THERMAL STRESSES IN GAS TURBINE EXHAUST DUCT EXPANSION JOINTS

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1 THE AMEFUCAN,SOCIETY.OP MECHANICAL' ENGINEERS ES7th St.,,New YorkelPi.T;i10017 The Society shall not be fesponsible for statements or opinions advanced In papers or discussion at meetings of the Society or of ii -Divislonier Sections, or printed In Its-publications. Discussion is printed only if the paper is published in an ASME Journal. Authorization to photocopy. material for internal or personal use under circumstance not falling within the fair use provisions of the Copyright Act is granted by ASME to ' 44' -libraries and other users registered with the Copyright Clearance Center (CCC) Transactional Reporting Service provided that the base fee of per page Is paid directly to the CCC, 27 Congress Street, Salem MA Requests for special permission or bulk reproduction should be addressed to the ASME Technical Publishing Department Copyright by ASME All Rights Reserved Printed in U.SA THERMAL STRESSES IN GAS TURBINE EXHAUST DUCT EXPANSION JOINTS Michel D. Ninacs Flexfab Niagara Inc. Montreal, Canada Rodney P. Bell Mu-Sigma Engineering Consultants Mississauga, Canada NOMENCLATURE Et3 / 12 (1 -n2 ) Elastic Modulus. Bending Moment Duct Radius Wall Thickness Temperature Difference Radial Expansion = RaDT Expansion Coefficient [3 ( 1 -n2 )/(R02 14 Poisson's Ratio Bending Stress Direct Stress Centre of gravity Suess intensity Allowable Stress Intensity (ASME Section VIII Div 2) Kt Elastic-Plastic correction factor (ASME Section VIII Div 2,App ) INTRODUCTION This paper discusses the methods used to derive an improved design for gas turbine exhaust duct expansion joints. Typically these joints are subjected to very rapid increase in internal exhaust gas temperatures that result in large temperature differentials within the joint structures. The thermal gradients can cause stress levels in excess of yield and when the turbine is used intermittently, such as pealcing power units would be, the net result is crack propagation and gas leakage. temperature. Hence the material is normally attached to the duct via a radial web about 5" to 6" (12 cm to 15 cm) deep. This web allows the temperature to reduce radially outwards so that the temperature at the material attachment point is about 400 to 500 F (220 to 280 C) below the gas temperature. A typical joint structure cross section. is shown in Figure 1. The main area of high stress is the up stream structure. Al this point the web of the fabric support flange restricts the radial growth of the duct The stresses in other half of the joint would be similar to the up stream section. This typical joint cross section would be used on both circular and rectangular ducts. The mechanism for the generation of high stresses is different for both duct shape. This will be explained first using simple models, before the design changes are discussed BASIC STRESS PROBLEM Circular Duct Joint The web of the fabric support frame acts as a restraint to the radial growth of the duct as it is subjected to the rapid rise in exhaust gas temperature. The simple model would be as shown A typical expansion joint uses a flexible material to in Figure 2. This model simulates the web disc give the joint flexibility. There is generally a restraining the cylindrical duct from radial temperature limit for the material that is expansion. The effect of the adjacent flange is considerably below the gas turbine exhaust Downloaded From: Presented at the International 10/27/2018 Terms Gas of Turbine Use: and Aeroengine Congress & Exhibition Birmingham, UK June 10-13, 1996

2 ignored in this model. The duct wall approaches the gas temperature within a minute or two of the turbine start up. The web takes considerably longer to heat up, and there is a time when the average temperature between the duct and the web is at a maximum. Using the data from Roark and Young (Table 30 Case 15), the bending stress in the duct adjacent to the web is given by:- 6M 12D 2 2 y t- t 2 1 Rectangular Duct Joint The same cross section used in a circular joint behaves differently when. used on a rectangular duct joint. The same radial temperature gradient is established, but now each side of the rectangular joint acts as a beam with a temperature gradient across it. Each side tries to bow inwards due to the thermal gradient This bowing movement is restricted by the restraint at each comer. If the corners fully restrain the sides from bending, the maximum bending stress would be:- Assuming that u = 0.3 and y the radial displacement is equal to RaAT, then the bending stress is simplified to:- crb = 1.815EaAT 2 Assuming that the average temperature difference between the web and the flange is about a half the temperature difference between ambient and the exhaust gas temperature, then the temperature gradient would be about 500 F ( 280 C). Using mild steel properties the resulting bending stress would be about +1-78,000 psi, (538 MPa) which is above the yield. This is a conservative and simple model of the real circular joint, but is illustrates the magnitude of the problem. AT Cb= ±-Ea 2 This stress is less than the same stress for a circular joint, but it only applies away from the corners. At the corners the stress level in the web increases direct (hoop) stress that is in the duct and outer flange cannot be transmitted around the corner, and this force is transferred to the web at that point. The bending moment that was carried by the whole cross section is now carried by the web only, and the duct and flange direct su css drop to a low value. The stress increase can therefor be approximated by the ratio of the effective moment of inertia of the full joint cross section to that of the web only. For a typical section, this ratio would be about 4.5, so now the stress at the corners would be:- a = 2.25EaAT 4 3 2

3 This stress is now larger than the simple model used for the circular joint. In fact a better representation of the rectangular joint would produce an even higher stress due to twisting of the corners caused by the non-symmetrical shape of the cross section. This is discussed later in the finite element modeling. DERIVATION OF IMPROVED DESIGN General It was realised that it would be necessary to investigate a number of design changes, so a mesh generator computer code was developed to generate suitable finite element models using a few basic shape definitions. The simplifying assumption was made that the insulation is ideal, and there is no heat loss though it. All heat flow is via exposed surfaces and through the metal:the potential errors involved with this assumption were Checked using an axisyrnmetric model of the joint that included insulation. Thermal analysis with actual and ideal insulation properties did not make significant changes to the thermal gradient between the duct and the outer flange. Ideal insulation resulted in a slightly higher gradient, and since it was conservative, this assumption was used for all models. Four basic model types could be generated using these mesh generator codes. They were:- Original design of an outside insulated end of a circular duct joint. Improved design of an outside insulated end of a circular duct joint. Original design of an outside insulated end of a rectangular duct joint. Improved design of an outside insulated end of a rectangular duct joint For each design, the duct dimensions, wall thickness, inside and outside film coefficients and emissivities, and general shape of the material support frame could be changed, and the code would then generate a suitable shell finite element model. The thermal gradients and resulting stresses were then computed using the H3DMAP code (Sauve, 1993). Although some of the designs indicated sn ns levels above yield, the assumption was made that the structure remained elastic. Fatigue estimates were then made based on the fatigue curves of Section VIII Division 2 of the ASME Pressure Vessel Code. To asses the improvements in the design, some basic parameters were held constant for all models. They are approximately what might be expected of a typical installation, but they do not correspond to any particular design now in the field. The parameters kept constant were as follows. Exhaust gas temperature transient. (A typical one with a temperature of 700 F reached in 10 seconds and I000 F in 2 minutes with a maximum gas temperature at a steady state of 1050 F was uced, as shown in Figure 3) Circular ducts had an inside diameter of 100" and rectangular ducts had walls 160" 3

4 by 120" The duct wall was made from mild steel plate 0.25" thick. A flange 2" deep was assumed to connect the joint to the remainder of the duct. The material support flange was 5" outside the duct outer wall. web, as would be expected from the simplified model above. If the web depth is increased from 5" to 6", the maximum stress level increases by about 10%. Increasing the fabric support flange from 2" to 3" increases the maximum stress by about 5%. Changing the material from mild steel to 304 stainless steel increases the maximum stress by 30% for the basic design. Modified Circular Duct Joint The inside film coefficient was 10 BTU/fI 2 hi F (56 W/m2K). The average emissivity between the duct wall and the gas was 0.6. The film coefficient on the outside flange supporting the fabric was 0.5 BTU/f'? hr F (2.3 W/m 2K), and the equivalent emissivity was 0.5 The fabric support flange was 2" wide and 0.25" thick. Original Design Circular Duct Joint Model The typical generic model for the circular duct is shown in Figure 4. The thermal gradients and resulting stresses were computed at various intervals after turbine start until a steady state was reached at about 80 minutes. The maximum stress intensity computed for this model was 61,948 psi (427 MPa) and it occurred 400 seconds after the turbine start. The maximum stress location was at the joint between the duct was and the support The cause of the high thermal stress that occurs with the original design is similar to that caused by a thin walled pipe attached to a vessel. When the fluid temperature in the pipe is significantly different from that in the vessel, high discontinuity stresses are generated. The normal engineering solution to this problem is to use a thermal sleeve, and this approach was used to improve the circular joint design, as indicated in Figure 5. In this case the aim is to have the main themial gradient in the axial direction along the outer sleeve, rather than in the radial direction in the web. The initial step is made small enough so that the radial restraint imposed by it is small enough to keep the sucss levels acceptably low. Heat can be transferred across the annular gap by radiation. Insulating the gap increases the stresses. The maximum stress using this modified design is now reduced to 36,500 psi (251 MPa), and it occurs in the outer sleeve where the metal temperature is lower. The length of the annular gap can be optimized to minimize the maximum stress for any particular set of boundary conditions 4

5 Original Design Rectangular Joint Model The finite element model of the rectangular joint is shown in Figure 6. A quarter model of the full joint is simulated. Symmetrical boundary conditions are assumed at the two center lines. Using the cross section as given in Figure I, the maximum stress intensity at the corner of the joint is 243,315 psi. (1,677MPa) This is a stress concentration effect due in part to the duct wall and the material support flange having greatly reduced direct stress at the corner. The restraining bending moment is taken by the web alone. A secondary effect causing additional bending stress in the web is the nonsymmetrical structure that causes the corner section to roll inwards. Away from the corner the stress in the support flange is about 60,000 psi (448 MPa). In practice this stress could obviously not exist; it would be relieved by buckling and plastic deformation. It is only that high because of the assumption of elastic analysis which is used to compare designs. Revised Rectangular Joint. A number of design modifications were attempted for the rectangular joint, including removing the sharp comer and replacing it with a section with a 6" radius, (which was not very effective). The most economical approach was to first of all remove the twisting moment by making the web attach to the material support flange in the center so that the structure resembled a symmetrical T rather than an inverted V. This reduced the maximum stress to 150,000 psi from about 200,000 psi. The next step was to increase the thickness of the duct and web cross section at the corners until the maximum stress appeared away from the comer. For the basic design chosen, this occurred when the corner thickness was increased from 0.25" to 0.75". The maximum stress then occurred in the material support flange and it had a value of about 65,000 psi. (448 MPa) The stress is higher than the simple model prediction of EctAT/2, because the section is not symmetrical parallel to the duct wall. The cg of the section is closer to the duct wall, and this increases the stress in the support flange. Increasing the thickness of the fabric support flange has the effect of increasing the thermally induced restraining moment at the corners and the stress level at this point is increased. To reduce the stresses further, the heat flow to the joint structure must be reduced by using a heat shield or insulation on the inside of the duct. Assuming that a suitable shield will reduce the equivalent film coefficient to 4 BTU/ft 2 hr 7 (23 W/m2K), (using for example 1" thick insulation on the inside) the maximum stress would be reduced to about 48,000 psi (331 MPa), and the time of occurrence would now be 2000 seconds after the gas turbine start, rather than 400 seconds for the other designs. This results in a relatively complex design, but it is the only method of reducing the thermal stresses to reasonable levels. FATIGUE EVALUATION The fatigue evaluation of the various designs uses the rules of Section VIII Division 2 for Fatigue Analysis. The nomenclature is that used in 5

6 Appendix 4 of that code. It is assumed in all cases that the cool down is slow, and the stresses generated on cool down can be ignored. Hence the maximum stress intensity found during heat up represents the maximum range of stress intensity seen by the structure. A summary of the significant results is given in the table below. ( See TABLE 1) Additional explanation of this table follows. Circular Joints From the analysis described above it was shown that the standard design for a circular joint had a maximum stress intensity of 80,379 psi (554 MPa) 400 seconds after start up. The temperature 400 seconds after start up at the point on the structure where the stress is a maximum is about 700 F (370 C), and S m for a typical mild steel at this temperature would be about 19,000 psi (130 MPa). This means that for the original design, the range of stress intensity just exceeded 3S m and K, =2.6. The adjusted alternating stress is about 104,000 psi (726 MPa) with an allowable number of cycles of 600. The improved design has a maximum range of stress intensity of 36,500 psi (252 MPa), K., =1 and an alternating stress of 18,750 psi (129 MPa). The number of design cycles now increases to about 100,000 cycles. Rectangular Joint In the original design, the maximum range of stress intensity of 243,315 psi (1677 MPa) is well in excess of 3Sa, and iç would be about 10 for mild steel. The equivalent alternating stress would the be about over 106 psi, which would mean a very limited fatigue life (less than 10 cycles). Because of the expected buckling, this estimate is very approximate. The revised design with thick corners and inside insulation under the web results in a peak stress intensity range of 46,000 psi (317 MPa). This is below 3S m so K, =1 and the estimated number of design cycles is 60,000. CONCLUSIONS The life expectancy of gas turbine expansion joint structures can be greatly improved from current industry practice if the design is such that the thermal stresses are reduced to acceptable levels. Different design solutions are required for the circular and rectangular expansion joints due to the different mechanisms involved in the generation of high stresses. Transfening high internal temperatures from the steel structural frames to the flexible composite elements can lower the thermal stresses generated but results in very limited life expectancy of the flexible composite element. It is now feasible to design gas turbine expansion joint structural support frames that generate significantly lower thermal stresses while maintaining a low temperature clamping surface for the flexible composite element. The result is reliability through greatly improved life expectancy and a predictable cyclic life sufficient to meet the needs of large high performance gas turbines of today and tomorrow.

7 REFERENCES Roark R.J. and Young W.C. Formulas for Stress and Strain. Fifth Edition McGraw-Hill 1975 Sauve R.G. H3DMAP A general Three Dimensional Finite Element Computer Code for Linear and Non- Linear Analysis of Structures. Ontario Hydro research Division Report # K Rev 2 Aug

8 DESIGN TYPE MAXIMUM RANGE OF STRESS Ke ALLOWABLE INTENSITY CYCLES Original Circular 80,379 psi 554 MPa Revised Circular 36,500 psi 129 MN ,000 Original Rect. 243,315 psi 1677 MPa 10. <10 Revised Rect. 46,000 psi 317 MPa ,000 TABLE 1 8