TPNA300 - Generating tube of heat with variable conductivity

Transcription

1 Titre : TPNA300 - Tube générateur de chaleur avec conducti[...] Date : 01/02/2011 Page : 1/12 TPNA300 - Generating tube of heat with variable conductivity Summary: This test is resulting from the validation independent of version 3 in nonlinear stationary thermics. It is about an axisymmetric problem 2D represented by four modelings, two axisymmetric, plane and the voluminal last. The features tested are the following ones: axisymmetric thermal element, thermal element plan, voluminal thermal element, variable properties, limiting conditions (source of heat, imposed temperature). The interest of the test lies in the taking into account of variable properties and the nonlinear behavior.

2 Titre : TPNA300 - Tube générateur de chaleur avec conducti[...] Date : 01/02/2011 Page : 2/12 1 Problem of reference 1.1 Geometry Y T e T i A r i B X (W/m/ C)... q r o (T) T( C) r i = m r e = m Properties of material = C 0 C 1 T W / m C Thermal conductivity with C 0 =21.461W / m C C 1 =0.234W /m C Boundary conditions and loadings interior surface: T i = C external surface: T e = C source of heat: Q= W /m3 1.4 Initial conditions Without object.

3 Titre : TPNA300 - Tube générateur de chaleur avec conducti[...] Date : 01/02/2011 Page : 3/12 2 Reference solution 2.1 Method of calculating used for the reference solution The original reference solution given in the book [bib1] is based on a graphic estimate. This reference is quoted in the handbook of checking of ANSYS [bib2]. 2.2 Results of reference Temperature along AB with r=2.167 mm 2.3 Uncertainty on the solution Unknown factor, it was not possible to get the original reference (delivers old, more published). 2.4 References bibliographical 1. Schneider, P.J., Conduction Heat Transfer, Addison-Wesley Publishing Co., Inc. Reading, Farmhouse., 2nd Printing, ANSYS, checking manual, 1st edition, June

4 Titre : TPNA300 - Tube générateur de chaleur avec conducti[...] Date : 01/02/2011 Page : 4/12 3 Modeling A 3.1 Characteristics of modeling AXIS (QUAD4, TRIA3) y(z) D C A E F G H I J K L B x(r) Conditions aux limites: cotés AB, CD: = 0 cotés AD, BC: T= C Noeud r z Points Noeud r z N E N N F N N G N N H N N I N N J N N K N N L N Characteristics of the grid Many nodes: 30 Many meshs and types: 27: (9 QUAD4, 18 TRIA3)

5 Titre : TPNA300 - Tube générateur de chaleur avec conducti[...] Date : 01/02/2011 Page : 5/12 4 Results of modeling A 4.1 Values tested Identification Reference Aster % difference tolerance Temperature ( C) N % N % N % N % N % N % N % N % N % N % N % N % N % N % N % N %

6 Titre : TPNA300 - Tube générateur de chaleur avec conducti[...] Date : 01/02/2011 Page : 6/12 5 Modeling B 5.1 Characteristics of modeling PLAN (QUAD8, TRIA6) Conditions aux limites: N294 C N285 cotés AB, CD: = 0 N268 cotés AD, BC: T= C N245 N214 y N184 N160 N211 N204 N134 N168 N181 N149 D N103 N117 N A N60 N46 N33 N21 N13 N7 N2 N5 B x 5.2 Characteristics of the grid Many nodes: 300 Many meshs and types: 95 (73 QUAD8, 22 TRIA6)

7 Titre : TPNA300 - Tube générateur de chaleur avec conducti[...] Date : 01/02/2011 Page : 7/12 6 Results of modeling B 6.1 Values tested Identification Reference Aster % difference tolerance Temperature ( C) N ,194 5% N ,491 5% N ,544 5% N ,082 5% N ,694 5% N ,665 5% N ,788 5% N ,089 5% N ,194 5% N ,491 5% N ,543 5% N ,082 5% N ,694 5% N ,665 5% N ,737 5% N ,089 5% N ,141 5% N ,365 5% N ,557 5% N ,078 5% N ,694 5% N ,650 5% N ,777 5% N ,075 5%

8 Titre : TPNA300 - Tube générateur de chaleur avec conducti[...] Date : 01/02/2011 Page : 8/12 7 Modeling C 7.1 Characteristics of modeling 3D (HEXA8, PENTA6) z y N7 N3 N11 Conditions aux limites: N14 N22 N19 N30 N43 N51 N67 N68 face interne et externe T= C autres = 0 N102 N90 N37 N61 N85 N114 N124 N150 N177 N208 N134 N220 N251 N151 N255 N291 N171 N266 N307 x 7.2 Characteristics of the grid Many nodes: 309 Many meshs and types: 190 (144 HEXA8, 46 PENTA6)

9 Titre : TPNA300 - Tube générateur de chaleur avec conducti[...] Date : 01/02/2011 Page : 9/12 8 Results of modeling C 8.1 Values tested Identification Reference Aster % difference tolerance Temperature ( C) N ,909 5% N ,933 5% N ,408 5% N ,561 5% N ,993 5% N ,217 5% N ,047 5% N ,960 5% N ,908 5% N ,933 5% N ,408 5% N ,561 5% N ,993 5% N ,217 5% N ,047 5% N ,960 5% N ,440 5% N ,596 5% N ,274 5% N ,260 5% N ,705 5% N ,536 5% N ,946 5% N ,474 2%

10 Titre : TPNA300 - Tube générateur de chaleur avec conducti[...] Date : 01/02/2011 Page : 10/12 9 Modeling D 9.1 Characteristics of modeling AXIS (QUAD9) y(z) D C A E F G H I J K L B x(r) Conditions aux limites: cotés AB, CD: = 0 cotés AD, BC: T= C Noeud r z Points Noeud r z N E N N F N N G N N H N N I N N J N N K N N L N Characteristics of the grid Many nodes: 95 Many meshs and types: 18 QUAD9

11 Titre : TPNA300 - Tube générateur de chaleur avec conducti[...] Date : 01/02/2011 Page : 11/12 10 Results of modeling D 10.1 Values tested Relative variation % Absolute deviation Identification Reference Aster difference tolerance difference tolerance Temperature ( C) N ,333 5% 0, N ,347 5% -0, N ,551 5% 0, N ,078 5% -0, N ,694 5% 0, N ,663 5% 0, N ,741 5% -0, N ,088 5% 0, N ,333 5% 0, N ,347 5% -0, N ,551 5% 0, N ,078 5% -0, N ,694 5% 0, N ,663 5% 0, N ,741 5% -0, N ,088 5% 0,

12 Titre : TPNA300 - Tube générateur de chaleur avec conducti[...] Date : 01/02/2011 Page : 12/12 11 Summary of the results Four modelings give results whose certain values exceed the tolerance fixed initially (5%): for modeling A (AXIS: QUAD4, TRIA3), the maximum change is of 15.3% and 4 values out of 16 exceed the tolerance, for modeling B (PLAN: QUAD8, TRIA6), the maximum change is of 13.8% and 3 values out of 24 exceed the tolerance, for modeling C (3D: HEXA8, PENTA6), the maximum change is of 15% and 5 values out of 24 exceed the tolerance, for modeling D (AXIS: QUAD9), the maximum change is of 13.7% and 4 values out of 16 exceed the tolerance. These goings beyond tolerance are observed for values close to 0. Calculations were carried out in C. The determination of the variation, by considering the temperatures in F (as in the reference solution), gives a maximum change very different from that obtained in C (3% instead of 15%). Moreover, it was not possible to get the original reference (delivers of Kreith), quoted in the handbook of checking of ANSYS. The method of acquisition the reference solution (graphic estimate) and its uncertainty are thus not known. The results are regarded as acceptable taking into account the points evoked above. This test made it possible to test the taking into account a variable thermal conductivity within several modelings. The principal orders tested are the following ones: DEFI_MATERIAU associated with the keyword THER_NL, allowing to define the characteristics of a material whose characteristics vary according to the temperature, THER_NON_LINE order allowing the resolution of a stationary thermal nonlinear problem or not.