Isolated fluid oxygen drop behavior in fluid hydrogen at rocket chamber pressures

Harstad, K.; Bellan, Josette

doi:10.1016/s0017-9310(98)00049-0

Cited by 104 publications

(43 citation statements)

References 5 publications

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“…Thus, the density ratio may be well below the 0(103) that characterizes its liquid/gas value, but the measurement will still identify a change in the index of refraction providing that the change is sudden (steep gradients). As shown by simulations of supercritical fluids (see Harstad and Bellan [7]), the density gradients may remain large during the initial stage of two supercritical fluids mixing, thus making them optically identifiable. Therefore, there is no inconsistency between the optical observation of 'drops' and 'ligaments' and the fluids (injected and surrounding) being both in a supercritical state.…”

Section: Experimental Observationsmentioning

confidence: 99%

Supercritical (and subcritical) fluid behavior and modeling: drops, streams, shear and mixing layers, jets and sprays

Bellan

2000

Progress in Energy and Combustion Science

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267

120

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A critical review of recent investigations in the realm of supercritical ( and subcritical) fluid behavior is presented with the goal of obtaining a perspective on. the peculiarities of high pressure observations. Experiments with drops, isolated or in groups, streams, shear and mix-1 ing layers, jets and sprays are tabulated and discussed as a precursor t,o €orming a conceptual picture of fluid comportment. The physics of fluid behavior in the supercritical and subcritical regimes is discussed, and major differences between the observations in these two regimes are identified and explained. A variety of supercritical fluid models is then examined in the context of drop studies, and salient aspects of fluid behavior are identified. In particular, a model that has been validated with microgravity drop experiments is described and summarized; in this validated model, the differences in subcritical/supercritical comportment are interpreted in terms of lengths scales and it is this difference that is responsible for the traditional Lewis

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Section: Experimental Observationsmentioning

confidence: 99%

Supercritical (and subcritical) fluid behavior and modeling: drops, streams, shear and mixing layers, jets and sprays

Bellan

2000

Progress in Energy and Combustion Science

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267

120

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“…The viscosity, the Schmidt number (Sc = μ/(ρα D D)) and the Prandtl number (P r = μC p /(mλ)) were calculated from high-pressure single-species transport properties using mixing rules, as in Harstad & Bellan (1998). The calculated values were correlated, as summarized in table 2, and these correlations are then used to compute the transport properties μ, D and λ.…”

Section: Transport Coefficientsmentioning

confidence: 99%

A posteriori study using a DNS database describing fluid disintegration and binary-species mixing under supercritical pressure: heptane and nitrogen

Taskinoglu

Bellan

2010

J. Fluid Mech.

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A large eddy simulation (LES) a posteriori study is conducted for a temporal mixing layer which initially contains different species in the lower and upper streams and in which the initial pressure is larger than the critical pressure of either species. A vorticity perturbation, initially imposed, promotes roll-up and a double pairing of four initial spanwise vortices to reach a transitional state. The LES equations consist of the differential conservation equations coupled with a real-gas equation of state, and the equations utilize transport properties depending on the thermodynamic variables. Unlike all LES models to date, the differential equations contain, additional to the subgrid-scale (SGS) fluxes, a new SGS term denoted a 'pressure correction' (p correction) in the momentum equation. This additional term results from filtering the Navier-Stokes equations and represents the gradient of the difference between the filtered p and p computed from the filtered flow field. A previous a priori analysis, using a direct numerical simulation (DNS) database for the same configuration, found this term to be of leading order in the momentum equation, a fact traced to the existence of regions of high density-gradient magnitude that populated the entire flow; in that study, the appropriateness of several SGS-flux models was assessed, and a model for the p-correction term was proposed.In the present study, the constant-coefficient SGS-flux models of the a priori investigation are tested a posteriori in LES devoid of, or including, the SGS pcorrection term. A new p-correction model, different from that of the a priori study, is used, and the results of the two p-correction models are compared. The results reveal that the former is less computationally intensive and more accurate than the latter in reproducing global and structural features of the flow. The constantcoefficient SGS-flux models encompass the Smagorinsky (SMC) model, in conjunction with the Yoshizawa (YO) model for the trace, the gradient (GRC) model and the scale similarity (SSC) models, all exercised with the a priori study constant-coefficient values calibrated at the transitional state. Further, dynamic SGS-flux model LESs are performed with the p correction included in all cases. The dynamic models are the Smagorinsky (SMD) model, in conjunction with the YO model, the gradient (GRD) model and 'mixed' models using SMD in combination with GRC or SSC utilized with their theoretical coefficient values. The LES comparison is performed with the filtered-and-coarsened DNS (FC-DNS) which represents an ideal LES solution. The constant-coefficient models including the p correction (SMCP, GRCP and SSCP) † Email address for correspondence: josette.bellan@jpl.nasa.gov 212 E. S. Taskinoglu and J. Bellan are substantially superior to those devoid of it; the SSCP model produces the best agreement with the FC-DNS template. For duplicating the local flow structure, the predictive superiority of the dynamic mixed models is demonstrated over the SMD model; however, even be...

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“…This particular region is chosen for two primary reasons: (1) The PR EOS was found to be highly accurate within this region when compared to the more accurate model of Harstad et al (1997) with the relative error being in no case greater than approximately 1% for both the entropy and enthalpy predictions (this error can be larger than 25% at p = 6 MPa and T = 350 K). (2) Contour plots (not shown) of the viscosity, and of the Schmidt (Sc) and Prandtl (P r) numbers based on accurate species transport properties calculated as in Harstad & Bellan (1998), revealed that the viscosity is predominantly a function of T alone, whereas Sc and P r are predominantly functions of the mass fraction. This leads to the relatively simplified diffusion coefficients 28) where µ R is a reference viscosity and the reference temperatures T 1 and T 2 correspond to the free-stream temperatures for mixing layer simulations.…”

Section: Equation Of Statementioning

confidence: 99%

Direct numerical simulations of supercritical fluid mixing layers applied to heptane–nitrogen

2001

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Direct numerical simulations (DNS) are conducted of a model hydrocarbon-nitrogen mixing layer under supercritical conditions. The temporally developing mixing layer configuration is studied using heptane and nitrogen supercritical fluid streams at a pressure of 60 atm as a model system related to practical hydrocarbon-fuel/air systems. An entirely self-consistent cubic Peng-Robinson equation of state is used to describe all thermodynamic mixture variables, including the pressure, internal energy, enthalpy, heat capacity, and speed of sound along with additional terms associated with the generalized heat and mass transport vectors. The Peng-Robinson formulation is based on pure-species reference states accurate to better than 1% relative error through comparisons with highly accurate state equations over the range of variables used in this study (600 6 T 6 1100 K, 40 6 p 6 80 atm) and is augmented by an accurate curve fit to the internal energy so as not to require iterative solutions. The DNS results of two-dimensional and three-dimensional layers elucidate the unique thermodynamic and mixing features associated with supercritical conditions. Departures from the perfect gas and ideal mixture conditions are quantified by the compression factor and by the mass diffusion factor, both of which show reductions from the unity value. It is found that the qualitative aspects of the mixing layer may be different according to the specification of the thermal diffusion factors whose value is generally unknown, and the reason for this difference is identified by examining the second-order statistics: the constant Bearman-Kirkwood (BK) thermal diffusion factor excites fluctuations that the constant Irwing-Kirkwood (IK) one does not, and thus enhances overall mixing. Combined with the effect of the mass diffusion factor, constant positive large BK thermal diffusion factors retard diffusional mixing, whereas constant moderate IK factors tend to promote diffusional mixing. Constant positive BK thermal diffusion factors also tend to maintain density gradients, with resulting greater shear and vorticity. These conclusions about IK and BK thermal diffusion factors are speciespair dependent, and therefore are not necessarily universal. Increasing the temperature of the lower stream to approach that of the higher stream results in increased layer growth as measured by the momentum thickness. The three-dimensional mixing layer exhibits slow formation of turbulent small scales, and transition to turbulence does not occur even for a relatively long non-dimensional time when compared to a previous, atmospheric conditions study. The primary reason for this delay is the initial density stratification of the flow, while the formation of strong density gradient regions both in the braid and between-the-braid planes may constitute a secondary reason for the hindering of transition through damping of emerging turbulent eddies. † Present address:

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Isolated fluid oxygen drop behavior in fluid hydrogen at rocket chamber pressures

Cited by 104 publications

References 5 publications

Supercritical (and subcritical) fluid behavior and modeling: drops, streams, shear and mixing layers, jets and sprays

Supercritical (and subcritical) fluid behavior and modeling: drops, streams, shear and mixing layers, jets and sprays

A posteriori study using a DNS database describing fluid disintegration and binary-species mixing under supercritical pressure: heptane and nitrogen

Direct numerical simulations of supercritical fluid mixing layers applied to heptane–nitrogen

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