報告書番号

U93038

タイトル（和文）

３次元境界適合座標系を用いた非等温流体の高次精度数値解析手法の開発－逆Ｕ字型ダクト内の温度成層化現象への適用－

タイトル（英文）

PREDICTION OF THERMAL STRATIFICATION IN CURVED DUCT WITH 3D BODY-FITTED COORDINATES

概要 （図表や脚注は「報告書全文」に掲載しております）

３次元に任意形状に適用可能な境界適合座標系を用いた非等温流体の数値解析コードを開発した。この解析コードでは，物理空間と写像空間の座標成分の関係が３次スプライン関数により定められる。流体の基礎方程式は，ラグランジュ法に基づいて解析されるが，基礎方程式中の移流項は，局所的に分布する３次元場の物理量に対して３次スプライン内挿を行うことにより精度良く解析される。また，浮力項や拡散項は，時間的・空間的に２次の精度を有するように離散化されている。境界条件に関しては，本研究では非直交曲線座標系を用いているが，ノイマン型の境界条件にも対応できるものとした。数値解析コードを逆Ｕ字型ダクト内の温度成層化現象に適用した結果，温度分布等が実験結果と良く一致しており，その有効性が検証された。

概要 （英文）

A NUMERICAL SIMULATION METHOD BASED ON THREE-DIMENSIONAL BODY-FITTED COORDINATES HAS BEEN DEVELOPED TO PREDICT BUOYANCY-INFLUENCED FLOWS SURROUNDED BY ARBITRARILY-SHAPED BOUNDARIES. THE CURVILINEAR COORDINATE SYSTEM IS GENERATED WITH THE AID OF GCSI,IN WHICH ALL VARIABLES IN THE COMPUTATIONAL DOMAIN ARE REFERENCED TO DERIVE CUBIC SPLINE FUNCTIONS,AND THE METRIC COEFFICIENTS ARE EVALUATED WITH LESS TRUNCATION ERRORS COMPARED TO THOSE RAISED BY THE USUAL METHODS. THE NUMERICAL ANALYSES OF THE TRANSFORMED GOVERNING EQUATIONS ARE BASED ON A LAGRANGIAN METHOD. THE CONVECTION TERMS ARE SOLVED WITH LCSI,WHICH ENABLES US TO OBTAIN MORE ACCURATE RESULTS THAN THIRD-ORDER POLYNOMIAL INTERPOLATION,AND THIRD-ORDER UPWIND DIFFERENCE IN A REASONABLE COMPUTATIONAL TIME. THE BUOYANCY AND DIFFUSION TERMS ARE DISCRETIZED IN THE LAGRANGIAN SCHEMES TO GIVE SECOND-ORDER ACCURACY WITH RESPECT TO TIME AND SPACE. IN ADDITION,THE FIRST AND SECOND DERIVATIVES INCLUDED IN THESE TERMS ARE OBTAINED BY USING GCSI RATHER THAN THE CENTRAL-DIFFERENCE METHOD. WITH REGARD TO THE BOUNDARY CONDITIONS,THE NEUMANN CONDITIONS,WHICH HAVE BEEN DIFFICULT FOR NON-ORTHOGONAL CURVILINEAR COORDINATES TO DEAL WITH,CAN BE IMPLEMENTED WITH SECOND-ORDER ACCURACY IN THE PRESENT NUMERICAL METHOD. THE DEVELOPED PREDICTION METHOD WAS APPLIED TO A STEADY ISOTHERMAL FLOW IN A PIPE WITH A 90-DEGREE BEND,AND A THERMALLY-STRATIFIED FLOW IN A CURVED DUCT. IN THE PREDICTED RESULTS OF PIPE FLOW, THE DEVELOPMENT OF THE SECONDARY FLOW PATTERN AS WELL AS THE AXIAL VELOCITY DISTRIBUTION ARE REASONABLY-WELL SIMULATED. IN ADDITION,REGARDING THE STRATIFIED FLOW IN A CURVED DUCT,SOME EXPERIMENTALLY-OBSERVED FEATURES,SUCH AS THE DECLINED SHAPED OF THE THERMAL INTERFACE,THE PROGRESS OF THERMAL STRATIFICATION AND VERTICAL TEMPERATURE DISTRIBUTIONS IN THE HORIZONTAL PART OF THE DUCT,ARE SATISFACTORILY PREDICTED.

報告者

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