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An efficient and robust algorithm for two dimensional time dependent incompressible Navier-Stokes equations: High Reynolds number flows

An algorithm is presented for unsteady two-dimensional incompressible Navier-Stokes calculations. This algorithm is based on the fourth order partial differential equation for incompressible fluid flow which uses the streamfunction as the only dependent variable. The algorithm is second order accurate in both time and space. It uses a multigrid solver at each time step. It is extremely efficient with respect to the use of both CPU time and physical memory. It is extremely robust with respect to Reynolds number.

Goodrich, John W.↗

An efficient and robust algorithm for two dimensional time dependent incompressible Navier-Stokes equations - High Reynolds number flows

An algorithm is presented for unsteady two-dimensional incompressible Navier-Stokes calculations. This algorithm is based on the fourth order partial differential equation for incompressible fluid flow which uses the streamfunction as the only dependent variable. The algorithm is second order accurate in both time and space. It uses a multigrid solver at each time step. It is extremely efficient with respect to the use of both CPU time and physical memory. It is extremely robust with respect to Reynolds number.

Goodrich, John W.↗

Advancements in 3D Structural Analysis of Geothermal Systems

Robust geothermal activity in the Great Basin, USA is a product of both anomalously high regional heat flow and active fault-controlled extension. Elevated permeability associated with some fault systems provides pathways for circulation of geothermal fluids. Constraining the local-scale 3D geometry of these structures and their roles as fluid flow conduits is crucial in order to mitigate both the costs and risks of geothermal exploration and to identify blind (no surface expression) geothermal resources. Ongoing studies have indicated that much of the robust geothermal activity in the Great Basin is associated with high density faulting at structurally complex fault intersection/interaction areas, such as accommodation/transfer zones between discrete fault systems, step-overs or relay ramps in fault systems, intersection zones between faults with different strikes or different senses of slip, and horse-tailing fault terminations. These conceptualized models are crucial for locating and characterizing geothermal systems in a regional context. At the local scale, however, pinpointing drilling targets and characterizing resource potential within known or probable geothermal areas requires precise 3D characterization of the system. Employing a variety of surface and subsurface data sets, we have conducted detailed 3D geologic analyses of two Great Basin geothermal systems. Using EarthVision (Dynamic Graphics Inc., Alameda, CA) we constructed 3D geologic models of both the actively producing Brady’s geothermal system and a ‘greenfield’ geothermal prospect at Astor Pass, NV. These 3D models allow spatial comparison of disparate data sets in 3D and are the basis for quantitative structural analyses that can aid geothermal resource assessment and be used to pinpoint discrete drilling targets. The relatively abundant data set at Brady’s, ~80 km NE of Reno, NV, includes 24 wells with lithologies interpreted from careful analysis of cuttings and core, a 1:24,000 scale detailed geologic map and cross-sections, 2D seismic reflection profiles and other geophysical data, and downhole temperature data. The 3D geologic model based on these data consists of 61 fault planes, 25 distinct stratigraphic units, and 2 intrusive bodies. Geothermal fluids are produced from a left step-over/relay ramp within the Brady’s Fault Zone (BFZ). Under local stress conditions, fault segments that strike NNE-to-NE are most likely to slip and/or dilate, and therefore transmit geothermal fluids. The 3D model defines the locations of discrete fault intersections within the BFZ and indicates that the densest zones of structurally controlled fracture permeability are ~10-to-10s of meters in diameter and plunge ~55° NW-NNW beneath the heart of the BFZ step over. The locations of high intersection density, high fault slip and dilation tendency, high subsurface temperature, and lithologies known to support high fracture permeability are combined to produce 3D ‘fairway’ maps useful in both assessments of geothermal resource potential and for defining drilling targets. Astor Pass is located on the Pyramid Lake Paiute Reservation, ~80 km north of Reno, NV. It is a prospective ‘greenfield’ geothermal area, and thus subsurface data are relatively sparse. Available data include: two relatively deep wells (~1400 m) and one shallower well (~500 m) with lithologies interpreted from drill cuttings, several 2D seismic reflection profiles, a 1:24,000 scale geologic map and cross-section, a shallow temperature survey, and downhole temperature data. 3D modeling based on these data has defined 19 distinct fault planes and 16 stratigraphic units. Based on the stress field calculated from borehole breakouts, drilling induced tensile cracks and petal-centerline cracks in the two relatively deep wells, 3D slip and dilation tendency analysis indicates that northerly striking fault segments are most likely to slip and/or dilate, and therefore transmit geothermal fluids. Analysis of fault intersection density indicates that the highest density of structurally controlled permeability within the field lies in a narrow (10-to-10s of m) zone plunging moderately (~35°) to the NNW beneath Pleistocene tufa deposits. This zone of increased fracture density, which we interpret as the primary upflow zone, is controlled by the intersection of N-to-NNW striking normal faults and a WNW striking dextral fault zone and represents the most promising target for future drilling. Construction of a 3D geologic model involves integration of a variety of data into an internally consistent framework. A robust model allows for spatial comparison between the various types of data (structural, stratigraphic, geophysical, temperature, etc.) that are commonly used independently to site geothermal wells. Furthermore, highly detailed 3D geologic models provide the basis for additional quantitative analysis, including 3D fault slip and dilation tendency analysis and the precise location of structurally controlled permeability pathways. These analyses provide detailed information relating to the internal dynamics of geothermal systems and can mitigate the costs and risks of geothermal exploration and development by contributing to better well targeting and more accurate evaluations of resource potential.

15 GEOTHERMAL ENERGY↗

Feasibility study for a numerical aerodynamic simulation facility. Volume 2: Hardware specifications/descriptions

An FMP (Flow Model Processor) was designed for use in the Numerical Aerodynamic Simulation Facility (NASF). The NASF was developed to simulate fluid flow over three-dimensional bodies in wind tunnel environments and in free space. The facility is applicable to studying aerodynamic and aircraft body designs. The following general topics are discussed in this volume: (1) FMP functional computer specifications; (2) FMP instruction specification; (3) standard product system components; (4) loosely coupled network (LCN) specifications/description; and (5) three appendices: performance of trunk allocation contention elimination (trace) method, LCN channel protocol and proposed LCN unified second level protocol.

Green, F. M.↗

Extracting energy from natural flow

Three concepts for extracting energy from wind, waterflow, and tides utilize flow instability to generate usable energy. Proposed converters respond to vortex excitation motion, galloping or plunging motion, and flutter. Fluid-flow instability is more efficient in developing lift than is direct flow.

Delionback, L. M.↗

An artificial energy method for calculating flows with shocks

The artificial-viscosity method, first proposed by von Neumann and Richtmyer, introduces an artificial viscous pressure term in regions of compression such that an increase in entropy occurs in shock transition zones. The paper describes how dissipative flows can be induced by reducing the total energy available for adiabatic processes in shock zones. A class of inviscid fluid flows, called semiflows, is described in which the flows exhibit thermodynamic differences. Induced dissipative flows modify the pressure in regions of compression in a manner analogous to the artificial-viscosity method and for a gas, the effect is equivalent to suitably modifying the gas constant in the equation of state. By employing MacCormack's method and the usual non-adiabatic equations, numerical solutions of a Riemann problem are compared with the modified artificial energy method, showing that the dissipation effect predicted by the analytical formulation is reflected in the numerical method as well.

Rose, M. E.↗

Impact cratering - The effect of crustal strength and planetary gravity

The effect of varying planetary crustal strength and surface gravity on the depth of impact craters is investigated, by coupling the results of compressible flow, finite difference calculations carried out to stress levels below the compressional dynamic yield point, in keeping with the incompressible fluid flow model of Maxwell (1973). The fundamental assumption in this description is that the amplitude of the particle velocity field decreases with time as kinetic energy is converted into heat and gravitational potential energy. By using a Mohr-Coulomb yield criterion, the effect of varying strength on transient crater depth and on crater formation time in the gravity field of the moon is investigated for the case of 5 km/sec impactors having radii in the 10 to 10 to the 7th cm range.

Okeefe, J. D.↗

Wrinkling phenomenon in structures. I - Model formulations

Those structural element models which can suffer the wrinkling phenomenon are analyzed. A laminated elastic material, defined as a one-parametrical family of surfaces whose in-plane strains are negligible in comparison to the strains in the transverse direction, is analyzed in terms of its geometry, geometrical compatibility equations, layer geometry, kinematics, kinematical compatibility equations, and governing dynamical equations. These aspects are also examined for the case of a soft shell, defined as a shell for which the in-plane strains of the middle surface are negligible compared to the strains in the transverse direction, and for the case of a soft rod, defined as a rod for which the strains along the axis are negligible compared to the strains in the transverse direction. The influence of internal fluid flow on the wrinkling phenomenon for layers of laminated material and for a flexible pipe containing an inviscid and incompressible fluid is also analyzed.

Zak, M.↗

Improved numerical methods for turbulent viscous flows aerothermal modeling program, phase 2

The details of a study to develop accurate and efficient numerical schemes to predict complex flows are described. In this program, several discretization schemes were evaluated using simple test cases. This assessment led to the selection of three schemes for an in-depth evaluation based on two-dimensional flows. The scheme with the superior overall performance was incorporated in a computer program for three-dimensional flows. To improve the computational efficiency, the selected discretization scheme was combined with a direct solution approach in which the fluid flow equations are solved simultaneously rather than sequentially.

Karki, K. C.↗

Computing high-speed flows past an oscillating cylinder near a vertical wall

A computational method to simulate unsteady flows involving moving rigid boundaries and interference has been developed. The method is used to solve inviscid equations governing the fluid flow and the dynamic equations governing the motion of rigid bodies. A second-order accurate, upwind-biased, and alterating-direction-implicit method is used to solve the governing equations of the flow. A kinematic domain decomposition (KDD) procedure is extended to treat 3D problems with a high degree of accuracy and generality. The method under consideration is applied to both transonic and supertransonic flows. Both cases involve flow past a cylinder which is forced to pitch sinusoidally near a vertical wall. Benefits of the proposed approach include accurate calculation of the flow around 3D moving multiple bodies with interference; reduction of a numerical error; in particular, the dispersion error which strongly affects wave propagation; and minimization of the phase error which is accumulated according to the time advance procedure.

Yen, Guan-Wei↗

A time-accurate finite volume method valid at all flow velocities

A finite volume method to solve the Navier-Stokes equations at all flow velocities (e.g., incompressible, subsonic, transonic, supersonic and hypersonic flows) is presented. The numerical method is based on a finite volume method that incorporates a pressure-staggered mesh and an incremental pressure equation for the conservation of mass. Comparison of three generally accepted time-advancing schemes, i.e., Simplified Marker-and-Cell (SMAC), Pressure-Implicit-Splitting of Operators (PISO), and Iterative-Time-Advancing (ITA) scheme, are made by solving a lid-driven polar cavity flow and self-sustained oscillatory flows over circular and square cylinders. Calculated results show that the ITA is the most stable numerically and yields the most accurate results. The SMAC is the most efficient computationally and is as stable as the ITA. It is shown that the PISO is the most weakly convergent and it exhibits an undesirable strong dependence on the time-step size. The degenerated numerical results obtained using the PISO are attributed to its second corrector step that cause the numerical results to deviate further from a divergence free velocity field. The accurate numerical results obtained using the ITA is attributed to its capability to resolve the nonlinearity of the Navier-Stokes equations. The present numerical method that incorporates the ITA is used to solve an unsteady transitional flow over an oscillating airfoil and a chemically reacting flow of hydrogen in a vitiated supersonic airstream. The turbulence fields in these flow cases are described using multiple-time-scale turbulence equations. For the unsteady transitional over an oscillating airfoil, the fluid flow is described using ensemble-averaged Navier-Stokes equations defined on the Lagrangian-Eulerian coordinates. It is shown that the numerical method successfully predicts the large dynamic stall vortex (DSV) and the trailing edge vortex (TEV) that are periodically generated by the oscillating airfoil. The calculated streaklines are in very good comparison with the experimentally obtained smoke picture. The calculated turbulent viscosity contours show that the transition from laminar to turbulent state and the relaminarization occur widely in space as well as in time. The ensemble-averaged velocity profiles are also in good agreement with the measured data and the good comparison indicates that the numerical method as well as the multipletime-scale turbulence equations successfully predict the unsteady transitional turbulence field. The chemical reactions for the hydrogen in the vitiated supersonic airstream are described using 9 chemical species and 48 reaction-steps. Consider that a fast chemistry can not be used to describe the fine details (such as the instability) of chemically reacting flows while a reduced chemical kinetics can not be used confidently due to the uncertainty contained in the reaction mechanisms. However, the use of a detailed finite rate chemistry may make it difficult to obtain a fully converged solution due to the coupling between the large number of flow, turbulence, and chemical equations. The numerical results obtained in the present study are in good agreement with the measured data. The good comparison is attributed to the numerical method that can yield strongly converged results for the reacting flow and to the use of the multiple-time-scale turbulence equations that can accurately describe the mixing of the fuel and the oxidant.

Kim, S.-W.↗

Impact of clays on the compressibility and permeability of sands during methane extraction from gas hydrate

The quantity of methane potentially recoverable from gas hydrate is large enough to motivate federally-supported production tests in several countries, which in turn motivates studies of reservoir production efficiency. Evaluating long-term production well viability involves modeling permeability evolution in the reservoir sediments around the production well because processes reducing the flow of gas into the production well also reduce the long-term economic viability of the well. Fine particles, such as clays, exist nearly ubiquitously in the permafrost and marine settings that typically host gas hydrate, and fines reacting to fluid flow by migrating and clogging pore throats can reduce flow toward the production well. Many fines are sensitive to variations in pore-fluid chemistry, swelling in reaction to in situ pore brine being displaced by fresh water liberated from hydrates during dissociation. Additionally, fine particles tend to collect at gas/water interfaces created by the multiphase flow of gas and water. Thus, as methane and fresh water flow from the hydrate-dissociation front toward the production well, fine particles in the reservoir sands, interbedded fine-grained layers and seal layers can be swelled, migrated (or both), potentially clogging pathways and limiting flow to the production well.

03 NATURAL GAS↗

Fluid Physics and Macromolecular Crystal Growth in Microgravity

The molecular structure of biological macromolecules is important in understanding how these molecules work and has direct application to rational drug design for new medicines and for the improvement and development of industrial enzymes. In order to obtain the molecular structure, large, well formed, single macromolecule crystals are required. The growth of macromolecule crystals is a difficult task and is often hampered on the ground by fluid flows that result from the interaction of gravity with the crystal growth process. One such effect is the bulk movement of the crystal through the fluid due to sedimentation. A second is buoyancy driven convection close to the crystal surface. On the ground the crystallization process itself induces both of these flows.

Pusey, M.↗

Investigation of Navier-Stokes Code Verification and Design Optimization

With rapid progress made in employing computational techniques for various complex Navier-Stokes fluid flow problems, design optimization problems traditionally based on empirical formulations and experiments are now being addressed with the aid of computational fluid dynamics (CFD). To be able to carry out an effective CFD-based optimization study, it is essential that the uncertainty and appropriate confidence limits of the CFD solutions be quantified over the chosen design space. The present dissertation investigates the issues related to code verification, surrogate model-based optimization and sensitivity evaluation. For Navier-Stokes (NS) CFD code verification a least square extrapolation (LSE) method is assessed. This method projects numerically computed NS solutions from multiple, coarser base grids onto a freer grid and improves solution accuracy by minimizing the residual of the discretized NS equations over the projected grid. In this dissertation, the finite volume (FV) formulation is focused on. The interplay between the xi concepts and the outcome of LSE, and the effects of solution gradients and singularities, nonlinear physics, and coupling of flow variables on the effectiveness of LSE are investigated. A CFD-based design optimization of a single element liquid rocket injector is conducted with surrogate models developed using response surface methodology (RSM) based on CFD solutions. The computational model consists of the NS equations, finite rate chemistry, and the k-6 turbulence closure. With the aid of these surrogate models, sensitivity and trade-off analyses are carried out for the injector design whose geometry (hydrogen flow angle, hydrogen and oxygen flow areas and oxygen post tip thickness) is optimized to attain desirable goals in performance (combustion length) and life/survivability (the maximum temperatures on the oxidizer post tip and injector face and a combustion chamber wall temperature). A preliminary multi-objective optimization study is carried out using a geometric mean approach. Following this, sensitivity analyses with the aid of variance-based non-parametric approach and partial correlation coefficients are conducted using data available from surrogate models of the objectives and the multi-objective optima to identify the contribution of the design variables to the objective variability and to analyze the variability of the design variables and the objectives. In summary the present dissertation offers insight into an improved coarse to fine grid extrapolation technique for Navier-Stokes computations and also suggests tools for a designer to conduct design optimization study and related sensitivity analyses for a given design problem.

Vaidyanathan, Rajkumar↗

Three-dimensional realizations of flood flow in large-scale rivers using the neural fuzzy-based machine-learning algorithms

Machine learning methods have been extensively used to study the dynamics of complex fluid flows. One such algorithm, known as adaptive neural fuzzy inference system (ANFIS), can generate data-driven predictions for flow fields, but has not been applied to natural geophysical flows in large-scale rivers. Herein, we demonstrate the potential of ANFIS to produce three-dimensional (3D) realizations of the instantaneous flood flow field in several large-scale, virtual meandering rivers. The 3D dynamics of flood flow in large-scale rivers were obtained using large-eddy simulation (LES). The LES results, i.e., the 3D velocity components, were employed to train the learnable coefficients of an ANFIS. Further, the trained ANFIS, along with a few time-steps of LES results (precursor data) were then used to produce 3D realizations of flood flow fields in large-scale rivers with geometries other than the one the ANFIS was trained with. We also used the trained ANFIS to generate 3D realizations of river flow at a discharge other than that the ANFIS was trained with. The flow field results obtained from ANFIS were validated using separate LES runs to assess the accuracy of the 3D instantaneous realizations of the machine learning algorithm. An error analysis was conducted to quantify the discrepancies among the ANFIS and LES results for various flood flow predictions in large-scale rivers.

54 ENVIRONMENTAL SCIENCES↗

Transonic airfoil and axial flow rotary machine

Sectional profiles close to a tip 124 and a part between a midportion 125 and a hub 123 are shifted to the upstream of an operating fluid flow in a sweep direction. Accordingly, an S shape is formed in which the tip 124 and the part between the midportion 125 and the hub 123 protrude. As a result, it is possible reduce various losses due to shook, waves, thereby forming a transonic airfoil having an excellent aerodynamic characteristic.

42 ENGINEERING↗

Transient Interfacial Phenomena in Miscible Polymer Systems (TIPMPS)

Almost one hundred years ago Korteweg published a theory of how stresses could be induced in miscible fluids by concentration gradients, causing phenomena that would appear to be the same as with immiscible fluids. Miscible fluids could manifest a transient or effective interfacial tension (EIT). To this day, there has been no definitive experiment to confirm Korteweg's model but numerous fascinating and suggestive experiments have been reported. The goal of TIPMPS is to answer the question: Can concentration and temperature gradients in miscible materials induce stresses that cause convection? Many polymer processes involving miscible monomer and polymer systems could be affected by fluid flow and so this work could help understand miscible polymer processing, not only in microgravity, but also on earth. Demonstrating the existence of this phenomenon in miscible fluids will open up a new area of study for materials science. The science objectives of TIPMPS are: (1) Determine if convection can be induced by variation of the width of a miscible interface; (2) Determine if convection can be induced by variation of temperature along a miscible interface; (3) Determine if convection can be induced by variation of conversion along a miscible interface An interface between two miscible fluids can best be created via a spatially-selective photopolymerization of dodecyl acrylate with a photoinitiator, which allows the creation of precise and accurate concentration gradients between polymer and monomer. Optical techniques will be used to measure the refractive index variation caused by the resultant temperature and concentration fields. The viscosity of the polymer will be measured from the increase in the fluorescence of pyrene. Because the large concentration and temperature gradients cause buoyancy-driven convection that prevents the observation of the predicted flows, the experiment must be done in microgravity. In this report, we will consider our efforts to estimate the square gradient parameter, k, and our use of the estimates in modeling of the planned TIPMPS experiments. We developed a model consisting of the heat and diffusion equations with convective terms and of the Navier-Stokes equations with an additional volume force written in the form of the Korteweg stresses arising from nonlocal interaction in the fluid. The fluid's viscosity dependence on polymer conversion and temperature was taken from measurements of poly(dodecyl acrylate). Numerical modeling demonstrated that significant flows would arise for conditions corresponding to the planned experiments.

Pojman, John A.↗

The mechanisms, dynamics, and implications of self-sealing and CO 2 resistance in wellbore cements

Here, this study analyzes the dynamics and mechanisms of the interactions of carbonated brine with hydrated-Portland-cement; in particular, the study focuses on self-sealing, a process whereby hydrated-Portland cement reacts with carbonated brine to for silica and calcium carbonate in sufficient quantities to seal the flow pathway. The analysis is based on a comprehensive set of reactive-transport simulations that explore the complex coupled dynamics between the fluid flow and mineral reactions that underlie self-sealing, and it relies heavily on the synthesis of the extensive body of work on wellbore integrity that has been conducted over the past decade. The analysis explores a large chemical and mineralogical diversity and a wide range in physical conditions and flow regimes, attempting to assess the robustness of the analysis. Self-sealing conditions arise over a wide range in cement properties and reservoir conditions. Although some properties and conditions promote a stronger self-sealing response, self-sealing occurs for a wide range of Ca:Si ratios in cement and for various reservoir fluid compositions. Self-sealing conditions move along a wellbore proportional to the flux of the leaking carbonated brine, and the reaction zone spreads out proportional to the fluid velocity, where volumetric flux and velocity are related by porosity (flux = velocity * porosity). However, self-sealing conditions can be maintained in a specific section of a wellbore by controlling the pressure drive and/or effective wellbore permeability, which in turn can limit the flux and velocity of any leaking fluid. Finally, the phases produced by hydrating Portland cement represent a carbonic cement that will react with a carbonated brine to produce end products (calcium carbonate and silica) that can maintain integrity in the presence of carbonic acid. Lastly, the attributes that make hydrated Portland cement phases a carbonic cement are required for self-sealing.

58 GEOSCIENCES↗