A Simple Computer Program to Model Three-Dimensional Underground Heat Flow With Realistic Boundary Conditions

1983 ◽  
Vol 105 (1) ◽  
pp. 42-49 ◽  
Author(s):  
P. D. Metz
Keyword(s):  
Heat Flow ◽  
Boundary Conditions ◽  
Computer Program ◽  
Three Dimensional ◽  
Companion Paper ◽  
Coupled Systems ◽  
Moisture Movement ◽  
Solar Heat ◽  
Flow Equations ◽  
Flow Features

A FORTRAN computer program called GROCS (Ground Coupled Systems) has been developed to study three-dimensional underground heat flow. Features include the use of up to 30 finite elements or “blocks” of earth which interact via finite difference heat flow equations and a subprogram which sets realistic time and depth-dependent boundary conditions. No explicit consideration of moisture movement or freezing is given. GROCS has been used to model the thermal behavior of buried solar heat storage tanks (with and without insulation) and serpentine pipe fields for solar heat pump space conditioning systems. The program is available independently or in a form compatible with specially written TRNSYS component TYPE subroutines. This paper first describes the approach taken in the design of GROCS, the mathematics contained and the program architecture. Then, the operation of the stand-alone version is explained. Finally, the validity of GROCS is discussed. A companion paper serves as a user’s guide to the TRNSYS-compatible subroutine version.

Toward Defining Objective Criteria for Assessing the Adequacy of Assumed Axisymmetry and Steadiness of Flows in Rotating Cavities

2005 ◽  
Vol 128 (4) ◽  
pp. 708-716 ◽  
Author(s):  
G. D. Snowsill ◽  
C. Young
Keyword(s):  
Boundary Conditions ◽  
A Priori ◽  
Three Dimensional ◽  
Cyclic Symmetry ◽  
Acceptable Solution ◽  
Inappropriate Use ◽  
Flow Features ◽  
Computational Fluid Dynamics Cfd ◽  
Aero Engines ◽  
Multiple Reference

The need to make a priori decisions about the level of approximation that can be accepted—and subsequently justified—in flows of industrial complexity is a perennial problem for computational fluid dynamics (CFD) analysts. This problem is particularly acute in the simulation of rotating cavity flows, where the stiffness of the equation set results in protracted convergence times, making any simplification extremely attractive. For example, it is common practice, in applications where the geometry and boundary conditions are axisymmetric, to assume that the flow solution will also be axisymmetric. It is known, however, that inappropriate imposition of this assumption can lead to significant errors. Similarly, where the geometry or boundary conditions exhibit cyclic symmetry, it is quite common for analysts to constrain the solutions to satisfy this symmetry through boundary condition definition. Examples of inappropriate use of these approximating assumptions are frequently encountered in rotating machinery applications, such as the ventilation of rotating cavities within aero-engines. Objective criteria are required to provide guidance regarding the level of approximation that is appropriate in such applications. In the present work, a study has been carried out into: (i) The extent to which local three-dimensional features influence solutions in a generally two-dimensional (2D) problem. Criteria are proposed to aid in decisions about when a 2D axisymmetric model is likely to deliver an acceptable solution; (ii) the influence of flow features which may have a cyclic symmetry that differs from the bounding geometry or imposed boundary conditions (or indeed have no cyclic symmetry); and (iii) the influence of unsteady flow features and the extent to which their effects can be represented by mixing plane or multiple reference frame approximations.

scholarly journals Transonic Turbomachinery Calculations Using a Hybrid Structured-Unstructured Grid Method

1994 ◽  
Author(s):  
Scott M. Richardson
Keyword(s):  
Unstructured Grid ◽  
Unstructured Mesh ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Grid Method ◽  
Navier Stokes ◽  
Flow Equations ◽  
Transonic Compressor ◽  
Flow Features ◽  
Grid Points

A method is presented for solving the two-dimensional Navier-Stokes equations on a solution-adaptive grid of both structured and unstructured meshes. Flow near airfoil surfaces is modeled using an implicit finite difference algorithm on a structured O-type mesh. The flow equations in the blade passages are written in a cell-vertex finite volume formulation and are solved on an unstructured mesh using a Runge-Kutta explicit algorithm. Both the structured and unstructured grid also include solution dependent adaptation to allow resolution of flow features with a minimum of grid points. The structured mesh divides to locally add grid lines, while the unstructured mesh allows the addition or removal of individual cells. An overlapping interface region is used to conservatively communicate flow variable information between the two grids. The quasi-three-dimensional effects of streamtube contraction and radius change are included to allow calculation of modern turbomachine designs. A study is included to determine the effect on cacade parameters of inclusion of viscous terms in the solution of the flow equations in the unstructured domain. Quasi-three-dimensional computations of flow through a transonic compressor and turbine cascade are compared with experimental data.

Meeting the Thermal-Hydraulic Analysis Needs for Advanced Gas Reactor Systems

2008 ◽  
Author(s):  
Richard R. Schultz
Keyword(s):  
Boundary Conditions ◽  
Systems Analysis ◽  
System Analysis ◽  
Three Dimensional ◽  
Coupled Systems ◽  
Analysis Tool ◽  
System Behavior ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Accident Conditions

Simulation of some fluid phenomena associated with Generation IV reactors requires the capability of modeling mixing in two- or three-dimensional flow. At the same time, the flow condition of interest is often transient and depends upon boundary conditions dictated by the system behavior as a whole. Computational fluid dynamics (CFD) is an ideal tool for simulating mixing and three-dimensional flow in system components, whereas a system analysis tool is ideal for modeling the entire system. This paper presents the reasoning which has led to coupled CFD and systems analysis code software to analyze the behavior of advanced reactor fluid system behavior. In addition, the kinds of scenarios where this capability is important are identified. The important role of a coupled CFD/systems analysis code tool in the overall calculation scheme for a Very High Temperature Reactor is described. The manner in which coupled systems analysis and CFD codes will be used to evaluate the mixing behavior in a plenum for transient boundary conditions is described. The calculation methodology forms the basis for future coupled calculations that will examine the behavior of such systems at a spectrum of conditions, including transient accident conditions, that define the operational and accident envelope of the subject system. The methodology and analysis techniques demonstrated herein are a key technology that in part forms the backbone of the advanced techniques employed in the evaluation of advanced designs and their operational characteristics for the Generation IV advanced reactor systems.

Three-dimensional computer program on horse digestive track

2002 ◽  
Vol 22 (5) ◽  
pp. 202-202
Author(s):  
Nasser Alidadi ◽  
Mohammad R. Mokhber Dezfouli ◽  
Mohammad Gholi Nadalian ◽  
Ali Rezakhani ◽  
Iradj Nouroozian
Keyword(s):  
Computer Program ◽  
Three Dimensional

scholarly journals Charge algebra in Al(A)dSn spacetimes

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Adrien Fiorucci ◽  
Romain Ruzziconi
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Three Dimensional ◽  
Dirichlet Boundary Conditions ◽  
Boundary Structure ◽  
Asymptotic Symmetry ◽  
Renormalization Procedure ◽  
Field Dependent ◽  
Odd Dimensions

Abstract The gravitational charge algebra of generic asymptotically locally (A)dS spacetimes is derived in n dimensions. The analysis is performed in the Starobinsky/Fefferman-Graham gauge, without assuming any further boundary condition than the minimal falloffs for conformal compactification. In particular, the boundary structure is allowed to fluctuate and plays the role of source yielding some symplectic flux at the boundary. Using the holographic renormalization procedure, the divergences are removed from the symplectic structure, which leads to finite expressions. The charges associated with boundary diffeomorphisms are generically non-vanishing, non-integrable and not conserved, while those associated with boundary Weyl rescalings are non-vanishing only in odd dimensions due to the presence of Weyl anomalies in the dual theory. The charge algebra exhibits a field-dependent 2-cocycle in odd dimensions. When the general framework is restricted to three-dimensional asymptotically AdS spacetimes with Dirichlet boundary conditions, the 2-cocycle reduces to the Brown-Henneaux central extension. The analysis is also specified to leaky boundary conditions in asymptotically locally (A)dS spacetimes that lead to the Λ-BMS asymptotic symmetry group. In the flat limit, the latter contracts into the BMS group in n dimensions.

An isotropic elasto-damage-plastic micromechanical framework of innovative pothole patching materials featuring high-toughness, low-viscosity nanomolecular resin

2021 ◽  
pp. 105678952110286
Author(s):  
H Zhang ◽  
J Woody Ju ◽  
WL Zhu ◽  
KY Yuan
Keyword(s):  
Strain Energy ◽  
Three Dimensional ◽  
Elastic Strain Energy ◽  
Companion Paper ◽  
Computational Algorithms ◽  
Mechanical Behaviors ◽  
High Toughness ◽  
Low Viscosity ◽  
Innovative Materials ◽  
Continuum Thermodynamic

In a recent companion paper, a three-dimensional isotropic elastic micromechanical framework was developed to predict the mechanical behaviors of the innovative asphalt patching materials reinforced with a high-toughness, low-viscosity nanomolecular resin, dicyclopentadiene (DCPD), under the splitting tension test (ASTM D6931). By taking advantage of the previously proposed isotropic elastic-damage framework and considering the plastic behaviors of asphalt mastic, a class of elasto-damage-plastic model, based on a continuum thermodynamic framework, is proposed within an initial elastic strain energy-based formulation to predict the behaviors of the innovative materials more accurately. Specifically, the governing damage evolution is characterized through the effective stress concept in conjunction with the hypothesis of strain equivalence; the plastic flow is introduced by means of an additive split of the stress tensor. Corresponding computational algorithms are implemented into three-dimensional finite elements numerical simulations, and the outcomes are systemically compared with suitably designed experimental results.

scholarly journals Boundary conditions in topological AdS4/CFT3

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Pietro Benetti Genolini ◽  
Matan Grinberg ◽  
Paul Richmond
Keyword(s):  
Field Theory ◽  
Free Energy ◽  
Boundary Conditions ◽  
Smooth Solution ◽  
Three Dimensional ◽  
Field Theories ◽  
Legendre Transformation ◽  
Generating Functional ◽  
Holographic Duals

Abstract We revisit the construction in four-dimensional gauged Spin(4) supergravity of the holographic duals to topologically twisted three-dimensional $$ \mathcal{N} $$ N = 4 field theories. Our focus in this paper is to highlight some subtleties related to preserving supersymmetry in AdS/CFT, namely the inclusion of finite counterterms and the necessity of a Legendre transformation to find the dual to the field theory generating functional. Studying the geometry of these supergravity solutions, we conclude that the gravitational free energy is indeed independent from the metric of the boundary, and it vanishes for any smooth solution.

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