Search NASA⌕ Search

SEARCH · Search NASA

Results for “deterministic walks”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

The structure of dilute combusting sprays

An experimental and theoretical study of drop processes in a turbulent flame is described. The experiments involved a monodisperse (105 and 180 micro m initial diameter) stream of methanol drops injected at the base of a turbulent methane-fueled diffusion flame burning in still air. The following measurements were made: mean and fluctuating phase velocities, mean drop number flux, drop-size distributions and mean gas-phase temperatures. Measurements were compared with predictions of two separated flow models: (1) deterministic separated flow, where drop-turbulence interactions are ignored; and (2) stochastic separated flow, where drop-turbulence interactions are considered using random-walk computations. The stochastic separated flow analysis yielded best agreement with measurements, since it provides for turbulent dispersion of drops which was important for present test conditions (and probably for most combusting sprays as well). Distinguishing the presence or absence of envelope flames around the drops, however, was relatively unimportant for present test conditions, since the drops spent most of their lifetime in fuel-rich regions of the flow where this distinction is irrelevant.

Shuen, J. S.↗

Particle-laden swirling free jets: Measurements and predictions

A theoretical and experimental investigation of single-phase and particle-laden weakly swirling jets was conducted. The jets were injected vertically downward from a 19 mm diameter tube with swirl numbers ranging from 0 to 0.33. The particle-laden jets had a single loading ratio (0.2) with particles having a SMD of 39 microns. Mean and fluctuating properties of both phases were measured using nonintrusive laser based methods while particle mass flux was measured using an isokinetic sampling probe. The continuous phase was analyzed using both a baseline kappa-epsilon turbulence model and an extended version with modifications based on the flux Richardson number to account for effects of streamline curvature. To highlight effects of interphase transport rates and particle/turbulence interactions, effects of the particles were analyzed as follows: (1) locally homogeneous flow (LHF) analysis, where interphase transport rates are assumed to be infinitely fast; (2) deterministic separated flow (DSF) analysis, where finite interphase transport rates are considered but particle/turbulence interactions are ignored; and (3) stochastic separated flow (SSF) analysis, where both effects are considered using random-walk computations.

Bulzan, D. L.↗

Particle-laden swirling free jets - Measurements and predictions

A theoretical and experimental investigation of single-phase and particle-laden weakly swirling jets was conducted. The jets were injected vertically downward from a 19 mm diameter tube with swirl numbers ranging from 0 to 0.33. The particle-laden jets had a single loading ratio (0.2) with particles having an SMD of 39 micrometers. Mean and fluctuating properties of both phases were measured using nonintrusive laser based methods while particle mass flux was measured using an isokinetic sampling probe. The continuous phase was analyzed using both a baseline k-epsilon turbulence model and an extended version with modifications based on the flux Richardson number to account for effects of streamline curvature. To highlight effects of interphase transport rates and particle/turbulence interactions, effects of the particles were analyzed as follows: (1) locally homogeneous flow (LHF) analysis, where interphase transport rates are assumed to be infinitely fast; (2) deterministic separated flow (DSF) analysis, where finite interphase transport rates are considered but particle/turbulence interactions are ignored; and (3) stochastic separated flow (SSF) analysis, where both effects are considered using random-walk computations.

Bulzan, D. L.↗

Structure of nonevaporating sprays. I - Initial conditions and mean properties

Structure measurements were completed within the dilute portion of axisymmetric nonevaporating sprays. Measurements included: mean velocities, velocity fluctuations, and Reynolds stress of the gas phase; and mean velocities, fluctuating velocities, mass flux, and diameter distributions of the drop phase. The measurements were used to evaluate three typical methods of analyzing sprays: (1) a locally homogeneous flow (LHF) analysis, where slip between the phases is neglected; (2) a deterministic separated flow (DSF) analysis, where slip is considered but effects of drop interactions with turbulence are ignored; and (3) a stochastic separated flow (SSF) analysis, where effects of both slip and turbulence are considered using random-walk computations for drop motion. Measurements of initial conditions of both phases near the injector, mean gas-phase properties, and liquid flux distributions are described herein. Best agreement between predictions and measurements was obtained with the SSF model, which provided a reasonable representation of turbulent dispersion of drops. A companion paper presents additional measurements of drop continuous phase properties.

Solomon, A. S. P.↗

The structure of particle-laden jets and nonevaporating sprays

Mean and fluctuating gas velocities, liquid mass fluxes and drop sizes were in nonevaporating sprays. These results, as well as existing measurements in solid particle-laden jets, were used to evaluate models of these processes. The following models were considered: (1) a locally homogeneous flow (LHF) model, where slip between the phases was neglected; (2) a deterministic separated flow (DSF) model, where slip was considered but effects of particle dispersion by turbulence were ignored; and (3) a stochastic separated flow (SSF) model, where effects of interphase slip and turbulent dispersion were considered using random-walk computations for particle motion. The LHF and DSF models did not provide very satisfactory predictions over the present data base. In contrast, the SSF model performed reasonably well - including conditions in nonevaporating sprays where enhanced dispersion of particles by turbulence caused the spray to spread more rapidly than single-phase jets for comparable conditions. While these results are encouraging, uncertainties in initial conditions limit the reliability of the evaluation. Current work is seeking to eliminate this deficiency.

Shuen, J. S.↗

A theoretical and experimental study of turbulent nonevaporating sprays

Measurements and analysis limited to the dilute portions of turbulent nonevaporating sprays injected into a still air environment were completed. Mean and fluctuating velocities and Reynolds stress were measured in the continuous phase. Liquid phase measurements included liquid mass fluxes, drop sizes and drop size and velocity correlation. Initial conditions needed for model evaluation were measured at a location as close to the injector exit as possible. The test sprays showed significant effects of slip and turbulent dispersion of the discrete phase. The measurements were used to evaluate three typical models of these processes: (1) a locally homogenous flow (LHF) model, where slip between the phases were neglected; (2) a deterministic separated flow (DSF) model, where slip was considered but effects of drop dispersion by turbulence were ignored; and (3) a stochastic separated flow (SSF) model, where effects of interphase slip and turbulent dispersion were considered using random-walk computations for drop motion. The LHF and DSF models did not provide very satisfactory predictions for the present measurements. In contrast, the SSF model performed reasonably well with no modifications in the prescription of eddy properties from its original calibration. Some effects of drops on turbulence properties were observed near the dense regions of the sprays.

Solomon, A. S. P.↗

A theoretical and experimental study of turbulent evaporating sprays

Measurements and analysis limited to the dilute portions of turbulent evaporating sprays, injected into a still air environment were completed. Mean and fluctuating velocities and Reynolds stress were measured in the continuous phase. Liquid phase measurements included liquid mass fluxes, drop sizes and drop size and velocity correlation. Initial conditions needed for model evaluation were measured at a location as close to the injector exit as possible. The test sprays showed significant effects of slip and turbulent dispersion of the discrete phase. The measurements were used to evaluate three typical models of these processes: (1) a locally homogeneous flow (LHF) model, where slip between the phases were neglected; (2) a deterministic separated flow (DSF) model, where slip was considered but effects of drop dispersion by turbulence were ignored; and (3) a stochastic separated flow (SSF) model, where effects of interphase slip and turbulent dispersion were considered using random-walk computations for drop motion. For all three models, a k-epsilon model as used to find the properties of the continuous phase. The LHF and DSF models did not provide very satisfactory predictions for the present measurements. In contrast, the SSF model performed reasonably well--with no modifications in the prescription of eddy properties from its original calibration.

Solomon, A. S. P.↗

Prediction of the structure of fuel sprays in gas turbine combustors

The structure of fuel sprays in a combustion chamber is theoretically investigated using computer models of current interest. Three representative spray models are considered: (1) a locally homogeneous flow (LHF) model, which assumes infinitely fast interphase transport rates; (2) a deterministic separated flow (DSF) model, which considers finite rates of interphase transport but ignores effects of droplet/turbulence interactions; and (3) a stochastic separated flow (SSF) model, which considers droplet/turbulence interactions using random sampling for turbulence properties in conjunction with random-walk computations for droplet motion and transport. Two flow conditions are studied to investigate the influence of swirl on droplet life histories and the effects of droplet/turbulence interactions on flow properties. Comparison of computed results with the experimental data show that general features of the flow structure can be predicted with reasonable accuracy using the two separated flow models. In contrast, the LHF model overpredicts the rate of development of the flow. While the SSF model provides better agreement with measurements than the DSF model, definitive evaluation of the significance of droplet/turbulence interaction is not achieved due to uncertainties in the spray initial conditions.

Shuen, J. S.↗

Prediction of the structure of fuel sprays in gas turbine combustors

The structure of fuel sprays in a combustion chamber is theoretically investigated using computer models of current interest. Three representative spray models are considered: (1) a locally homogeneous flow (LHF) model, which assumes infinitely fast interphase transport rates; (2) a deterministic separated flow (DSF) model, which considers finite rates of interphase transport but ignores effects of droplet/turbulence interactions; and (3) a stochastic separated flow (SSF) model, which considers droplet/turbulence interactions using random sampling for turbulence properties in conjunction with random-walk computations for droplet motion and transport. Two flow conditions are studied to investigate the influence of swirl on droplet life histories and the effects of droplet/turbulence interactions on flow properties. Comparison of computed results with the experimental data show that general features of the flow structure can be predicted with reasonable accuracy using the two separated flow models. In contrast, the LHF model overpredicts the rate of development of the flow. While the SSF model provides better agreement with measurements than the DSF model, definitive evaluation of the significance of droplet/turbulence interaction is not achieved due to uncertainties in the spray initial conditions.

Shuen, J.-S.↗

Particle-laden weakly swirling free jets: Measurements and predictions

A theoretical and experimental investigation of particle-laden, weakly swirling, turbulent free jets was conducted. Glass particles, having a Sauter mean diameter of 39 microns, with a standard deviation of 15 microns, were used. A single loading ratio (the mass flow rate of particles per unit mass flow rate of air) of 0.2 was used in the experiments. Measurements are reported for three swirl numbers, ranging from 0 to 0.33. The measurements included mean and fluctuating velocities of both phases, and particle mass flux distributions. Measurements were also completed for single-phase non-swirling and swirling jets, as baselines. Measurements were compared with predictions from three types of multiphase flow analysis, as follows: (1) locally homogeneous flow (LHF) where slip between the phases was neglected; (2) deterministic separated flow (DSF), where slip was considered but effects of turbulence/particle interactions were neglected; and (3) stochastic separated flow (SSF), where effects of both interphase slip and turbulence/particle interactions were considered using random sampling for turbulence properties in conjunction with random-walk computations for particle motion. Single-phase weakly swirling jets were considered first. Predictions using a standard k-epsilon turbulence model, as well as two versions modified to account for effects of streamline curvature, were compared with measurements. Predictions using a streamline curvature modification based on the flux Richardson number gave better agreement with measurements for the single-phase swirling jets than the standard k-epsilon model. For the particle-laden jets, the LHF and DSF models did not provide very satisfactory predictions. The LHF model generally overestimated the rate of decay of particle mean axial and angular velocities with streamwise distance, and predicted particle mass fluxes also showed poor agreement with measurements, due to the assumption of no-slip between phases. The DSF model also performed quite poorly for predictions of particle mass flux because turbulent dispersion of the particles was neglected. The SSF model, which accounts for both particle inertia and turbulent dispersion of the particles, yielded reasonably good predictions throughout the flow field for the particle-laden jets.

Bulzan, Daniel L.↗

Structure of nonevaporating sprays - Measurements and predictions

Structure measurements were completed within the dilute portion of axisymmetric nonevaporating sprays (SMD of 30 and 87 microns) injected into a still air environment, including: mean and fluctuating gas velocities and Reynolds stress using laser-Doppler anemometry; mean liquid fluxes using isokinetic sampling; drop sizes using slide impaction; and drop sizes and velocities using multiflash photography. The new measurements were used to evaluate three representative models of sprays: (1) a locally homogeneous flow (LHF) model, where slip between the phases was neglected; (2) a deterministic separated flow (DSF) model, where slip was considered but effects of drop interaction with turbulent fluctuations were ignored; and (3) a stochastic separated flow (SSF) model, where effects of both interphase slip and turbulent fluctuations were considered using random sampling for turbulence properties in conjunction with random-walk computations for drop motion. The LHF and DSF models were unsatisfactory for present test conditions-both underestimating flow widths and the rate of spread of drops. In contrast, the SSF model provided reasonably accurate predictions, including effects of enhanced spreading rates of sprays due to drop dispersion by turbulence, with all empirical parameters fixed from earlier work.

Solomon, A. S. P.↗

The structure of evaporating and combusting sprays: Measurements and predictions

The structure of particle-laden jets and nonevaporating and evaporating sprays was measured in order to evaluate models of these processes. Three models are being evaluated: (1) a locally homogeneous flow model, where slip between the phases is neglected and the flow is assumed to be in local thermodynamic equilibrium; (2) a deterministic separated flow model, where slip and finite interphase transport rates are considered but effects of particle/drop dispersion by turbulence and effects of turbulence on interphase transport rates are ignored; and (3) a stochastic separated flow model, where effects of interphase slip, turbulent dispersion and turbulent fluctuations are considered using random sampling for turbulence properties in conjunction with random-walk computations for particle motion. All three models use a k-e-g turbulence model. All testing and data reduction are completed for the particle laden jets. Mean and fluctuating velocities of the continuous phase and mean mixture fraction were measured in the evaporating sprays.

Shuen, J. S.↗

Investigation for improving Global Positioning System (GPS) orbits using a discrete sequential estimator and stochastic models of selected physical processes

GEODYNII is a conventional batch least-squares differential corrector computer program with deterministic models of the physical environment. Conventional algorithms were used to process differenced phase and pseudorange data to determine eight-day Global Positioning system (GPS) orbits with several meter accuracy. However, random physical processes drive the errors whose magnitudes prevent improving the GPS orbit accuracy. To improve the orbit accuracy, these random processes should be modeled stochastically. The conventional batch least-squares algorithm cannot accommodate stochastic models, only a stochastic estimation algorithm is suitable, such as a sequential filter/smoother. Also, GEODYNII cannot currently model the correlation among data values. Differenced pseudorange, and especially differenced phase, are precise data types that can be used to improve the GPS orbit precision. To overcome these limitations and improve the accuracy of GPS orbits computed using GEODYNII, we proposed to develop a sequential stochastic filter/smoother processor by using GEODYNII as a type of trajectory preprocessor. Our proposed processor is now completed. It contains a correlated double difference range processing capability, first order Gauss Markov models for the solar radiation pressure scale coefficient and y-bias acceleration, and a random walk model for the tropospheric refraction correction. The development approach was to interface the standard GEODYNII output files (measurement partials and variationals) with software modules containing the stochastic estimator, the stochastic models, and a double differenced phase range processing routine. Thus, no modifications to the original GEODYNII software were required. A schematic of the development is shown. The observational data are edited in the preprocessor and the data are passed to GEODYNII as one of its standard data types. A reference orbit is determined using GEODYNII as a batch least-squares processor and the GEODYNII measurement partial (FTN90) and variational (FTN80, V-matrix) files are generated. These two files along with a control statement file and a satellite identification and mass file are passed to the filter/smoother to estimate time-varying parameter states at each epoch, improved satellite initial elements, and improved estimates of constant parameters.

Goad, Clyde C.↗