Numerical Stability Analysis of a Natural Circulation Steam Generator with a Non-uniform Heating Profile over the tube length HEIMO WALTER Institute for Thermodynamics and Energy Conversion Vienna University of Technology Getreidemarkt 9, A-1060 Vienna AUSTRIA Abstract: In this article the results of a numerical stability analysis of a static instability, namely reverse flow, will be presented. The investigation was done for a natural circulation two-pass boiler at different operation pressures (80 bar to 12 bars) and three different heating profiles over the tube length. The total heat load to the evaporator tubes was varied between 8 MW and 0.8 MW. The results of the investigation have shown that a critical heat absorption ratio between a stable upward flow direction and a possible downward flow direction of the working medium in the lower heated riser system exists. A further result of the analysis was that a higher heat flow to the upper end of the lower heated riser system increases the stability of the circulation system. Key-Words: Natural circulation, Reverse flow, Numerical stability analysis, Steam generator, Two-pass boiler 1 Introduction Natural circulation systems have a wide range of applications such as e. g. power cycles or industrial heating processes. The natural circulation steam generator belongs to the water tube boilers. The cooling of the evaporator tubes is done without a circulation pump (see Fig. 1). The density of the water-steam mixture in the heated riser tubes is lower than that of the water in the less or unheated downcomer tubes, which results in a lifting force in the riser system and in a circulation of the working medium. The two-phase flow will be separated in the drum by e. g. gravity or cyclones. Natural circulation steam generators have many advantages compared to forced- and once-through circulation boilers. One of the main advantages is the lower power for the feed water pump and the simple design which results in an unproblematic operation. The circulation of the fluid in the evaporator tubes is controlled by the heat input. The steam quality of the water-steam mixture in the evaporator tubes of natural circulation steam generators is in the normal operation case not higher than approximately 30 %. Therefore film boiling respectively critical heat flux can only occur under unfavorable conditions. The limitation of the drum pressure at approximately 180 bars and the low rate of pressure (temperature) change of the heavy-walled components, which are implemented in the saturation region of the boiler, at load change is a disadvantage of the natural circulation steam generator. Figure 1 shows the sketch of the analysed natural circulation two-pass boiler. The boiler consist of a drum, unheated downcomer tubes, headers, the lower heated evaporator tubes of the convective (second) pass, and the higher heated tubes of the combustion chamber wall. The unheated downcomer tubes are connected with the tubes of the convection pass as well as with the tubes of the combustion chamber wall. For such a system e. g. Linzer [1] and Walter [2] have shown in their investigations that the static instability, namely flow reversal, can occur in the lower heated tubes. Burner Sidewall header Furnace Sidewall header Drum Distributor Header Downcomer Convection pass Fig. 1: Sketch of a natural circulation two-pass boiler Linzer and Walter [1] made their investigations under steady state and transient conditions at a constant operation pressure of 80 bars and a uniform heating profile over the tube length of all heated tubes. The study has shown that for every system pressure, heat load and boiler configuration a special critical heat absorption
ratio V crit exists. This critical heat absorption ratio must be determined for every configuration of such a boiler. The critical heat absorption ratio depends also on the thermo-hydraulic behavior of the circulation system. They analysed also the influence of disturbances in the heating profile at the startup period when the boiler operates close to the critical heat absorption ratio. The dynamic simulations of the boiler have shown that such a circulation system when, operated to close to the critical heat absorption ratio, can shift from stable to unstable conditions during startup or load changes. Different methods to determine the mass flow distribution in a heated natural circulation tube network were presented by Walter and Linzer in [2]. They identified reverse flow using a graphical and numerical analysis (steady state and dynamical). The investigations in [2] are also done with a uniform heating profile over the tube length of all heated tubes. In this paper the static instability, namely the reverse flow, will be analysed. The investigations have been done at different operation pressures (full and part load of the boiler), different boiler designs and with three different heating profiles for the tubes of the convective pass. The aim of the analysis was to study the influence of the heating profile and the operating pressure on the stability of the boiler. 2 Description of the analysed boiler 20 m 15 m Feed water Steam to superheater P D Drum Riser relief tube Intermediate header the furnace and the lower heated riser system 1 represents the tubes of the wall in the second pass. The large diameter downcomer is unheated. In the present study three different boiler designs are analysed: The tubes of both riser systems are connected with the drum (design case 1 or base design). No intermediate headers and riser relief tubes (broken lines in Fig. 1) are implemented in this case. The unheated part of both riser systems is replaced by an intermediate header and two riser relief tubes per riser system (design case 2). The unheated part of both riser systems is replaced by an intermediate header and two riser relief tubes for the lower heated system and four riser relief tubes for the higher heated riser system (design case 3). 2.1 Boundary and initial conditions The following initial conditions are used for the dynamic simulations: the steam generators are filled with water near boiling condition the pressure distribution of the fluid is due to gravity and the velocity of the working fluid in the tube network of the evaporator is zero and the fluid temperature in the evaporator of the boiler is equivalent to the boiling temperature at drum pressure. The drum pressure of the steam generator is constant during the whole simulation. The heat fluxes to the two riser systems of the two-pass boiler are boundary conditions for the simulation. The water level was controlled at the drum centerline. The system pressure will be varied in steps between 80 bars and 12 bars (80 bar, 65 bar, 50 bar, 40 bar, 30 bar 20 bar and 12 bar). 6000.0 ṁ 0 ṁ 1 ṁ 2 0 m Downcomer Riser system 1 Lower header q. 1 Riser system 2 q. 2 Fig. 2: Model of the two-pass boiler Figure 2 shows the simplified model of the investigated two-pass natural circulation steam generator presented in Fig. 1. The higher heated riser system 2 corresponds to H eating [kw ] 4000.0 2000.0 Riser system 2 Riser system 1 0.0 0.0 200.0 400.0 600.0 800.0 Time [s] Fig. 3: Heating ramp for the riser systems The heating ramp for the simulated hot startup was selected according to [3] and is shown in Fig. 3. It can be seen that during the first period of the simulation the heat flow increases up to 30 % of the full load. Between
30 and 150 s after the ignition of the burner the load is constant. During the time period between 150 s and 400 s the ramp-like heat input reaches the full load. The total time for the simulation was 10000 seconds. The total heat absorption (i. e. the heat absorption for both riser systems) will be varied in steps between 8 MW and 0.8 MW (8 MW, 6.4 MW, 4.8 MW, 3.2 MW, 1.6 MW and 0.8 MW). The value of 8 MW was chosen as an upper extreme. For industrial furnaces with oil firing the corresponding heat absorption can be assumed between 5 MW - 6 MW. The value of 0.8 MW can represent the condition for low load operation or special equipment in process engineering (e. g. refuse incineration plant). 1.5 q 0.5 q q q q used and for the convective term the UPWIND scheme was selected. The collectors and distributors respectively are assumed to be points. The steam, which enters the header, is evenly distributed to the outlet tubes. A detailed description of the computer code is given in [7]. 4 Results and discussion The following agreement for the sign of the mass flow is used in all figures: A positive sign in the riser tubes describes a flow direction from the lower header to the drum. A positive sign in the downcomer tubes indicates a flow direction from the drum to the lower header. 4.1 Results for the base design Figure 5 shows the mass flow in the tubes of the boiler for a heat absorption ratio of V = 20 (full line) and V = 20.5 (broken line). The simulations are done with a uniform heating profile for both riser systems (see Fig. 4a). 0.5 q 1.5 q a) b) c) Fig. 4: Heating profile for the lower heated riser system Figure 4 shows the different analysed heating profiles along the evaporator tubes of the lower heated riser system 1. The heating profile for the higher heated riser system 2 was for all simulations identical with the profile a) shown in Fig. 4. A non-uniform heating profile along the evaporator tubes can be the result of the different primary heat transfer mechanisms in the two passes of the boiler or can be caused by e. g. a different heat transfer coefficient along the second flue gas pass, a wall which is partially covered by insulation or fouling of the heating surface. During one simulation the drum pressure, the heat absorption ratio V = 2 1 between the two riser systems and the heating profile was constant. First results of this investigation are presented in [4]. 3 Mathematical model The one-dimensional mathematical model for the flow in the tubes, which was used for all calculations, includes a homogeneous equilibrium model for the two phase flow and applies a correction factor for the two phase pressure loss according to Friedel [5]. The discretization of the partial differential equations for the conservation laws was done with the aid of the finite-volume-method. The pressure-velocity coupling and overall solution procedure are based on the SIMPLER algorithm [6]. To prevent checkerboard pressure fields a staggered grid is Fig. 5: Mass flow for the boiler with the base geometry and uniform heating profile In the following the curves for V = 20 will be described. It can be seen that in the first period of the hot startup the mass flow in the lower heated riser system starts in the downward direction while the fluid in the higher heated riser system 2 is directed upward. With the beginning of the steam production in the lower heated riser system 1 the mass flow starts to decrease. During the time period between approximately 640 s and 680 s the steam production in the lower heated riser system 1 is high enough to slow down the reverse mass flow and change the flow direction of the working medium rapidly from downward to upward. This flow direction exists also at full load. The situation for the circulation mass flow after a moderate change of the heat absorption ratio from V = 20 to V = 20.5 is different. The mass flow in the tubes of the boiler at V = 20.5 starts similar to that shown for a heat absorption ratio of V = 20. The mass flow of the working fluid in riser system 1 starts in the downward direction too. With the beginning of the steam production in the lower heated system 1, the mass flow starts to slow
down. But, compared to the case with V = 20 the heat flux to riser system 1 is not high enough to change the flow direction. Therefore the flow direction remains different in both riser systems at full load. The heat absorption ratio of 20 represents the critical value V crit between a stable upward flow in both riser systems and a possible operation condition with reverse flow in the lower heated riser system 1. Figure 6 shows the chronological evolution of the total pressure difference between the drum and the lower header Δp DH and the pressure difference due to height Δp H (static head) for both riser systems. pressure and low heated load region the critical heat absorption ratio is smaller than 5 even at 80 bars. Fig. 7: Critical heat absorption ratio for the uniform heating profile Fig. 6: Pressure difference for the boiler with the base geometry and uniform heating profile At first the results for the heat absorption ratio of V = 20 (full line) will be described: During the first phase of the hot startup, the total pressure difference between the drum and the lower header Δp DH is smaller than the static head Δp H of the lower heated riser system and therefore the mass flow in riser system 1 is directed downward. With the beginning of the steam production in the lower heated riser system 1 the static head decreases. During the time difference of approximately 640 s and 680 s the increasing steam production reduces the static head and the curve for Δp H crosses the graph of the Δp DH. In this period the mass flow in the lower heated system changes the flow direction from downward to upward. The pressure difference due to height Δp H in case of a heat absorption ratio of V = 20.5 is always higher than Δp DH (see Fig. 6). Therefore the mass flow is always directed downward in the lower heated riser system 1 also at full load. The critical heat absorption ratio for the base design of the boiler at different operation pressure and heat loads is shown in Fig. 7. The calculations are done for the uniform heating profile. For a better readability of the figure lines with a constant V crit (broken lines) are included. A heat absorption ratio of V crit 5 is assumed to be a design criterion for the two-pass boiler for stable operation at all heat loads. It can be seen, that in the low As described above, the heat flow to the evaporator tubes can be shifted. Figure 8 shows the critical heat absorption ratios V crit for the heating profile b) of Fig. 4. It can be seen, that a higher heat load at the upper tube end results in an increase of V crit at all heat loads and operation pressures. The region with V crit < 5 is moved in direction of lower heat load and lower operation pressure. The boiler is stable in a greater operation range than in the case of a uniform heating profile. Fig. 8: Critical heat absorption ratio for the heating profile b) An opposite behavior can be seen at the results presented in Fig. 9. In this case the heating profile was identical to the profile shown in Fig. 4 c). A higher heat absorption at the lower tube end (entrance of the working fluid into the tube from the lower header in case of upward flow direction) results in a decreasing of the stability of the boiler. A detailed description for this reason is given in [4].
Fig. 9: Critical heat absorption ratio for the heating profile c) of the thermo-hydraulic behavior by increasing the pressure loss in the riser system results in higher values for V crit at all operation pressures and heat loads. Compared with the results shown in Fig. 7 the region with V crit < 5 is moved towards lower heat loads and operation pressure. The same behavior can be seen in Fig. 11 by changing the heating profile from the uniform heat flow to a higher heat flow in the upper region of the tube (heating profile b). In this case the values for the critical heat absorption ratios are increased up to values higher than 40 at high heat load and operation pressure. The boundary for a stable operation at all heat loads is also moved in direction of lower operation pressure and heat loads. The results for the base design of the two-pass boiler have shown that the region with V crit < 5 is also given at high pressures and low heat loads. Therefore a redesigning of the boiler is necessary. One of the most successful methods to get a higher stability is to modify the thermo-hydraulic behavior of the circulation system. This can be done by reducing the pressure loss in the downcomer or increasing the pressure loss in the riser systems [4], [8]. 4.2 Results for the design cases 2 and 3 In this section only the results for the heating profile a) and b) will be presented. Because, the simulations done with the heating profile c) have shown that the critical heat absorption ratio is always lower than V crit calculated with the uniform heating profile a). Fig. 11: Critical heat absorption ratio for the design case 2 and a heating profile b) The results for the test case 3 - the unheated part of both riser systems is replaced by an intermediate header and two riser relief tubes for the lower heated and four riser relief tubes for the higher heated riser system is shown in Fig. 12 and 13. Fig. 10: Critical heat absorption ratio for the design case 2 and uniform heating profile Figure 10 shows the 3-dimensional surface of the critical heat absorption ratios for the second test case the unheated part of both riser systems is replaced by an intermediate header and two riser relief tubes per riser system and a uniform heating profile. The modification Fig. 12: Critical heat absorption ratio for the design case 3 and a uniform heating profile
It can be seen in Fig. 12 that the stability of the boiler is improved in comparison to the same case of the base design. But the increase of V crit is smaller than in test case 2. This is a consequence of the reduced pressure loss at the higher heated riser system compared to test case 2. Because the number of riser relief tubes at the higher heated riser system has changed from two to four in test case 3. Fig. 14 shows the velocity for the base design (test case 1) and a uniform heating profile corresponding to the critical heat absorption ratio presented in Fig. 7. A broken line with a constant velocity of w = 12 m/s is included in the figure. It can be seen that only in the region for higher heat loads and lower operation pressure the velocity is higher than 12 m/s. Fig. 15: Velocity in the riser relief tube of the higher heated riser system 2 for the design case 2 and a uniform heating profile Fig. 13: Critical heat absorption ratio for the design case 3 and a heating profile b) The boiler design case 2 shows from the viewpoint of the boiler stability the best results at all analysed cases. But besides the circulation ratio the fluid velocity is also of important interest for the boiler design. Because, in a certain temperature (pressure) range high velocity can be the reason for erosion-corrosion [9], [10]. Therefore the velocity of the water/steam mixture should be approximately 12 m/s and the velocity in the downcomer 4m/s [8]. In the following chapter the velocity in the tubes of the higher heated riser system should be presented. 4.3 Velocity of the working fluid in the tubes of the higher heated riser system Fig. 14: Velocity in the higher heated riser system 2 for the base design and a uniform heating profile Figure 15 clearly demonstrates that the fluid velocity is too high in the high heat load region even at 80 bars. Therefore test case 2 is not suitable for the design of the two-pass boiler under the analysed conditions. Fig. 16: Velocity in the riser relief tube of the higher heated riser system 2 for the design case 3 and a uniform heating profile Figure 16 shows the simulation results for the velocities of test case 3. A comparison of the data with the results for the base design has shown that only a minor difference in the fluid velocities is given. The velocities for the heating profile b) and c) will be not presented. Because, the results for these two heating profiles show the same tendency. Differences between the results for the uniform heating profile and the other two cases are negligible. That applies also for the position of the curve with a constant velocity of w = 12 m/s.
5 Conclusion In this article the results of a numerical stability analysis, namely reverse flow, for a two-pass boiler under hot startup conditions were presented. The investigation was done for three different boiler configurations, an operation range between 80 bars and 12 bars, a total heat load to both riser systems between 8 MW and 0.8 MW and three different heating profiles over the tube length. It could be shown that a critical heat absorption ratio V crit exists, which must be determined for every steam generator configuration and heat load. A higher stability of the boiler can be achieved by changing the thermo-hydraulic behavior of the boiler. This was done by increasing the pressure loss in the riser systems. In this case the boiler design case 2 shows the best results for all analysed heating profiles (from the viewpoint of the boiler stability). The method to improve the boiler stability by increasing the pressure loss in the riser systems is restricted by the fluid velocity in the riser tubes. Therefore the boiler design with the intermediate header and the two riser relief tubes for the lower heated system and the four riser relief tubes for the higher heated riser system 2 is the preferable case taking into account the velocity. The investigation has also shown that a higher heat flux at the upper end of the lower heated tubes (the end where the fluid leaves the tube in case of upward flow direction) improves the stability whereas a higher heat flux at the lower end of the lower heated tube system decreases the boiler stability. 6 Nomenclature m& 0 m& 1 m& 2 Δp DH Δp H 1 2 Mass flow in the downcomer [kg/s] Mass flow in riser system 1 [kg/s] Mass flow in riser system 2 [kg/s] Total pressure difference between the drum and the lower header [bar] Pressure difference of the static head [bar] Heat flow [kw] Heat flow to riser system 1 [kw] Heat flow to riser system 2 [kw] V Heat absorption ratio [-] V crit Critical heat absorption ratio [-] References: [1] Linzer, W. and Walter, H., Flow reversal in natural circulation systems, Applied Thermal Engineering, Vol.23, No.18, 2003, pp. 2363-2372. [2] Walter, H. and Linzer, W., Stability Analysis of Natural Circulation Systems, Proceedings of the 2006 WSEAS/IASME International Conference on Heat and Mass Transfer, Miami, Florida, USA, January 18-20, 2006, pp. 62-68. [3] Linzer, W., Das Ausströmen von Siedewasser und Sattdampf aus Behältern, Brennstoff-Wärme-Kraft, Vol.22, No.10, 1970, pp. 470-476. [4] Walter, H. and Linzer, W., Investigation of the Stability of a Natural Circulation Two-Pass Boiler, Heat and Mass Transfer, Vol.42, No.6, 2006, pp. 562-568. [5] Friedl, L., Improved Friction Pressure Drop Correlation for Horizontal and Vertical Two-Phase Pipe Flow. European Two-Phase Group Meeting, Ispra, Italy, 5. 8. June 1979, Paper E 2, pp. 1-25. [6] Patankar, S. V., 1980, Numerical Heat Transfer and Fluid Flow, Series in Computational Methods in Mechanics and Thermal Sciences, Hemisphere Publ. Corp., Washington, New York, London. [7] Walter, H., Modeling and Numerical Simulation of Natural Circulation Steam Generators, progressreport VDI, Series 6, No.457, VDI-Verlag, Düsseldorf, 2001. [8] Walter, H. and Linzer, W., The influence of the operating pressure on the stability of natural circulation systems, Applied Thermal Engineering, Vol.26, No.8/9, 2006, pp. 892-897. [9] Loos C. and Heitz E., The mechanism of the erosion corrosion in fast fluid flows. Werkstoff und Korrosion, Vol.24, No.1, 1973, pp. 38-48. [10] Kastner W., Riedle K. and Tratz H., Experimental investigation to the material abrasion through erosion corrosion. VGB Kraftwerkstechnik, Vol.64, No.5, 1984, 452-465.