Browsing by Subject "Hydrodynamics"

Now showing 1 - 13 of 13

A viscous vorticity method for the prediction of turbulent flows around hydrofoils and propellers
(2023-12) You, Rui, Ph. D.; Kinnas, Spyros A.; Hodges, Ben R.; Sepehrnoori, Kamy; Bogard, David G.; Raja, Laxminarayan L.
Marine propellers operate in turbulent flows, presenting a significant challenge for numerical analysis and design. Conventional linear and potential flow theories have limitations in predicting turbulent flows. Viscous flow methods, though capable of handling turbulence by incorporating a turbulence model, are often computationally intensive. The primary objective of this dissertation is to develop an efficient viscous numerical solver for simulating turbulent flows around propellers. The VIScous Vorticity Equation (VISVE) numerical solver was previously developed to handle laminar flow problems. This dissertation aims to extend this solver to allow for turbulence modeling and cavitation. The focus is on implementing the k − ω SST turbulence model in both 2-D and 3-D versions of the VISVE solver. The turbulence model is discretized using the Finite Volume Method (FVM), and a hybrid OpenMP/MPI parallelization strategy is adopted to fully leverage High-Performance Computing (HPC) resources. The developed method is first applied to 2-D hydrofoils in turbulent flow, showcasing excellent agreement with predictions from a Reynolds-Averaged Navier-Stokes (RANS) solver. The influence of Reynolds number (Re) on vorticity, velocity, and turbulent viscosity is studied across a range of Re values. The turbulent VISVE model is also successfully applied to a hydrofoil with a cupped trailing edge, capturing turbulent separated flow at high Reynolds numbers. The method is then extended to 3-D analysis, demonstrating consistency with RANS solver results for infinitely long hydrofoils and rectangular wings. The turbulent VISVE solver is further employed to study propellers in turbulent flow, with a focus on a 5-bladed propeller (e.g., the NSRCD propeller 4381) under various loading conditions. In addition to investigating 2-D and 3-D turbulent flow scenarios, the 2-D solver is extended to address turbulent cavitating conditions. A pressure calculation scheme is proposed for 2-D turbulent and cavitating flow, and multiphase and cavitation models are implemented in the 2-D turbulent VISVE solver, using the mixture model. Scalability tests are conducted to optimize computational resources, enhancing the solver’s efficiency. Notably, the VISVE method offers advantages such as a significantly smaller computational domain and post-processing pressure calculation. Moreover, the computational grid size, unknowns, and computation time for the propeller system are significantly reduced by considering the effects of all other blades using the key blade’s solution from an earlier time step. Overall, this research contributes to the development of a robust and efficient numerical solver for simulating turbulent flows around hydrofoils and propellers. The implementation of turbulence models and parallelization strategies advances the understanding and analysis of turbulent propeller flows, with potential applications in marine propulsion design and performance analysis.
Core-envelope haloes in scalar field dark matter with repulsive self-interaction : fluid dynamics beyond the de Broglie wavelength
(2021-07-29) Dawoodbhoy, Taha Aliasger; Shapiro, Paul R.; Boylan-Kolchin, Michael; Gebhardt, Karl; Kilic, Can; Offner, Stella
Scalar Field Dark Matter (SFDM) comprised of ultralight bosons has attracted great interest as an alternative to standard, collisionless Cold Dark Matter (CDM) because of its novel structure-formation dynamics, described by the coupled Schrödinger-Poisson equations. In the free-field (“fuzzy”) limit of SFDM (FDM), structure is inhibited below the de Broglie wavelength, but resembles CDM on larger scales. Virialized haloes have “solitonic” cores of radius ~ [italic lambda] [subscript deB], surrounded by CDM-like envelopes. When a strong enough repulsive self-interaction (SI) is also present, structure can be inhibited below a second length scale, [italic lambda] [subscript SI], with [italic lambda] [subscript SI] > [italic lambda] [subscript deB] --called the Thomas-Fermi (TF) regime. FDM dynamics differs from CDM because of quantum pressure, and SFDM-TF differs further by adding SI pressure. In the small-[italic lambda] [subscript deB] limit, however, we can model all three by fluid conservation equations for a compressible, γ = 5/3 ideal gas, with ideal gas pressure sourced by internal velocity dispersion and, for the TF regime, an added SI pressure, P [subscript SI] [is proportional to] p². We use these fluid equations to simulate halo formation from gravitational collapse in 1D, spherical symmetry, demonstrating for the first time that SFDM-TF haloes form with cores the size of R [subscript TF], the radius of an SI-pressure-supported (n = 1)- polytrope, surrounded by CDM-like envelopes. In comparison with rotation curves of dwarf galaxies in the local Universe, SFDM-TF haloes pass the [“too-big-to-fail” + “cusp-core”]-test if R [subscript TF] [is greater than about] 1 kpc
From viscous to inertial forces : defining the limits of hydrodynamic regimes for larval fishes
(2005) Sarkisian, Brie Laura; Fuiman, Lee A.
The larval period in fishes is characterized by rapid growth which produces significant changes in the hydrodynamic conditions during swimming. The point of this study was to examine the changes in hydro-dynamic forces that act on red drum larvae, Sciaenops ocellatus, and to identify the hydrodynamic transition points throughout their development. I experimentally altered hydrodynamic conditions by changing the size of the fish under study (5-6 mm, 8 - 9.5 mm, 13 - 15.5 mm, and 29 - 35 mm in total length) and the kinematic viscosity of test solutions (0.8, 1.2, 1.6, and 2.0 x 10⁶ m² s⁻¹), in order to achieve a wide range of Reynolds numbers based on body length (ReL ranged from 12 to 4695). Five kinematic variables (swim-ming speed, stride length, tail-beat frequency, transverse tail speed, and tail amplitude) were measured for fish swimming at a constant speed along a linear path. Within a size class, increases in fluid kinematic viscosity reduced only swimming speed and stride length and only for the two intermediate size classes. Transitions in hydrodynamic regimes, from viscous to intermediate and intermediate to inertial, were estimated from plots of stride length against indices of viscous and inertial drag forces. The upper limit of the viscous hydrodynamic regime occurred at ReL approximately 600. The lower limit of the inertial regime was at ReL of approximately 1300. These estimates illustrate that fish are exposed to viscous forces over a wider range of ReL than originally predicted
Hydrodynamic instabilities of radiative blast waves
(2013-12) Kim, In Tai; Ditmire, Todd R.
We present the results from a series of experimental investigations into the hydrodynamic instabilities that occur in radiative blast waves. In particular, we examine the Vishniac instability in which the perturbation modes oscillate in time and, for certain mode numbers and polytropic index of the medium, can exhibit a growth in their amplitudes. Experiments were conducted on the GHOST laser laboratory in which a source of atomic clusters was irradiated by a 1J-2J, 115fs laser pulse to produce cylindrical blast waves. The thrust of this thesis falls into two categories. First, we analyze the effects radiative cooling has on the evolution of blast waves such as the lowering of the effective polytropic index and consequently the lowering of their deceleration parameter. Radiation from the blast wave surface results in a preheated ionization precursor in the upstream material and is indicated by a gradual decline in the electron density profile of the blast wave rather than a sharp jump. This mechanism, if strong enough, can also create a secondary shock wave to form ahead of the main blast wave. The second set of experiments investigates the temporal evolution of longitudinal perturbations induced on the blast waves by use of a transverse interferometric beam that modifies the cluster medium prior to the onset of the main pump beam. These perturbations are analyzed and compared to theory set forth in Vishniac's mechanism for oscillatory instabilities and their growth rate.
Imaging particle migration with electrical impedance tomography: an investigation into the behavior and modeling of suspension flows
(2004) Norman, Jay Thomas; Bonnecaze, R. T. (Roger T.)
Neutrally buoyant particles in low Reynolds number, pressure-driven suspension flows migrate from regions of high to low shear, and this migration is a strong function of the local concentration. When the particle density differs from that of the suspending fluid, buoyancy forces also affect particle migration. It is the ratio between the buoyancy and viscous forces, as quantified by a dimensionless buoyancy number, which determines the phase distribution of the suspension once the flow is fully developed. Although several experiments have verified shear-induced particle migration in neutrally buoyant suspensions, there is little data for particle migration when buoyancy effects are important. An accurate and efficient electrical impedance tomography (EIT) imaging technique is developed to non-invasively measure the distribution of positively and negatively buoyant particles in low Reynolds number pressure-driven flow in a pipe. vii Additionally, a bimodal suspension of heavy particles in a low Reynolds number pressure-driven pipe flow is investigated. The effects for a range of buoyancy numbers were probed by varying the flow rate. In all of the experiments, a significant fraction of the particle phase is observed to migrate towards the top or bottom of the pipe, depending on the relative density of the particles. The amount of migration away from the center of the pipe increases with increasing magnitude of the buoyancy number. The bimodal suspension displayed an adverse density gradient for low buoyancy numbers. A scaling analysis is introduced to predict the formation of an unstable particle distribution. Furthermore, observations of the phase distribution at several positions downstream of the inlet indicate that suspension flows of buoyant particles become fully developed earlier than that observed for neutrally buoyant particles, with higher buoyancy numbers becoming fully developed more rapidly. A scaling for the prediction of the fully developed length is presented that matches experimental observations reasonably well. The experimental observations of the particle distributions were favorably compared to the predictions of an isotropic suspension balance model.
Multidimensional multiscale dynamics of high-energy astrophysical flows
(2010-05) Couch, Sean Michael; Wheeler, J. Craig; Milosavljević, Miloš; Bromm, Volker; Hoeflich, Peter; Jaffe, Daniel; Kumar, Pawan
Astrophysical flows have an enormous dynamic range of relevant length scales. The physics occurring on the smallest scales often influences the physics of the largest scales, and vice versa. I present a detailed study of the multiscale and multidimensional behavior of three high-energy astrophysical flows: jet-driven supernovae, massive black hole accretion, and current-driven instabilities in gamma-ray burst external shocks. Both theory and observations of core-collapse supernovae indicate these events are not spherically-symmetric; however, the observations are often modeled assuming a spherically-symmetric explosion. I present an in-depth exploration of the effects of aspherical explosions on the observational characteristics of supernovae. This is accomplished in large part by high-resolution, multidimensional numerical simulations of jet-driven supernovae. The existence of supermassive black holes in the centers of most large galaxies is a well-established fact in observational astronomy. How such black holes came to be so massive, however, is not well established. In this work, I discuss the implications of radiative feedback and multidimensional behavior on black hole accretion. I show that the accretion rate is drastically reduced relative to the Eddington rate, making it unlikely that stellar mass black holes could grow to supermassive black holes in less than a Hubble time. Finally, I discuss a mechanism by which magnetic field strength could be enhanced behind a gamma-ray burst external shock. This mechanism relies on a current-driven instability that would cause reorganization of the pre-shock plasma into clumps. Once shocked, these clumps generate vorticity in the post-shock plasma and ultimately enhance the magnetic energy via a relativistic dynamo process.
Non-Darcy flow through porous media
(2000) Bené, James Edward; Sharp, John Malcolm, Jr., 1944-
Since its introduction, Darcy's law has been implemented as a mathematical tool that allows simple calculation and prediction of low velocity subsurface flows. However, turbulence, non-isothermal conditions, as well as other factors can create conditions where Darcy's law does not accurately describe the head and velocity distributions within a given porous matrix. Darcy's law has been widely applied to analytical and numerical modeling of fluid flow through porous matrix, regardless of the hydrogeologic setting. This study attempts to quantify the error incurred by these models through simultaneous numerical modeling of the mass continuity equation using Darcy's law as well as Forchheimer's relation. To this end, results from steady-state and transient Darcy-based and Forchheimer-based numerical models are presented in this study.
Reactive transport modeling in fractures and two-phase flow
(2003) Noh, Myeong Hwan; Lake, Larry W.
This study presents a mathematical model to simulate hydrodynamics and fluid-mineral reactions in a fracture within permeable media. Fluid convection, diffusion and precipitation / dissolution (PD) reactions inside a finite space are solved as a simplified representation of natural fracture mineralization. The problem involves mass transfer within the fluid accompanied by chemical reaction at the fracture surface. Mass-conservation equations for components in the fluid are solved, and these are coupled with chemical reaction at the fracture surface. The intent of this model is to show the time evolution of fracture aperture shrinkage patterns caused by the calcite cementation. We present the aperture width distribution along the fracture. In this study, we consider the precipitate as porous media and allow porosity and permeability in the cement. Therefore, the calcite cementation completely fills eventually. As a second subject, the reactive transport model of CO2 sequestration in aquifers is studied. Geologic formations are considered as a target for the sequesvi tration ofCO2 from stationary sources such as power plants or large industrial facilities. Deep saline aquifers have a large potential storage capacity for CO2 and they are ubiquitous in sedimentary formations. CO2 can be sequestered in geologic formations by three principal mechanisms: hydrodynamic trapping, solubility trapping and mineral trapping. Mineral trapping is the most stable way of CO2 sequestration in aquifers. Storage capacities of CO2 for each trapping mechanism are presented using GEM, a commercial program from Computer Modeling Group Ltd. We also present the anlaytical solutions for the miscible displacement and compare them with the numerical results. Developing methods for increasing the mineral trapping creates stable repositories of carbon dioxide and that decreases mobile hazards such as leakage of CO2 to the surface.
Regional analysis of Residual Oil Zone potential in the Permian Basin
(2014-08) West, Logan Mitchell; Tinker, Scott W. (Scott Wheeler)
This study provides independent analysis of Residual Oil Zones (ROZs) in the Permian Basin from a regional perspective, focusing on the formation mechanism and present ROZ locations. Results demonstrate widespread potential for ROZs, defined here as thick volumes of reservoir rock containing near-residual saturations of predominantly immobile oil formed by natural imbibition and displacement of oil by dynamic buoyant or hydrodynamic forces. Previous work suggests hydrodynamic forces generated by regional tectonic uplift drove widespread oil remobilization and ROZ creation. To test the hypothesis, uplift and tilting are quantified and the resulting peak regional potentiometric gradient used as a physical constraint to compute and compare predicted ROZ thicknesses from hydrodynamics for several ROZ-bearing San Andres fields with known ROZ thicknesses. Late-Albian Edwards Group geologic contacts, which are interpreted to have been deposited near sea level prior to uplift, are used as a regional datum. Approximate elevations determined for the present datum show ~1800 m of differential uplift since Edwards deposition, with an average regional slope of ~0.128˚. This post-Edwards tilting increased the pre-existing regional structural gradient of the San Andres Formation to ~0.289˚. Using the calculated post-Edwards gradient results in to prediction of ROZ thicknesses from hydrodynamics that is consistent with measured ROZ thicknesses at several fields. When compared with countervailing buoyancy forces, hydrodynamics is calculated to be the more dominant driving force of oil movement for reservoirs with structural dips less than 1.5˚, which is the common dip for San Andres Formation platform deposits where ROZs have been identified. To predict the location of ROZs, ROZ-related oil field properties were identified and analyzed for over 2,800 Permian Basin reservoirs. A strong basin-wide correlation between API and crude sulfur content is consistent with the expected outcome of oil degradation driven by oil-water interaction, and supports the use of API and sulfur content as proxies for ROZ potential in the Permian Basin. Spatial analysis of sulfur data shows that the highest probability for ROZ existence exists in Leonardian through Guadalupian-age reservoirs, distributed primarily in shelf and platform areas of Permian structures. Combined, these results support the widespread potential for ROZs across the Permian Basin generated primarily by regional scale tilting and resultant hydrodynamic forces.
Simulations of granular materials: kinetics and hydrodynamic phenomena
(2003) Moon, Sung Joon; Swift, Jack B.
Granular materials often exhibit fluid-like behavior in the presence of an external forcing. This dissertation deals with kinetics and hydrodynamic phenomena in granular fluids subject to two types of forcing, vertical oscillation and homogeneous bulk heating, using a molecular dynamics simulation of frictional inelastic hard spheres. The oscillated granular fluid is simulated to probe microscopic dynamics of the transition from a wave pattern to spatiotemporal chaos, and to reveal a new kind of convection, transport, and segregation mechanism that is induced by a kink (a boundary between domains oscillating out of phase by π). We also examine the role of friction in the wave pattern, and find that a pattern loses its stability without friction. Due to their dissipative nature, granular fluids are always far from equilibrium, and the velocity distributions deviate from the Maxwellian. The single particle distribution functions both in homogeneously heated and vertically oscillated granular gases are studied. High energy tails of the distributions are described by stretched exponentials ∼ exp(−Av α ), and the exponent α depends on the system and material parameters. Precollisional velocities are strongly correlated (up to 15% of the granular temperature), and the correlations decay algebraically with the distance from a grain (∼ r −(1+δ) , where 0.2 < δ < 0.3) in a three-dimensional system. The normal shock wave in vertically oscillated layers of frictionless inelastic hard spheres are studied, and the results are compared with a continuum model; the agreement is shown to be remarkably good, even with the failure of the molecular chaos assumption and mean-field approximation that are used in the derivation of the model. Continuum equations for realistic granular fluids might include friction and a velocity-dependent coefficient of restitution, and the derivation of the equations accounting for such properties is still far from complete. We show that the coarse-grained integration/bifurcation method can be successfully applied to granular fluids. This method enables the accomplishment of some of the tasks traditionally performed only by use of continuum equations, even without the knowledge of the equations.
Simulations of high-energy astrophysical phenomena
(2014-12) Lindner, Christopher Carl; Milosavljević, Miloš
Supercomputer technology has revolutionized our studies of the most energetic astrophysical phenomena. Here, I present my simulations of energetic outbursts of gamma rays and the explosions of massive stars, and my efforts to further the computational astrophysics frontier with the development of a radiation hydrodynamics code. First, I present axisymmetric hydrodynamical simulations of the long-term accretion of a rotating gamma-ray burst (GRB) progenitor star, a "collapsar," onto the central compact object, which we assume is a black hole. The simulations were carried out with the adaptive mesh refinement code FLASH in two spatial dimensions and with an explicit shear viscosity. The evolution of the central accretion rate exhibits phases reminiscent of the long GRB [gamma]-ray and X-ray light curve, which lends support to the proposal by Kumar et al. (2008a,b) that the luminosity is modulated by the central accretion rate. In the first "prompt" phase, the black hole acquires most of its final mass through supersonic quasiradial accretion occurring at a steady rate of ~ 0.2 [solar mass] s⁻¹. After a few tens of seconds, an accretion shock sweeps outward through the star. The formation and outward expansion of the accretion shock is accompanied by a sudden and rapid power-law decline in the central accretion rate [mathematical formula], which resembles the L [subscript x] [is proportional to] t⁻³ decline observed in the X-ray light curves. The collapsed, shock-heated stellar envelope settles into a thick, low-mass equatorial disk embedded within a massive, pressure-supported atmosphere. After a few hundred seconds, the inflow of low-angular-momentum material in the axial funnel reverses into an outflow from the thick disk. Meanwhile, the rapid decline of the accretion rate slows, which is potentially suggestive of the "plateau"' phase in the X-ray light curve. We complement our adiabatic simulations with an analytical model that takes into account the cooling by neutrino emission and estimate that the duration of the prompt phase will be ~ 20 s. The model suggests that the steep decline in GRB X-ray light curves is triggered by the circularization of the infalling stellar envelope at radii where the virial temperature is below 10¹⁰ K, such that neutrino cooling is inefficient and an outward expansion of the accretion shock becomes imminent; GRBs with longer prompt [gamma]-ray emission should have more slowly rotating envelopes. Observational evidence suggests a link between long GRBs and Type Ic supernovae. I propose a potential mechanism for Type Ic supernovae in LGRB progenitors powered solely by accretion energy. I present spherically-symmetric hydrodynamic simulations of the long-term accretion of a rotating gamma-ray burst progenitor star, a "collapsar," onto the central compact object, which we take to be a black hole. The simulations were carried out with the adaptive mesh refinement code FLASH in one spatial dimension and with rotation, explicit shear viscosity, and convection in the mixing length theory approximation. Once the accretion flow becomes rotationally supported outside of the black hole, an accretion shock forms and traverses the stellar envelope. Energy is carried from the central geometrically thick accretion disk to the stellar envelope by convection. Energy losses through neutrino emission and nuclear photodisintegration are calculated but do not seem important following the rapid early drop of the accretion rate following circularization. We find that the shock velocity, energy, and unbound mass are sensitive to convective efficiency, effective viscosity, and initial stellar angular momentum. Our simulations show that given the appropriate combinations of stellar and physical parameters, explosions with energies ~ 5 x 10⁵⁰ ergs, velocities ~ 3000 km s⁻¹, and unbound material masses > 5 [solar mass] are possible in a rapidly rotating 16 [solar mass] main sequence progenitor star. Further work is needed to constrain the values of these parameters, to identify the likely outcomes in more plausible and massive LRGB progenitors, and to explore nucleosynthetic implications. In many high-energy astrophysical phenomena, the force of radiation pressure will have a direct effect on the hydrodynamics. Observing radiation is also the primary way we investigate our universe. With this in mind, I present my expansion of the FLASH hydrodynamics code, where I have implemented a gray, flux-limited diffusion (FLD) radiation hydrodynamics (RHD) solver. My solver utilizes the FLASH's diffusion packages that are powered by HYPRE. I have written a new, efficient radiation-matter coupling solver, which exactly integrates the equations for radiation-matter coupling and operates without any time step restrictions. I have also rewritten the unsplit hydrodynamics solver in FLASH to incorporate the changes in PPM characteristic tracing and the Riemann solver required to properly capture the radiation pressure force in regions that are not entirely optically thick. This has required the addition of a new Riemann solver to FLASH, similar to the Riemann solver in the CASTRO RHD code. I then present my validation tests of the code. This code will be made publicly available.
Superluminous supernovae : theory and observations
(2013-05) Chatzopoulos, Emmanouil; Wheeler, J. Craig
The discovery of superluminous supernovae in the past decade challenged our understanding of explosive stellar death. Subsequent extensive observations of superluminous supernova light curves and spectra has provided some insight for the nature of these events. We present observations of one of the most luminous self-interacting supernovae ever observed, the hydrogen-rich SN 2008am discovered by the Robotic Optical Transient Search Experiment Supernova Verification Project with the ROTSE-IIIb telescope located in the McDonald Observatory. We provide theoretical modeling of superluminous supernova light curves and fit the models to a number of observed events and similar transients in order to understand the mechanism that is responsible for the vast amounts of energy emitted by these explosions. The models we investigate include deposition of energy due to the radioactive decays of massive amounts of nickel-56, interaction of supernova ejecta with a dense circumstellar medium and magnetar spin-down. To probe the nature of superluminous supernovae progenitor stars we study the evolution of massive stars, including important effects such as rotation and magnetic fields, and perform multi-dimensional hydrodynamics simulations of the resulting explosions. The effects of rotational mixing are also studied in solar-type secondary stars in cataclysmic variable binary star systems in order to provide an explanation for some carbon-depleted examples of this class. We find that most superluminous supernovae can be explained by violent interaction of the SN ejecta with >1 Msun dense circumstellar shells ejected by the progenitor stars in the decades preceding the SN explosion.
Turbulence measurements in open-channel flow with transverse bed slope
(1992) Lee, Ka Leung, 1963-; Holley, Edward R. (Edward Raymond)
In a meandering river, both the bends and the transverse bed slopes influence the turbulence in the flow. As part of a research project to study the turbulence characteristics in a meandering laboratory river channel, turbulence measurements were made in a straight flume with a transversely sloping plane bed to evaluate the effect of the transverse bed slope. The flume was 30 in. wide and had a 10% transverse bed slope. The bottom of the flume was formed by sand of 2 mm nominal size coated with paint. The depths were 0.4 in. on the shallow side and 3.5 in. on the deep side. The average velocity was 1.3 ft/s. Constant temperature hot film anemometry was used and all measurements were made with single sensor probes. Some problems encountered in the application of hot film anemometry are discussed. A detailed account of the development of the techniques for data acquisition, processing and analysis is also given. The parameters used to characterize the turbulence include the mean velocity, turbulent intensity, autocorrelation coefficient, cross-correlation coefficient, spectrum, macroscale, Taylor microscale, energy dissipation rate, Kolmogorov microscale, and skewness and kurtosis of the probability distribution of the velocity fluctuations. Some of the variations of these parameters can be attributed to the depth variation and velocity variation across the flume. The mean velocities on a vertical normalized with respect to the depth-averaged velocity were found to vary in a similar way with the relative depth for different verticals. The same observation is obtained for the relative turbulent intensity, the energy dissipation rate and the Kolmogorov micro-length scale. For the other parameters, interesting patterns of variation can be identified. These findings will be compared with those of similar measurements in the meandering laboratory river channel so that the effect of transverse bed slope on the turbulence in natural river flow can be evaluated