Jean-Pierre Hickey

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.

Transitional–turbulent spots and turbulent–turbulent spots in boundary layers

Significance Uncovering the constitutive coherent structure in the inner layer of the canonical turbulent boundary layer has remained a central fluid mechanics theme, because it tests our intellectual ability to understand even the simplest external flow. We describe here how turbulent spots are initiated in bypass boundary-layer transition and uncover the ubiquity of concentrations of vortices in the fully turbulent region with characteristics remarkably like transitional–turbulent spots. We present strong evidence that these concentrations of vortices are the constitutive coherent structure of the inner layer near the wall. This study contributes to the unification of understanding of phenomena occurring in boundary-layer late-stage transition with near-wall turbulent boundary-layer structure and dynamics in the developed flow. Two observations drawn from a thoroughly validated direct numerical simulation of the canonical spatially developing, zero-pressure gradient, smooth, flat-plate boundary layer are presented here. The first is that, for bypass transition in the narrow sense defined herein, we found that the transitional–turbulent spot inception mechanism is analogous to the secondary instability of boundary-layer natural transition, namely a spanwise vortex filament becomes a Λ vortex and then, a hairpin packet. Long streak meandering does occur but usually when a streak is infected by a nearby existing transitional–turbulent spot. Streak waviness and breakdown are, therefore, not the mechanisms for the inception of transitional–turbulent spots found here. Rather, they only facilitate the growth and spreading of existing transitional–turbulent spots. The second observation is the discovery, in the inner layer of the developed turbulent boundary layer, of what we call turbulent–turbulent spots. These turbulent–turbulent spots are dense concentrations of small-scale vortices with high swirling strength originating from hairpin packets. Although structurally quite similar to the transitional–turbulent spots, these turbulent–turbulent spots are generated locally in the fully turbulent environment, and they are persistent with a systematic variation of detection threshold level. They exert indentation, segmentation, and termination on the viscous sublayer streaks, and they coincide with local concentrations of high levels of Reynolds shear stress, enstrophy, and temperature fluctuations. The sublayer streaks seem to be passive and are often simply the rims of the indentation pockets arising from the turbulent–turbulent spots.

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.

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.

Visualization of Continuous Stream of Grid Turbulence Past the Langston Turbine Cascade

This paper describes a direct numerical simulation visualization study on the migration and distortion of a continuous stream of grid turbulence passing through a representative turbine cascade with and without being segregated by the blade leading edge. For the nonimpinging case, as the turbulent stream starts to enter the turbine cascade, there is a coarsening and reorientation of the small-scale and random grid-turbulence structures into short vortex tubes; inside the cascade, these short vortex tubes are further stretched into relatively long quasi-streamwise vortices. For the impinging case, very long streamwise vortices on the pressure surface are observed that correspond nicely to the “colored-fingers” phenomenon reported in previous turbine heat transfer experiments. The spanwise locations of the observed vortices vary with time. The origin of such turbine pressure-side streamwise vortices is revealedusing a relatively complete sequence of images documenting their life cycle. For the impinging case, the short vortex tubes formed at the stagnation are gradually distorted into the shape of a hockey stick. The long stick is nearly parallel to the blade pressure surface, whereas the short end is bent toward the freestream. This process can be well explained by invoking results from previous fundamental studies on simple stagnation flows and on the stretching and rotation of material lines by the mean strain-rate field under the assumption of rapid distortion. Taken together with earlier investigations on turbine distortion ofmigrating planarwake andmigrating isolated turbulent block, it is quite likely that Taylor–Goertler centrifugal instabilitymay not be an important player in the formation of pressureside elongated streamwise vortices in turbomachinery applications.

Turbulence modeling of cavitating flows in liquid rocket turbopumps

An accurate prediction of the performance characteristics of cavitating cryogenic turbopump inducers is essential for an increased reliance on numerical simulations in the early turbopump design stages of liquid rocket engines (LRE). This work focuses on the sensitivities related to the choice of turbulence models on the cavitation prediction in flow setups relevant to cryogenic turbopump inducers. To isolate the influence of the turbulence closure models for Reynolds-Averaged Navier–Stokes (RANS) equations, four canonical problems are abstracted and studied individually to separately consider cavitation occurring in flows with a bluff body pressure drop, adverse pressure gradient, blade passage contraction, and rotation. The choice of turbulence model plays a significant role in the prediction of the phase distribution in the flow. It was found that the sensitivity to the closure model depends on the choice of cavitation model itself; the barotropic equation of state (BES) cavitation models are far more sensitive to the turbulence closure than the transport-based models. The sensitivity of the turbulence model is also strongly dependent on the type of flow. For bounded cavitation flows (blade passage), stark variations in the cavitation topology are observed based on the selection of the turbulence model. For unbounded problems, the spread in the results due to the choice of turbulence models is similar to noncavitating, single-phase flow cases.

Large Eddy Simulation of Supercritical Mixing and Combustion for Rocket Applications

We report on the implementation of the real fluid capabilities to CharlesX, the in-house, unstructured, large eddy simulation code used at the Center for Turbulence Research at Stanford University. A conceptually distinct implementation was needed for the puremixing and the flamelet/progress-variable (FPV) model combustion case. For the nonreacting simulations, a Newton-Raphson based iterative algorithm is used to determine the temperature from the transported density and energy. For the reacting simulations, an extended flamelet table is used that tabulates the departure functions as well as the compressibility factor. These tabulated parameters are used to correct the transported thermodynamic properties. The real fluid extension to CharlesX was used to investigate a non-reacting and a reacting case. In both of these cases, a second-order essentially nonoscillatory (ENO) schemes is locally applied to the flux computation on the faces identified with a dual-threshold relative density sensor. This avoids spurious oscillations of the numerical solution with limited numerical dissipation. This preliminary work illustrates the capability CharlesX to capture the important physics in a typical rocket engine configuration.

Numerical Investigation of Transcritical-T Heat-and-Mass-Transfer Dynamics in Compressible Turbulent Channel Flow

We have carried out turbulent channel flow simulations of supercritical-p R-134a (1,1,1,2tetrafluoroethane, CH2FCF3) in transcritical-T conditions where the top and bottom walls are kept at supercritical-T (Ttop > Tpb) and subcritical-T (Tbot < Tpb) conditions, respectively, where Tpb is the pseudo-boiling temperature. A high-order numerical scheme for the solution of the fully compressible Navier–Stokes equations in conservative form is coupled with the Peng-Robinsion (PR) equation of state and Chung’s method to model real fluid effects. The simulations are carried out at a bulk pressure of pb = 1.1pc where pc = 40.59 bar is the critical pressure for R-134a, a bulk velocity of Ub = 36 m/s, and top-to-bottom temperature differences, ∆T = Ttop − Tbot, of 5 K and 10 K. Viscosity has been increased by a factor of 60 to allow for adequate numerical resolution to be achieved at physically relevant channel sizes. The average location of the pseudo-phase change is y/h = -0.25 and 0.66 for ∆T = 5 K and 10 K, respectively where h is the channel half-height and y is the wall-normal distance from the centerline. The average density on the bottom wall at ∆T = 10 K equals approximately twice that on the top wall (ρtop = 314.9 kg/m , ρbot = 638.0 kg/m). The best collapse of the mean streamwise velocity profiles in the log-law region is achieved via conventional scaling based on wall units, rather than semi-local scaling strategies. The average location of pseudo-transition correlates with mixing rate enhancement and attenuation of hydrodynamic turbulent fluctuation. A grid convergence study has shown variations of at most 7.33 % in the thermodynamic RMS quantities between the coarsest and finest grid systems spanning resolutions of ∆x = 20.94–68.44. Instantaneous visualizations reveal strong ejections of dense fluid from the pseudo-liquid viscous sublayer into the channel core creating a third RMS peak in the thermodynamic quantities near the channel centerline such events are correlated with streamwise elongated streaks in the temperature gradients at the wall.