuss properties of supercritical and real fluids, following the overarching question: ‘What is a supercritical fluid?’. It seems there is little common ground when researchers in our field discuss these matters as no systematic assessment of this material is available. This paper follows an exploratory approach, in which we analyze whether common terminology and assumptions have a solid footing in the underlying physics. We use molecular dynamics (MD) simulations and fluid reference data to compare physical properties of fluids with respect to the critical isobar and isotherm, and find that there is no contradiction between a fluid being supercritical and an ideal gas; that there is no difference between a liquid and a transcritical fluid; that there are different thermodynamic states in the supercritical domain which may be uniquely identified as either liquid or gaseous. This suggests a revised state diagram, in which low-temperature liquid states and higher temperature gaseous states are divided by the coexistence-line (subcritical) and pseudoboiling-line (supercritical). As a corollary, we investigate whether this implies the existence of a supercritical latent heat of vaporization and show that for pressures smaller than three times the critical pressure, any isobaric heating process from a liquid to an ideal gas state requires approximately the same amount of energy, regardless of pressure. Finally, we use 1D flamelet data and large-eddy-simulation results to demonstrate that these pure fluid considerations are relevant for injection and mixing in combustion chambers.

Widom Lines in Binary Mixtures of Supercritical Fluids

Recent experiments on pure fluids have identified distinct liquid-like and gas-like regimes even under supercritical conditions. The supercritical liquid-gas transition is marked by maxima in response functions that define a line emanating from the critical point, referred to as Widom line. However, the structure of analogous state transitions in mixtures of supercritical fluids has not been determined, and it is not clear whether a Widom line can be identified for binary mixtures. Here, we present first evidence for the existence of multiple Widom lines in binary mixtures from molecular dynamics simulations. By considering mixtures of noble gases, we show that, depending on the phase behavior, mixtures transition from a liquid-like to a gas-like regime via distinctly different pathways, leading to phase relationships of surprising complexity and variety. Specifically, we show that miscible binary mixtures have behavior analogous to a pure fluid and the supercritical state space is characterized by a single liquid-gas transition. In contrast, immiscible binary mixture undergo a phase separation in which the clusters transition separately at different temperatures, resulting in multiple distinct Widom lines. The presence of this unique transition behavior emphasizes the complexity of the supercritical state to be expected in high-order mixtures of practical relevance.

A Flamelet Model with Heat-Loss Effects for Predicting Wall-Heat Transfer in Rocket Engines

A flamelet-based combustion model is proposed for the prediction of wall-heat transfer in rocket engines and confined combustion systems. To account for the impact of the flame due to convective heat loss on the wall, a permeable thermal boundary condition is introduced in the counter-flow diffusion flame configuration. The solution of the resulting non-adiabatic flame structure forms a three-dimensional manifold, which is parameterized in terms of mixture fraction, progress variable, and temperature. The performance of the model is first evaluated through a DNS analysis of a H2/O2 diffusion flame that is stabilized at an inert isothermal wall. The developed non-adiabatic flamelet model is shown to accurately predict the temperature, chemical composition, and wall heat transfer. Combined with a presumed PDF-closure, the model is then applied to LES of a single-injector rocket combustor to examine effects of heat-transfer on the turbulent flame structure in rocket engines.

Large-eddy simulations of fuel effects on gas turbine lean blow-out

Towards the implementation of alternative jet fuels in aviation gas turbines, testing in combustor rigs and engines is required to evaluate the fuel performance on combustion stability, relight, and lean-blow out (LBO) characteristics. The objective of this work is to evaluate the effect of different fuel candidates on the operability of gas turbines by comparing a conventional petroleum-based fuel with two other alternative fuel candidates. Numerical investigations are performed to examine the performance of these fuels on the stable condition close to blow-out and LBO-behavior in a referee gas turbine combustor. Large-eddy simulations (LES) are performed at stationary conditions near LBO to examine effects of the fuel properties on evaporation, gaseous-fuel deposition, flame anchoring.