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At least 397 records · Page 22

Dynamic responses of submerged components in advanced reactors: experimental and numerical studies

The seismic design of an advanced nuclear reactor must consider the interaction of vessel internal components with the surrounding coolant: fluid–structure interaction (FSI). Available analytical solutions for FSI of submerged components do not accommodate multiple-component, intense seismic inputs and complex reactor and internal geometries. Physical testing of reactor vessels and internals to inform seismic design is impractical and cost-prohibitive, leaving the use of verified and validated, robust numerical models as the only plausible option for analysis and design. Physical data that could be used for validating such numerical models for multi-component shaking are not available. This article describes an experimental program performed on a 6-degree-of-freedom earthquake simulator to generate data that could support validation of seismic FSI numerical models for submerged components in commercial finite element codes. A scaled model of a base-supported reactor vessel with simplified representations of submerged internals was tested to generate submerged-component response histories for a range of seismic inputs. The generated data were used to validate numerical models in the finite element code LS-DYNA. Numerical models were validated for calculation of hydrodynamic pressure responses on internals, in-water frequencies of internals, and acceleration responses of internals. The generated data and the analysis recommendations could aid engineering analysts designing submerged components and systems for seismic effects.

Engineering↗

CCUS 2024, Interpreting the strain tensor Larry Murdoch Interpreting strain tensor data to characterize and monitor reservoirs for CO2 storage and other applications

Recent advances in instrumentation have made it feasible to measure the transient strain tensor caused by small changes in fluid volume or pressure in the subsurface and this has opened the door to new opportunities for characterization and monitoring during CCUS. We have demonstrated this method by deploying strainmeters at shallow depths (30 to 40m) and then conducting injection well tests in an underlying reservoir at 530m depth. The resulting data indicated that the horizontal strain at shallow strainmeters was tensile and the vertical strain was compressive. The radial strain was less than the horizontal strain, and the strain rates decreased from 100 nanostrain/day to roughly 10 ne/d over a few days (1 nanostrain = 1 part per billion strain). We then used the strain data to estimate reservoir properties, geometry and pressure through inversion of poroelastic forward models using both numerical and novel analytical methods. The average horizontal strain in the caprock resembles the transient pressure in the underlying reservoir and classic type-curve methods from transient well testing can be used for preliminary interpretations of strain data. We have developed fast, closed-form analytical solutions to a pressurized poroelastic inclusion and inhomogeneity in a half-space. Numerical models developed using finite element methods allow more details of the subsurface to be included in the inversion, but they require much longer run times and this makes inversion cumbersome using standard methods. We have developed an inversion approach that uses a proxy model created using machine learning to do most of the forward calculations. This approach markedly reduces the computational requirements and makes it feasible to use Bayesian inversion with large numerical models. Bayesian inversion is important because it provides predictions with uncertainties, which makes the results useful for decision making. We have shown with field tests and simulations that the strain tensor in the caprock is sensitive to pressure in the reservoir, reservoir properties and boundaries, and pressure in the caprock caused by leaks. These results indicate that measuring and interpreting the shallow strain tensor could be a valuable tool for both initial reservoir characterization efforts and long-term monitoring during CCUS. Recent advances in instrumentation have made it feasible to measure the transient strain tensor caused by small changes in fluid volume or pressure in the subsurface and our objective was to evaluate opportunities for strain monitoring during characterization and monitoring for CCUS. Our approach was to deploy strainmeters at shallow depths (30 to 40m) and then conduct injection well tests in an underlying reservoir at 530m depth. The results indicate that the horizontal strain at shallow strainmeters was tensile and the vertical strain was compressive. The radial strain was less than the horizontal strain, and the strain rates decreased from 100 nanostrain/day to roughly 10 ne/d over a few days (1 nanostrain = 1 part per billion strain). We then used the strain data to estimate reservoir properties, geometry and pressure through inversion of poroelastic forward models using both numerical and novel analytical methods. The average horizontal strain in the caprock resembles the transient pressure in the underlying reservoir and classic type-curve methods from transient well testing can be used for preliminary interpretations of strain data. We have developed fast, closed-form analytical solutions to a pressurized poroelastic inclusion and inhomogeneity in a half-space. Numerical models developed using finite element methods allow more details of the subsurface to be included in the inversion, but they require much longer run times and this makes inversion cumbersome using standard methods. We have developed an inversion approach that uses a proxy model created using machine learning to do most of the forward calculations. This approach markedly reduces the computational requirements and makes it feasible to use Bayesian inversion with large numerical models. Bayesian inversion is important because it provides predictions with uncertainties, which makes the results useful for decision making. In conclusion, we have shown with field tests and simulations that the strain tensor in the caprock is sensitive to pressure in the reservoir, reservoir properties and boundaries, and pressure in the caprock caused by leaks. These results indicate that measuring and interpreting the shallow strain tensor could be a valuable tool for both initial reservoir characterization efforts and long-term monitoring during CCUS.

Murdoch, Larry↗

Analytic numerical solutions for shock waves

Study of weak solutions of simple wave equation, inviscid Burgers equation, and Euler equations has resulted in technique for accurate prediction of shock waves occurring in inviscid supersonic flows.

Maccormack, R. W.↗

Numerical integration of nearly-Hamiltonian systems

The reported investigation is concerned with the solution of systems of differential equations which are derived from a Hamiltonian function in the extended phase space. The problem selected involves a one-dimensional perturbed harmonic oscillator. The van der Pol equation considered has an exact asymptotic value for its amplitude. Comparisons are made between a numerical solution and a known analytical solution. In addition to the van der Pol problem, known solutions regarding the restricted problem of three bodies are used as examples for perturbed Keplerian motion. The extended phase space Hamiltonian discussed by Stiefel and Scheifele (1971) is considered. A description is presented of two canonical formulations of the perturbed harmonic oscillator.

Bond, V. R.↗

A modified proportional navigation scheme for rendezvous and docking with tumbling targets: The Planar case

A two-phase proportional navigation scheme is developed for the case of two rigid bodies engaged in a rendezvous/docking maneuver. The target vehicle is nonmaneuvering, but does have constant nonzero angular and linear velocities. Under these conditions, it is shown that previously obtained solutions are not applicable. Analytical solutions are obtained leading to relationships between the transverse and LOS navigation constants. It is shown that the transverse navigation constant for the second phase of the maneuver must be 2. Also, initial conditions necessary for rendezvous are presented.

Fitz-Coy, Norman↗

The luminosity functions of embedded stellar clusters. 1: Method of solution and analytic results

We describe a method for computing the history of the luminosity function in a young cluster still forming within a molecular cloud complex. Our method, which utilizes detailed results from stellar evolution theory, assumes that clusters arise from the continuous collapse of dense cloud cores over a protracted period of time. It is also assumed that stars reaching the main sequence are distributed in mass according to a prescribed initial mass function (IMF). We keep track separately of the contributions to the luminosity function from the populations of protostars, pre-main-sequence stars, and main-sequence stars. We derive expressions for the fractional contribution of these populations to both the total number of stars produced and the total cluster luminosity. In our model, the number of protostars rises quickly at first, but then levels off to a nearly constant value, which it maintains until the dispersal of the cloud complex. The number fraction of protostars always decreases with time. Averaged over the life of the parent cloud, this fraction is typically a few percent. The protostar mass distribution can be expressed as an integral over the IMF.

Fletcher, Andre B.↗

A transient solution for domain wall motion

An analytic solution of transient wall motion in a bulk ferromagnetic material is obtained from the dynamic torque equations with a Gilbert damping term. The steady state solution reduces to previously obtained, well known solutions.

Bourne, H. C., Jr.↗

Numerical solutions for inviscid supersonic corner flows

Analytical solutions for inviscid supersonic corner flows are virtually nonexistent due to the complexity of the interference geometry. In view of this, numerical solutions for compressive-compressive and expansive-compressive corner flows are obtained. The governing equations are written in strong conservation-law form and are solved iteratively in nonorthogonal conical coordinates by use of a second-order, shock-capturing, finite-difference technique. The computed wave structure and surface pressure distributions are compared with high Reynolds number (Re greater than 2,500,000 ft) experimental data. The results clearly show that the wave structure in the corner is dominated by the inviscid field.

Shankar, V. S. V.↗

SU(n) and Quantum SU(n) Symmetries in Physical Systems [Slides]

Presence of SU(n) or other Lie group symmetry in a physical system is its powerful, usually underutilized property. In many cases it allows for finding analytical solutions to nonlinear differential equations describing this system. Power of the method is presented on diversified examples from mathematical physics: Lie-group symmetries in finding solutions of generalized, multidimensional theory of gravity; analytical Dirac–equation solutions for description of conducting polymers; stability of qubit states in quantum computers; spatial defects in condensed matter; reconstruction of 3D object from its 2D tomographic image; significant improvement of numerical solutions stability for Euler equations. The next question after obtaining such Lie group symmetric solution is: does a generalized solution with appropriate quantum group symmetry exists for the given physical system, and if yes what is the physical meaning of the deformation parameter q introduced by such solution. In many cases it can be identified. Any SU(n) solution is by its nature singular, assuming a perfect symmetry of the physical system discussed. Such solution gives a powerful insight to theoretical physics, yet the assumption may be too demanding for experimental applications. Deformation parameter q from a quantum group symmetry allows for a continuum of solutions, more applicable to experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Multipole-based Cable Braid Magnetic Penetration Model for Conducting Wires

In this report, we investigate the effects of conductor losses in a multipole-based cable braid magnetic penetration model. Our multipole model uses a mesh of the actual cable geometry, which enables us to model more complicated structures. After summarizing the first principles model formulation, we consider a one-dimensional array of wires, for which an analytical solution is known in the lossless case. We extend this solution to the lossy case by using a complex-valued radius. We also model this structure analytically using a conformal-mapping solution. We then compare both the self-impedance and the transfer impedance results from our first principles cable braid electromagnetic penetration model to those obtained using the analytical solutions. An analysis for various frequencies (and skin depths) usually encountered in cable modeling is reported. These results are found in good agreement up to a radius to half spacing ratio of about 0.7, demonstrating a robustness needed for many commercial and non-commercial cables.

36 MATERIALS SCIENCE↗

Elastic Solutions to 2D Plane Strain Problems: Nonlinear Contact and Settlement Analysis for Shallow Foundations

The classical Neumann boundary value problem of an isotropic, homogeneous elastic half-plane under plane strain conditions is readdressed as the limiting case of the fully three-dimensional problem. Analytical solutions of the stress and strain tensors are obtained by taking the limit from known three-dimensional solutions. It is shown that the displacement fields for the plane strain problem are not well defined. A small number of simple expressions are developed, which provide a general solution for linearly-varying traction over arbitrary regions on the boundary. A simple, efficient, and rapidly convergent algorithm is developed which uses these solutions as analytic elements and provides a solution approach to the general boundary value problem. The method is verified against known solutions for Hertzian contact between parallel cylinders. Two numerical examples are presented for the analysis of shallow foundation systems. In the first, the boundary conditions are informed by analytical elastoplastic calculations and a strain influence analysis is performed and compared with the Schmertmann method. Subsequently, empirical laboratory contact traction distributions measured by Bauer et al., in both the normal and tangential directions are employed as boundary conditions for an analysis of the underlying stress field.

42 ENGINEERING↗

Verification of Bison fission product species conservation under TRISO reactor conditions

When assessing the reliability and predictive capabilities of a simulation tool, code verification is used to ensure that the implemented numerical algorithm is a faithful representation of its underlying mathematical model, including partial differential or integral equations, initial and boundary conditions, and auxiliary relationships. During this process, numerical results in a discrete solution are compared to the analytical solution of the mathematical model. Here, in this paper, the code verification process is applied to one-dimensional spatiotemporal problems that exercise partial differential equation governing the conservation of fission product species (or mass diffusion). Numerical experiments were performed in the Bison fuel performance code to evaluate its predictive capability under various TRISO reactor conditions such as base irradiation and safety heating test conditions for either short- or long-lived fission product species, as well as a case concerning evaporation from the outer surface of a particle. The code predictions were compared with the expected exact results obtained from the analytical expressions, and the fact that they demonstrate the correct analytical behavior provides strong evidence of proper numerical algorithm implementation.

07 ISOTOPE AND RADIATION SOURCES↗

An explicitly solvable energy-conserving algorithm for pitch-angle scattering in magnetized plasmas

In this work, we develop an Explicitly Solvable Energy-Conserving (ESEC) algorithm for the Stochastic Differential Equation (SDE) describing the pitch-angle scattering process in magnetized plasmas. The Cayley transform is used to calculate both the deterministic gyromotion and stochastic scattering, affording the algorithm to be explicitly solvable and exactly energy conserving. An unusual property of the SDE for pitch-angle scattering is that its coefficients diverge at the zero velocity and do not satisfy the global Lipschitz condition. Consequently, when standard numerical methods, such as the Euler-Maruyama (EM), are applied, numerical convergence is difficult to establish. For the proposed ESEC algorithm, its energy-preserving property enables us to overcome this obstacle. We rigorously prove that the ESEC algorithm is order 1/2 strongly convergent. This result is confirmed by detailed numerical studies. For the case of pitch-angle scattering in a magnetized plasma with a constant magnetic field, the numerical solution is benchmarked against the analytical solution, and excellent agreements are found.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Correlation of turbulent trailing vortex decay data

A correlation function, derived on the basis of self similar variable eddy viscosity decay, is introduced and utilized to correlate aircraft trailing vortex velocity data from ground and flight experiments. The correlation function collapses maximum tangential velocity data from scale model and flight tests to a single curve. The resulting curve clearly shows both the inviscid plateau and the downstream decay regions. A comparison between experimental data and numerical solution shows closer agreement with the variable eddy viscosity solution than the constant viscosity analytical solution.

Iversen, J. D.↗

Correlation of turbulent trailing vortex decay data

A correlation function, derived on the basis of self-similar variable eddy-viscosity decay, is introduced and utilized to correlate aircraft trailing vortex velocity data from ground and flight experiments. The correlation function collapses maximum tangential velocity data from scale-model and flight tests to a single curve. The resulting curve clearly shows both the inviscid plateau and the downstream decay regions. A comparison between experimental data and numerical solution shows closer agreement with the variable eddy viscosity solution than the constant viscosity analytical solution.

Iversen, J. D.↗

Opening of the magnetic field lines in a fast rotating magnetosphere, with an application to Jupiter

A simple model of a magnetosphere rotating around a rotating Jupiter-like object with a spin-aligned dipolar moment mu is considered. A low-energy plasma is released by inner sources located beyond the corotation radius and is diffused outward through closed lines. The lines form a closed thin equatorial disk, maintaining a quasi-static balance between the centrifugal force and the magnetic tension. Solutions are obtained for the analytical equations characterizing the plasma in the closed region; the structure of the magnetic field outside the disk; and the self-consistent value of the critical radius r sub zero. The analytical solutions are compared to the observed properties of the Jovian magnetosphere, and the results are discussed in detail.

Aly, J. J.↗