DYNAMIC FLOW INSTABILITY OF NATURAL CIRCULATION HEAT RECOVERY STEAM GENERATORS

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1 ISTP-16, 2005, PRAGUE 16 TH INTERNATIONAL SYMPOSIUM ON TRANSPORT PHENOMENA DYNAMIC FLOW INSTABILITY OF NATURAL CIRCULATION HEAT RECOVERY STEAM GENERATORS Heimo WALTER, Wladimir LINZER and Thomas SCHMID Vienna University of Technology, Institute for Thermodynamics and Energy Conversion, Getreidemarkt 9/302, A-1060 Vienna Corresponding author: Phone: , Fax: Keywords: Dynamic instabilities, density-wave instability, natural circulation, heat recovery steam generator Abstract This paper presents the results of a theoretical stability analysis of a Heat Recovery Steam Generator (HRSG) with a horizontal tube bank. The investigation was done for different configurations of a natural circulation HRSG at low system pressure. In these cases the dynamic flow instability of density wave oscillations is analysed. The investigations of the HRSG show, that changes of the bundle geometry can improve the flow stability under operating conditions where density wave oscillations occur. To improve the flow stability the flow resistance at the tube inlet (single phase flow) of the bundle heating surface should be increased. A faster decay of the density wave oscillations will be also achieved by the homogenization of the heat absorption in the individual layers of the bundle heating surface. This provision should be combined with additional flow resistance at the tube inlet. 1 Introduction In the energy and process technology most of the high power steam generators (for example a Heat Recovery Steam Generator (HRSG) arranged behind a gas turbine) are designed as water tube boilers. For high efficiency combined cycle HRSGs, three pressure stages are frequently used. Normally, the fluid flows in the evaporator of the natural circulation steam generator from the downcomer through the heated tube bank and straight to the riser. The driving force of the natural circulation is the difference of the density of the water in the downcomer and the water/steam mixture in the tube bank and the riser. A natural circulation system has various types of instabilities depending on the geometry, fluid properties and operation conditions. The natural circulation system with a horizontally arranged bundle heating surface (vertical type HRSG) tends to be more unstable than a system with vertical evaporator tubes. The typical tube length per layer of such a boiler is up to 20 m. Because of the horizontal tubes the water-steam-mixture at start-up of the boiler has no favourable preferred flow direction. Especially low pressure systems show the tendency to dynamic flow instabilities. The flow instabilities and thermo-hydraulic oscillations have been analysed for a long period of time and many works have been performed by many researchers since flow excursion was at first investigated by Ledinegg [1]. A large part of the studies is focused on forced circulation (see e. g. [2] - [6]) and relative less work has been done on natural circulation systems (see [7] - [10]). A main classification of the thermohydrodynamic instabilities can be seen e. g. in Bouré et al. [11], Bergles [12] or Yadigaroglu [13]. These classifications are based on the distinction between the static and dynamic character of the 1

2 conservation laws which are used to explain the dynamics of the unstable equilibrium state. The static instabilities are subdivided into following types: Flow excursion (Ledinegg instability) Relaxation instabilities such as flow pattern transition instability, bumping, geysering and chugging. These types of instability can be predicted with the help of a steady-state consideration. Such a static instability can lead to another steady-state condition or to a periodic behaviour [11]. In contrast to the static instability, the dynamic instability is caused by transient inertia or dynamic feedback effects if they have essential impact in the process. The following types of dynamic instabilities are known: Acoustic oscillation Density-wave instability (DWO) Thermal oscillation Pressure-drop oscillation Parallel-channel instability While the first 3 types of instabilities (acoustic oscillation, DWO and thermal oscillation) are fundamental instabilities, the pressure drop oscillation and the parallelchannel instability occur only in combination with other instabilities. For the determination of the stability boundaries of such a dynamic instability the steady state principles are not sufficient enough, because several elementary physical instability mechanism often contribute to the overall behaviour of the system. The instabilities can be qualified as compound when several mechanism interact simultaneously [13]. The authors have performed a theoretical stability analysis for the vertical type heat recovery steam generator. The most important type of instability for natural circulation systems - the density-wave instability - was analysed. First results of the investigation are presented in [14]. The knowledge of the dynamic behaviour of the HRSG is important for the safe and reliable operation of the steam generator. Because self induced DWO can lead to a damage of boiler components caused by vibrations and/or thermal waves. In contrast to the analysis of static instabilities e. g. reverse flow, which is a part of the standard procedure of the boiler layout, the calculations for predicting the dynamic instabilities are more complicated and can only be done with a simulation program. Such a program was developed at the Institute of Thermodynamics and Energy Conversion (ITE) at the Vienna University of Technology and is published in [15]. The mathematical model for the working medium is one-dimensional in flow direction and uses a homogeneous equilibrium model for the two-phase flow and applies a correction factor for the two phase pressure loss according to Friedel [19]. The heat exchange between the fluid and the tube wall is governed by Newton's law of cooling and the heat transfer through the wall is assumed to be in the radial direction only. The collectors and distributors respectively are assumed to be points. The steam, which enters the header, is evenly distributed to the outlet tubes. 2 Physical mechanisms of the density wave oscillation Generally, the DWO is the most common type of dynamic instability encountered in twophase flow systems [13]. The instability is a result of the multiple feedback effects in relationship between the flow rate, steam generation and pressure drop in a boiling channel. An inlet flow fluctuation creates a perturbation of the enthalpy in the single phase region. When the enthalpy perturbation reaches the boiling region they are transformed in void fraction and quality perturbations. These fluctuations follow the flow along the channel. This disturbance affects the pressure drop as well as the heat transfer behaviour. The combination of the void fraction and flow perturbation and the change in the lengths of the two-phase area creates a pressure-drop oscillation in the two-phase region. If the overall pressure drop of the channel is imposed by the external characteristic of the channel (e. g. natural circulation), then the two-phase pressure-drop fluctuations will create a feedback pressure perturbation in the single phase region 2

3 DYNAMIC FLOW INSTABILITY OF NATURAL CIRCULATION HEAT RECOVERY STEAM GENERATORS with the opposite sign. This pressure perturbation in the single phase region can attenuate or re-enforce the imposed oscillation by creating a feedback inlet flow perturbation. For certain combinations of the geometry arrangements, boundary conditions and operating conditions the pressure-drop perturbation can acquire a 180 out of phase pressure fluctuation at the exit which leads to a selfsustaining of the flow at the inlet. Further details to the physical mechanism of the DWO instability are described in e. g. [13], [16] and [17]. The DWO is characterised by large amplitudes and a nearly sinusoidal period (see Fig. 2). DWO is a low frequency oscillation (~1 Hz) related to a period of one or two times which is necessary for a fluid particle to travel along the channel [18]. The transportation delays in the channels are of paramount importance for the stability of the system. The oscillation of the pressure and the mass flux are in phase. In Fig. 1 the time dependent distribution of the steam quality along a tube path of the bundle heating surface during the hot start-up of a HRSG is shown. The figure shows the time period for approximately two oscillation cycles of the DWO. The fast increase of the steam quality in the first part (layer 1) of the tube is given by the higher heat flux to the tube compared to the second part (layer 7) of the tube. The second part of the tube path is arranged downstream in the flue gas pass (see Fig. 3). Fig. 1: Development of the steam quality along a tube path of the bundle heating surface of the HRSG Fig. 2 shows the mass flow of the working medium in the downcomer and at the inlet of the first tube path (layer 1). Fig. 1 and Fig. 2 are results of the same hot start-up simulation. The small sketch in Fig. 2 shows additionally the mass flow at the inlet (full line) and at the outlet (broken line) of the heated tube path for the corresponding time period as used in Fig. 1. It can be seen, that for a short period of time reverse flow of the fluid at the inlet of layer 1 is given. This short time period of reverse flow is responsible for the circumstance of the increase and decrease of the steam quality in the unheated part of layer 1 (part of the tube path between the heated section and the connection of the tube to the lower header, see Fig. 3) during the oscillation (see Fig. 1). The oscillation is damped during its way through the tube paths from e. g. the inlet of layer 1 to the outlet of the tube path. The phase displacement of the oscillation at the inlet and the outlet of the tube path is shifted in time. Fig. 2: Mass flow in downcomer and at the inlet of layer 1 3 Simulated heat recovery boiler The present study was done by the help of different boiler configurations. Fig. 3 shows the schematic design of the analysed HRSG. The boiler in Fig. 3 consists of a tube bank with four parallel tube paths arranged in 8 layers. The four tubes paths are connected to a lower and an upper header. The upper header is connected to the drum by the riser relief tube. The working fluid enters the drum subcooled through the feed water tube and leaves the drum saturated through the downcomer. The downcomer is feeding the lower header with water with boiling temperature at drum pressure. The water 3

4 level is controlled and held at the centerline of the drum. Fig. 3: Sketch of the simulated HRSG The dimensions of the HRSG can be seen in Tab. 1. Variable Dim. Value Number of layers [-] 8 Num. of parallel tubes [-] 70 per layer Tube length per layer [m] 20 Dim. of the evap. tubes [mm] Ø 48.3 x 3.2 Number of fins [-] 236 Fin height [mm] 12.7 Averaged fin thickness [mm] 1 Fin segment width [mm] 4.5 Outer downcomer [mm] diameter Outer riser relief diam. [mm] Drum height [m] 9.1 Tube roughness [mm] 0.1 Table 1: Dimensions of the HRSG The drum height is defined as the difference in height between the center of the drum and the center of the lower header. The difference in height between the lowest point of the siphon and the centerline of the lower header is 1.4 m. The arrangement of the tube rows of the bundle heating surface in all test cases was staggered. 3.1 Initial and boundary conditions For all test cases the following initial conditions for the dynamic simulation of the hot start-up of the HRSG are used: The steam generator is filled with water near boiling condition. The pressure distribution of the working medium in the tube network of the boiler is affected by gravity. The velocity of the fluid at the start of the calculation process is equal to zero. The initial fluid temperature in the evaporator of the boiler is identical to the boiling temperature at drum pressure. The drum pressure is constant during the whole simulation. The flue gas temperature and mass flow are given as a function of time (see Fig. 4), and are input boundary conditions for the simulation. Fig. 4: Flue gas mass flow and temperature The total time for the simulation was 2000 s. The flue gas ramps are the same for all simulations. 4 Analysed boiler configurations Table 1 shows the dimensions of the simulated HRSG at the base configuration. For this configuration the drum pressure was 14 bars and the overall circulation ratio at steady state was approximately In the following the six test cases 1 to 6 are considered: In test case 1 additionally to the drum pressure of the base configuration (14 bars) the system pressures of 10 bars, 18 bars and 20 bars are investigated. For the other test cases 2 to 6 the system pressure was kept 4

5 DYNAMIC FLOW INSTABILITY OF NATURAL CIRCULATION HEAT RECOVERY STEAM GENERATORS constant at 14 bars. At these further test cases the tube diameter of the downcomer, the tube roughness, the position of the drum of height, the flow resistance at the inlet of the four tube paths and the heat flux to the individual layers of the bundle heating surface is varied. The variation of the heat flux at test case 6 is linked with a change of the number of fins per meter of tube. The different layers of the tube bank got a theoretical number of fins per meter. This results in a homogenization of the heat absorption in the individual layers of the bundle heating surface (the heat flux to each layer of the bundle heating surface is approximately the same). During one start-up simulation only one of the investigated parameters is varied. oscillation amplitude of the mass flow in the downcomer is approximately 7 kg/s while the oscillation amplitude e. g. at the inlet of layer 1 is 105 kg/s or at the inlet of the layer 4 is 28 kg/s. At the inlet of the layers 1 to 4 the amplitude of the oscillation is high compared to the outlet, and therefore reverse flow of the working medium can occur inside these tubes for short time periods during the oscillation. As a result of the interaction between the four tube paths the oscillation of the mass flow in all other tubes (e. g. the downcomer or riser relief tubes) is in some cases not nearly sinusoidal as described above (see e. g. Fig. 5 or 6). This behavior increases with decreasing system pressure at given power and geometry. 5 Results and discussion Fig. 5: Mass flow in representative tubes of the HRSG Fig. 5 shows as a result of the dynamic simulation of the hot start-up of the HRSG with base configuration the mass flow in selected points. The overall circulation ratio at steady state is The phase displacement of the oscillation in the four tubes paths of the evaporator (not all included in Fig. 5) is shifted in time. The oscillation amplitude at the inlet of the first four layers is higher compared to the outlet of the lower heated layers. The oscillation is damped during its way through the tube paths from e. g. the inlet of layer 1 (approximately 105 kg/s at steady state) to the outlet of the associated layer 7 (approximately 21 kg/s at steady state). Therefore the influence on the circulation mass flow in the downcomer and riser as well as on the steam rate is small (see Fig. 5). The Fig. 6: Mass flow in the downcomer at different drum pressures In Fig. 6 a comparison of the DWO in the downcomer of the HRSG at different system pressures is shown. It can be seen that with increasing system pressure the mass flow in the downcomer also increases. This leads to an increase of the overall circulation ratio at steady state from 14.3 at 10 bars to 15.7 at 20 bars. The system pressure of 18 bars is very close to the stability boundary of the analysed system. The oscillation amplitude of the DWO decreases very slowly. Approximately 5000 s after the simulation start the oscillation is over. With the increasing of the system pressure the steam production respectively the void fraction generation decreases at the given power input. This decrease void fraction generation leads to a decrease of the two-phase friction pressure drop. A damping of the DWO is the consequence of the increasing system pressure, 5

6 which can be seen in the decreasing of the oscillation amplitude. Fig. 7: Mass flow in the downcomer at different tube roughness Fig. 7 shows the influence of the tube roughness on the circulating mass flow in the downcomer and the amplitude of the DWO. In this investigation the tube roughness k is changed in all tubes of the HRSG. The overall circulation ratio at steady state changes from approximately (k = 0.05 mm) to approximately 13.9 in case of a tube roughness of k = 0.2 mm. The tube roughness has an important influence on the friction pressure drop of the system and consequently to the circulation rate of the working medium. With the decrease of the tube roughness the pressure drop due to friction decreases in the single as well as in the two-phase region of the HRSG. This decrease of the pressure drop effects a low decrease of the oscillation amplitude of the DWO. Fig. 8: Mass flow in the downcomer at different tube roughness in the downcomer In Fig. 8 the results of a further analysis of the influence of the tube roughness on the stability of the HRSG is shown. In this investigation only the tube roughness of the downcomer is varied from k = 0.1 mm (base configuration of the boiler, broken line) to k = 0.05 mm and k = 0.2 mm. The k-values in all other tubes are constant at the value of the boiler base configuration. The study shows that the change of the tube roughness only in the downcomer has no significant influence on the DWO. The amplitudes of the DWO in all three analysed test cases are approximately the same. This is a result of the circumstance that the instability is a result of the multiple feedback effects in relationship between the flow rate, steam generation and pressure drop in a boiling channel. The change of the tube roughness in the downcomer influences only the circulation mass flow rate in the boiler (compare Fig. 7 and Fig. 8). The circulation ratio at steady state changes from approximately 15.1 (k = 0.05 mm) to approximately in case of a tube roughness of k = 0.2 mm. Fig. 9: Mass flow in the downcomer at different tube roughness in the tube bank A further variation of the tube roughness is shown in Fig. 9. In this investigation the tube roughness of the four tube paths is changed from k = 0.05 mm to k = 0.2 mm. The tube roughness of all other boiler tubes is constant at the value of the base configuration. Compared with the variations of the tube roughness in the test cases before, the change of the roughness k in the evaporator tubes of the boiler shows an influence on the oscillation amplitude. With increasing of the tube roughness in the evaporator tubes the oscillation amplitude of the DWO increases. This results in a more unstable mass flow circulation of the 6

7 DYNAMIC FLOW INSTABILITY OF NATURAL CIRCULATION HEAT RECOVERY STEAM GENERATORS working fluid in the boiler. The stronger increase of the frictional pressure drop in the two-phase region with the increase of the tube roughness is the reason for this circumstance. The amplitude of the DWO for k = 0.2 mm is approximately 15.8 % higher and approximately 6.3 % lower (k = 0.05 mm) than the oscillation amplitude for k = 0.1 mm. The frequency of the DWO in the test cases presented in Fig 7 to 9 are approximately the same. bundle heating surface compared to the base configuration. Fig. 11: Mass flow in the downcomer at different drum heights The physical mechanism for the improvement of the boiler circulation behavior is the same as in the case of an increase of the system pressure. This mechanism is described in detail above. Fig. 10: Mass flow in the downcomer at different outer downcomer diameters In Fig. 9 the simulation results for the hot start-up of the HRSG for different downcomer diameters is shown. The increase of the outer downcomer diameter is equatable with a decrease of the frictional pressure drop in the downcomer (see Fig. 8). As a result of the decreased pressure drop due to friction the system gets more unstable. This can be seen in the increasing oscillation amplitude of the DWO. The overall circulation ratios at steady state changes from approximately 14.8 (base configuration) to In a further investigation the operation conditions at different drum heights are analysed. The initial drum height at base configuration is included in Tab. 1. With the modification of the drum height, the static head of the system will be changed. It can be seen in Fig. 10 that the increase of the static head causes a low decrease of the oscillation amplitude. Because the increase of the drum height results in an increase of the pressure due to height and in consequence in an increase of the total pressure in the region of the Fig. 12: Mass flow in the downcomer at different additional flow resistance at tube path inlet Fig. 12 shows the results of the start-up calculations with additional flow resistance ξ add at the inlet of the four tube paths of the bundle heating surface. In the figure the mass flow of the fluid in the downcomer is shown. The tube roughness for this investigation was identical to the base configuration. It can be seen that the oscillation amplitude of the fluid in the downcomer with additional flow resistance ξ add > 0 is approximately the same as the oscillation amplitude of the DWO with ξ add = 0 (base configuration). This result is not in contrary to the results presented e. g. in [14]. The authors have reported that an orifice 7

8 implemented in the single phase region of a heated channel reduces the oscillation amplitude and improves the flow stability. The authors have shown that an additional flow resistance (orifice) included at the tube outlet (two-phase region) increases the two-phase pressure drop, which is not in phase with the inlet flow. This leads to a more unstable behavior of the boiler. In our case the amplitude of the DWO in the downcomer is the sum of the oscillations in the different tube paths of the evaporator. As described above, the phases of the oscillations in the different tube paths are shifted in time. As a result of the shifted phases the amplitude in the downcomer is approximately constant. Fig. 13 shows the DWO in the most heated layer 1 of the bundle heating surface for the different additional flow resistance. This layer includes the highest oscillation amplitude at the tube inlet. Fig. 13: Mass flow at the inlet of layer 1 at different flow resistance The figure shows that the amplitude of the DOW decreases with the increase of the flow resistance. It can be seen also that reverse flow is given. The DOW of the base configuration (ξ add = 0) oscillates with an amplitude of approximately 106 kg/s. The highest value for the mass flow against the flow direction from the lower header to the drum (reverse flow) is approximately 16.8 kg/s. A reduction of the oscillation amplitude of approximately 24.2 % is given at an additional flow resistance of ξ add = 10 and of approximately 44.6 % at ξ add = 20. The reverse mass flow reduces from approximately 9.9 kg/s to 1.5 kg/s respectively. Fig. 14: Mass flow in the downcomer at different tube roughness and flow resistance Fig. 14 shows the mass flow in the downcomer at different tube roughness and additional flow resistance. The tube roughness was changed in all tubes of the HRSG. This figure clearly demonstrates the decrease of the oscillation amplitude of the DWO in the downcomer also in case of the implementation of an orifice at the inlet of the tube paths in combination with the tube roughness. With decreasing tube roughness the amplitude of the DWO decreases. This results in a more stable behavior of the HRSG. The decrease of the tube roughness increases the region for stable operation conditions of the boiler. The investigations have shown that with ξ add = 15.5 a stability boundary is found for this boiler geometry (tube roughness of k = 0.05 mm) and operation condition (system pressure of 14 bars). In the sixth test case the number of fins per meter are varied. The variation was done in such a way, that the heat absorption of every layer of the bundle heating surface of the HRSG was the same. In the first part of this test case, the number of fins are changed for every tube to a so called "theoretical" value. This theoretical values are different from the number of fins presently found in catalogues (see Tab. 2). In the second part of this investigation the number of fins are changed in such a way, that the theoretical values are replaced by a number of fins found in catalogues (Tab. 2). 8

9 DYNAMIC FLOW INSTABILITY OF NATURAL CIRCULATION HEAT RECOVERY STEAM GENERATORS number of fins per meter layer theoretical catalogue 1 6 smooth tube 2 12 smooth tube two extreme positions. While the hot start-up of the boiler with the base geometry results in a mass flow oscillation, the homogenized evaporator shows a stable behavior at steady state. Compared with the base geometry, the calculation result with the homogenized number of fins corresponding to the catalogue shows also a decrease of the oscillation amplitude of the DWO. Table 2: Number of fins per meter tube The calculation with the flue gas ramp shown in Fig. 4 results under the use of the theoretical number of fins in a 15 % smaller overall heat flux to the evaporator. For a better comparison of the simulation results with all other analysed test cases the value of the flue gas mass flow at steady state is changed from 77 kg/s to 93 kg/s. With this change the same overall heat flux to the tube bank at steady state is given. The simulation results for a system pressure of 14 bars show, that an evenly distributed heat flux to the evaporator tubes leads to a stable mass flow circulation. This result is given for the theoretical number of fins as well as for the number of fins found in catalogues. Fig. 15: Mass flow in the downcomer at different homogenization of the tube bank at 12 bars Fig. 15 shows the mass flow in the downcomer for a different level of the homogenization. The calculations are done for a drum pressure of 12 bars. The simulation results with the base geometry (no homogenization) and with the theoretical number of fins specify the Fig. 16: Steam quality in the different layers at different homogenization of the tube bank at 12 bars In Fig. 16 the steam quality at the end of heated layers is presented. The figure shows the steam quality respectively for the two most heated layers of the different homogenization cases. With a decrease of the non-uniform heat flux to the individual layers of the evaporator, the oscillation amplitude of the steam quality decreases. This leads to a decrease of the twophase friction pressure drop oscillation which results in a more stable mass flow circulation. A final analysis was done with the homogenized number of fins corresponding to the catalogue and a additional flow resistance ξ add = 10 and ξ add = 5 at the inlet of the four tube paths of the bundle heating surface. This investigation was also done for a drum pressure of 12 bars. The investigation shows that a flow resistant of ξ add = 10 was high enough to damp the DWO. 6 Conclusion In this article the results of a theoretical stability analysis are presented. The investiga 9

10 tions are done for a natural circulation HRSG with a horizontal bundle heating surface under hot start-up conditions. In this analysis the geometry of the boiler, the tube roughness, the system pressure, the flow resistance at the inlet of the four tube paths and the heat flux to the individual layers of the bundle heating surface is varied The analysis for the HRSG shows, that a decrease of the downcomer diameter improves the flow stability under operating conditions where density wave oscillations occur. Changes in the drum height and in the tube roughness has no significant influence on the oscillation amplitudes of the DWO. To improve the flow stability the flow resistance at the tube inlet (flow restriction, e. g. orifice) of the bundle heating surface should be increased. A faster decay of the DWO will be also achieved by the homogenization of the heat absorption in the individual layers of the bundle heating surface. This provision should be combined with additional flow resistance at the tube inlet. The variation of the system pressure has clearly demonstrated its important influence to the boiler stability. With decreasing system pressure the boiler tends to a more unstable behavior. The amplitude of the mass flow oscillation is quite large and flow reversal can also occur during the oscillation at the inlet of the heated evaporator tubes. References [1] Ledinegg M. Instability of flow during natural and forced circulation. Die Wärme, Vol. 61, No. 48, pp , [2] Takitani K. and Takemura T. Density Wave Instability in Once-Through Boiling Flow System, (I) Experiment. Journal of Nuclear Science and Technology, Vol. 15, No. 5, pp , [3] Takitani K. and Sakano K. Density Wave Instability in Once-Through Boiling Flow System, (III) Distributed Parameter Model. Journal of Nuclear Science and Technology, Vol. 16, No. 1, pp , [4] Ünal H. C. The Period of Density Wave Oscillations in Forced Convection Steam Generator Tubes. International Journal of Heat and Mass Transfer, Vol. 25, No. 3, pp , [5] Wang Q., Chen X. J., Kakac S. and Ding Y. An Experimental Investigation of Density-Wave-Type Oscillations in a Convective Boiling Upflow System. International Journal of Heat and Fluid Flow, Vol. 15, No. 3, pp , [6] Karsli S., Yilmaz M. and Comakli O. The Effect of Internal Surface Modification on Flow Instabilities in Forced Convection Boiling in a Horizontal Tube. International Journal of Heat and Fluid Flow, Vol. 23, pp , [7] Nayak A. K., Vijayan P. K., Saha D., Raj, V. V. and Aritomi M. Analytical Study of Nuclear-Coupled Density-Wave Instability in a Natural Circulation Pressure Tube Type Boiling Water Reactor. Nuclear Engineering and Design, Vol. 195, pp , [8] Guanghui S., Dounan J., Fukuda K. and Yujun G. Theoretical and Experimental Study on Density Wave Oscillation of Two-Phase Natural Circulation of Low Equilibrium Quality. Nuclear Engineering and Design, Vol. 215, pp , [9] Baars A. Steady and Unsteady operation conditions of a natural circulation steam generator. Fortschritt- Bericht VDI, Serie 3, No. 779, VDI-Verlag, Düsseldorf (in German) [10] Yun G., Su G. H., Wang J. Q., Tian W. X., Qiu S. Z., Jia D. N. and Zhang J. W. Two-Phase Instability Analysis in Natural Circulation Loops of China Advanced Research Reactor. Annals of Nuclear Energy, Vol. 32, pp , [11] Bouré J. A., Bergles A. E. and Tong L. S. Review of two-phase flow instability. Nuclear Engineering and Design, Vol. 25, pp , [12] Bergles A. E. Review of Instabilities in Two-Phase Systems. In "Two-Phase Flows and Heat Transfer". Hrsg. Kakac S. and Mayinger F., Vol.1, Washington, Hemisphere Pub. Corp [13] Yadigaroglu G. Two-Phase Flow Instabilities and Propagation Phenomena. In "Thermohydraulics of Two-Phase Systems for Industrial Design and Nuclear Engineering". Hrsg. Delhaye J. M., Giot M. and Riethmuller M. L., New York, McGraw-Hill Book Company [14] Walter H. and Linzer W. Flow Stability of Heat Recovery Steam Generators. In Proceedings of the ASME Turbo Expo 2004, Power for Land, Sea and Air, Vienna, Austria June, Paper No. GT , p. 1-9, [15] Walter H. Modelling and Numerical Simulation of Natural Circulation Steam Generators. Fortschritt- Bericht VDI, Serie 6, No. 457, VDI-Verlag, Düsseldorf (in German) 10

11 DYNAMIC FLOW INSTABILITY OF NATURAL CIRCULATION HEAT RECOVERY STEAM GENERATORS [16] Yadigaroglu G. and Bergles, A: E. Fundamental and Higher-Mode Density Wave Oscillations in Two- Phase Flow. Trans. of ASME, Series C, Journal of Heat Transfer, Vol. 94, pp , [17] Tong, L. S. and Tang, Y. S. Boiling Heat Transfer and Two-Phase Flow. Series in Chemical and Mechanical Engineering, 2nd edition, Taylor & Francis, [18] Saha P., Ishii M. and Zuber N. An Experimental Investigation of the Thermally Induced Flow Oscillations in Two-Phase Systems. Trans. of ASME, Series C, Journal of Heat Transfer, Vol. 98, pp , [19] Friedel L. "Improved Friction Pressure Drop Correlations for Horizontal and Vertical Two-Phase Pipe Flow". European Two-Phase Group Meeting, Ispra, Italy, 5-8 June, Paper E 2, pp 1-25,