Lambrescu, I.

Popa, A.

Pupazescu, A.

Electronic Sumy State University Institutional Repository

Some aspects regarding the stress distribution in the vessel element – asymmetric conic reduction Part I – Building the modelIonuţ Lambrescu, Alexandru Pupăzescu, Alexandru Popa Petroleum Gas University from Ploieşti, RomaniaIntroductionIn the technological installations in petroleum and petrochemical industry one currently uses heat exchangers with vapors space (Kettle type re-boiler), either as  re-boilers of a fractioning column [1], or as  steams generators [2]. Figure 1Such a heat exchanger (see figure 1), catalogued AKT in the standard TEMA [3] comprises – for assuring the vapor space – a conical asymmetric reduction.In current design, because an analytical method of calculus does not exist, for determining the thickness of the reduction wall (see figure 2.a), one uses the formulas for the symmetric conical reductions, whose dimensions are correlated with the relation (see figure 2.b):R=d/2; R=D-d/2.Because up to now, for the exact calculus of the tensions in an asymmetric conical reduction, one does not dispose of an analytical method, this paper will have as the main aim determining the tensions in this type of structures, using the Finite Element Method (FEM). In the first part, one presents the building of the geometric model, while in the second part, the analysis itself is performed. For determining the tensions through the FEM, it is necessary to use a dedicated software, such as ANSYS, COSMOSM, or NASTRAN. All these packages have preprocessing modules (including geometric modeling), that allow the building of the structure and establishing the material characteristics. The preprocessing module of ANSYS for example, although well developed (it includes boolean operations that ease the modeling process), for the particular type of structure we speak about in this paper, especially taking into account the future mesh generation, do not provide good and easy to use tools for building the geometry of the asymmetric conical reduction. Figure 2We are thinking especially to the two round radiuses r1 and r2 respectively that are not constant over the circumference. Solving this problem in ANSYS proves to be quite a difficult task. The problem gets even more complicated if we consider the fact that a range of asymmetric conical reductions have to be analyzed. This situation imposed a multidisciplinary approach, involving Microsoft Excel and Solid Edge V14.Geometrical modeling of a asymmetric conical reduction like structureFigure 3 presents the conical asymmetric reduction zone of a heat exchanger (one in a dimensional series that will be presented further on in the paper). Only the median surface has been presented. The geometric modeling of such a structure does not raise in itself special problems. These problems will appear only later, in the area where the conical and cylindrical surfaces are filleted with the radiuses r1 and r2, during the mesh generation process. The conical reduction generation can be approached in two ways. The first, let us call it “classic’, starts from two cylinders united through the conical asymmetric zone. In the Solid Edge environment (that was used for the geometric modeling) the conical zone can be obtained like a lofted protrusion characteristic. In the last phase of the process, the two filleting are done (for the junctions cylinder-cone and cone-cylinder). We will though obtain, besides the three surfaces – two cylindrical and one conical – another two surfaces – the filleting surfaces. Figure 3In figure 4, the filleting surfaces are drawn in gray color. It is easy to imagine what kind of problems this topology will generate during the meshing process: distorted, skewed elements with angles approaching 0 where the filleting surfaces get thinner and thinner. It is obvious that triangular shell like elements will be used. Figure 4In order to avoid this type of problem (that could compromise the accuracy of the results in the zone where skewed elements have been generated) one proposes the second approach for the geometric modeling of the asymmetric conical reduction. One will use also the Solid Edge environment, but this time one will chose using the Blue Surf primitives. In figure 5, it is presented the same conical asymmetric reduction, obtained through the use of Blue Surf primitives.  Figure 5For the generation of an asymmetric conical reduction one will start from two categories of 2D primitives: profile curves (circles 1 and 2 in figure 5), respectively path curves (traces 3 and 4 in the same figure 5). Such an approach will produce an object that comprises a single surface, so all the subsequent problems that would have appeared during the meshing process are avoided. Geometric modeling of a family of asymmetric conical reduction like structures.Parametric approachFor solving geometric modeling problems for a large number of asymmetric conical reductions like structures one proposes a parametric approach that will integrate facilities of the Solid Edge environment, but also of a spreadsheet package, like Excel. In figure 6, one tries to illustrate this type of approach: one starts from a table in an Excel sheet, table that contains all the dimensional elements necessary to construct the 4 2D primitives that appeared in figure 5; the next step consist in establishing links between the model dimensions and cells in the Excel sheet. Figure 6In order to better emphasize the parametric character of the approach, the 4 2D profiles (curves) – already presented in figure 5 – were created. They have been dimensioned as can be seen in figures 8, 9 and 10. The comparison of the dimensions with table in figure 7 is very useful in understanding the way the process works.Figure 7In figure 10 are presented the geometric constraints imposed to the profile number 3 (as is appeared in figure 5). One speaks of tangency constraints that assure the smoothness of the path number 3 – the tangency constraints are symbolized by the small circles in the joining points between profiles. Figure 8Figure 9Figure 10As can be seen in figure 7, the dimensions values are connected with the cells of an Excel sheet. In this sheet, one macro has been created that brings in the positions that appear in the last column in the table in figure 7, the dimensions that correspond to a specific conical reduction. Though, for all of the reductions described by the table, through a simple click, a reduction is generated in Solid Edge. In figure 11 it is presented the Excel file structure – on row 4 appear the dimensions linked with the Solid Edge model. The table itself lays on rows 7-14. For the modification of the dimensions (drawing another reduction), the row with the dimensions in the table is selected, the macro is run – it replaces the row number 4 with the one selected in the table. At the first opening of the Solid Edge file, the conical desired conical reduction is obtained.  Figure 11Starting from the 4 profiles (see figure 5), one will generate a Blue Surf primitive. This object will describe the whole reduction, so the problems that would have appeared during the meshing phase are completely avoided.  ConclusionsThe proposed working methodology has the following advantages:-	The possibility to produce in a short time a whole family of conical reductions, starting from an Excel file, respectively a Solid Edge file; -	The associative and parametric character of Solid Edge will allow quick adjustments of the model;-	The created model can be exported in a FEM package, such as ANSYS, DESIGNSTAR; The export can be done directly (Designstar) or through the parasolid or IGES formats.-	The use of the Draft module of Solid Edge allows obtaining quickly of the 2D drafts of the model.  References 1.	Suciu, G., C., - Ingineria prelucrării hidrocarburilor, vol. 2, Ed. Tehnică, Bucureşti, 1985; 2.	Suciu, G., C., -  Ingineria prelucrării hidrocarburilor, vol. 4, Ed. Tehnică, Bucureşti, 1993.Надійшла до редакції 2 березня 2004р.38	«Вісник СумДУ», №13(72), 200443«Вісник СумДУ», №13(72), 2004

Some aspects regarding the stress distribution in the vessel element – asymmetric conic reduction. Part I – building the model

SocioEconomic Challenges Journal (Sumy State University)

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Some aspects regarding the stress distribution in the vessel element – asymmetric conic reduction. Part I – building the model

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