Internal Pressure Levels Research Articles

Determination of the safe level of internal pressure for glass piping

Determination of the safe level of internal pressure for glass piping

Elastic-Plastic Analyses of Surface Flaws in a Reactor Vessel

Elastic-plastic analyses have been performed for the ASME Maximum Postulated Flaw and for three other semielliptical surface flaws in the beltline region of a nuclear reactor pressure vessel, with internal radius to thickness ratio, R/t, equal to 10, using nonlinear 3-D finite element methods based upon the deformation theory of plasticity. Three of the flaws had a maximum depth, a, equal to t/4, with aspect ratios, 2c/a, equal to 6 (the ASME Maximum Postulated Flaw), 4 and 3, respectively, where 2c is the surface length of the flaw. These flaws were analyzed for internal pressure varying from one to three times the design pressure, which is well into the fully plastic regime for the uncracked vessel. The fourth flaw had an aspect ratio, 2c/a, equal to 6, and its maximum depth, a, was equal to 3t/4. This deep flaw was analyzed for internal pressure varying from 60 percent of design pressure to twice the design pressure. The crack driving force was calculated as the energy release rate, J, using the virtual crack extension method. The results illustrate that, at the design pressure, plasticity near the crack front is so limited for the three flaws with a/t = 1/4 that an elastic analysis is adequate. At higher pressures, however, the elastic analyses become increasingly nonconservative and would grossly underestimate the severity of the flaws. The variation of both J and crack opening displacement, COD, along the crack front were studied. Generally, the values at the maximum depth location, denoted J* and COD*, respectively, were the maximum values, with minimum values occurring at the free surface. A simple normalization scheme was found which collapsed the J* versus pressure results for the four semielliptical flaws into a single curve. A similar normalization also collapsed the COD* versus pressure results for the four flaws into a single curve. In addition, a unique linear relationship between J* and COD* was found to apply for the results from all four sets of analyses for internal pressure levels up to at least 2.5 times the design pressure. The analyses therefore demonstrate that J and COD are equivalent measures of the crack driving force, and further demonstrate that a realistic 3-D elastic-plastic analysis is needed to properly assess the severity of surface flaws.

Comment On "Vapor Flow Calculations in a Flat-Plate Heat Pipe"

V OOI JEN and Hoogendoorn formulated an analysis of vapor flow in a heat pipe and built a laboratory model using a porous flat plate with injection and suction zones to represent the evaporator and condenser, respectively. Their paper is interesting and informative because it attacks a difficult problem from two viewpoints. The heat-pipe flow problem has attracted investigators for many years, but theoretical solutions have met with varying degrees of success. Few have attempted, as the authors have, to perform experiments to confirm their own analyses. The authors are to be commended for their care and attention to detail. Their paper, however, exhibits deficiencies in both the theoretical and laboratory models. One of the authors' objectives was to explore pressure as an independent variable for steady incompressible, twodimensional heat-pipe flow. Their claim to be the first to treat pressure as an independent variable is unfounded. Galowin et al. analyzed the flow in a cylindrical porous tube which represented the condenser section of a heat pipe. The axial static pressure and the suction velocity were permitted to vary according to conservation principles. A second-order, o^rdinary, nonlinear differential equation was derived and integrated numerically to obtain flow property distributions. In both analyses, constant radial and normal static pressures in the condenser zone and Poiseuille flow at the condenser inlet were assumed. A fundamental assumption used by van Ooijen and Hoogendoorn is that the suction velocity through the porous wall is constant in the condenser zone, viz., v(x,Q)=v0. Decoupling of the suction velocity in the flow equations is characteristic of similarity solutions. The analysis of Galowin et al. has revealed that flow distributions predicted by the similarity approach are incorrect. A lengthy explanation of separation zones in the condenser section for Rer > 10 is given. It is not clear whether recirculation is developed because of the numerical procedure or the physics of the flow. Many apparently suitable boundary conditions can show flow separation at stagnation points in sink or suction flow; however, many of these cases are not physically realistic. To prove their hypothesis the authors state that a sharp increase in measured pressure at the condenser end wall reveals a strong recirculation (in agreement with their numerical results). Actually, they have demonstrated only that the axial pressure increases in the vicinity of the stagnation point, which is in agreement with the analysis of Galowin et al. and the results of Quaile and Levy. Van Ooijen and Hoogendoorn emphasize that at higher values of Rer (e.g., 50) the stream patterns in the evaporation and condensation zones become strongly coupled. The conclusion is that any calculation denying this coupling will lead to incorrect results. The fact is that the flow has been decoupled a priori by assuming that v0 is constant no matter what Rer is chosen. A constant v0 can cause the appearance of recirculation zones to satisfy continuity and can account for the deviations from Poiseuille velocity profiles at high Rer. Thus, there appears to be a contradiction in their conclusion. The next part of our discussion concerns the laboratory model. The suction velocity cannot be uniform in their experiment because of the sintered steel plate. Studies conducted with sintered porous walls for rocket and jet engine cooling have demonstrated that both lateral and normal velocity components occur at the wall. More importantly, in this experimental arrangement most of the flow entering the condenser section will exit near the downstream end, because the only mechanism for changing the momentum vector is the stagnation zone and not the sintered porous plate. Only a very carefully designed thin porous wall containing small circular holes, i.e., orifices which vary in diameter and are distributed appropriately over the axial length, will produce a uniform outflow. The nonuniformity of v0 is borne out by Fig. 14 of the authors' paper which shows that the varying internal pressure levels are lower toward the downstream end of the condenser. The interpretation is that the flow velocity through the wall is higher where the larger pressure differences occur across the wall and variable over the length, not constant as they assume. In conclusion, we would like to offer two suggestions to improve an already promising study put forth by van Ooijen and Hoogendoorn. The analysis should be recast to permit variation of the suction velocity in the condenser section. This can be done by relating pressure to velocity in the form of Darcy's law:

Calculation of Residual Stresses in Plastic Deformation Processes

Three problems, namely, autofrettage process, plastic upsetting of a solid cylinder, and plane-strain and axisymmetric extrusion, are treated for residual stress calculation. A thick-walled cylinder consisting of two loosely fitted concentric cylinders of different materials is subjected to various levels of internal pressure. The residual stresses were calculated with an emphasis on the case where the inner surface of the cylinder yields again upon removal of the internal pressure. Comparison between the calculations and the measurements is given. The residual stresses in plastic upsetting of a solid cylinder were calculated by the finite-element method. An attempt was also made to simulate the real situation in extrusion by the finite-element method. An estimation of the residual stress distribution is then discussed for axisymmetric extrusion problems.