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Numerical based design of exhaust gas system in a cogeneration power plant
Applied Energy 86 (2009) 857–866
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Applied Energy journal homepage: www.elsevier.com/locate/apenergy
Numerical based design of exhaust gas system in a cogeneration power plant M. Pinelli a,*, G. Bucci b a b
Dipartimento di Ingegneria, Università di Ferrara, Via Saragat, 1, 44100 Ferrara, Italy Sinapsi Innotec Srl, Via Trevisago 35, 25080 Manerba del Garda (BS), Italy
a r t i c l e
i n f o
Article history: Received 21 May 2008 Received in revised form 4 August 2008 Accepted 15 August 2008 Available online 26 October 2008 Keywords: Stack Cogeneration power plant Multidisciplinary design CFD
a b s t r a c t Among the various aspects that have to be analysed in a cogeneration and combined cycle plant design, the exhaust gas stack design can represent a critical aspect, in particular when a by-pass stack, which allows the modulation of heat-to-power generation, is present, since it may influence the entire system working condition. To properly take into account the large number of the different requirements which enter in an exhaust gas system design, a multidisciplinary analysis involving numerical integrated approaches can be adopted in order to obtain an optimally designed stack system. In this paper, the design of the exhaust gas system in a cogeneration plant is analysed. The design is performed numerically through a three-dimensional integrated numerical code. Different design solutions are simulated and the results discussed in detail. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction The use of gas turbines for power generation has increased in recent years and is likely to continue to increase particularly for distributed power and heat production, either for large-sized or for small-sized (<5 MW) plants [1]. The optimal thermodynamic and economical design of this kind of plants requires the study of their main components, which essentially are the gas turbine (GT), the steam turbine (if present) and the Heat recovery steam generator (HRSG), which is used to produce steam and/or hot water, either to be used in a steam cycle or to feed industrial/civil utilities. The HRSG performances and its matching with other components of the plant are crucial issues for the optimisation of cogeneration and combined cycle plants [2]. Many authors have dealt theoretically with the HRSG thermodynamic optimisation in terms of heat transfer area, heat exchanger tube displacement, steam circulation, mode operation, etc. In this field, interesting models and optimisation strategies are presented in [3] and [4]. Recently, the design of HRSG has also taken advantage of the development and of the extensive use of CFD calculations. In [5], the simulation of an existing entire fired HRSG of the horizontal type has been performed and the results have been compared with experimental data. In particular, emphasis has been given to experimental and numerical pressure drop evaluation through the HRSG and the exhaust duct. CFD analysis of the gas-side flow path of the HRSG as an integral tool in the design process is presented in [6]. * Corresponding author. Tel.: +39 0532 974889; fax: +39 0532 974870. E-mail address: [email protected] (M. Pinelli). 0306-2619/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2008.08.016
The work focuses on how CFD analysis can be used to assess the impact of the gas-side flow on the HRSG performance and identify design modifications. CFD simulations of flow and heat transfer in HRSG of vertical- and horizontal-tube designs were also used in [7], in which two modifications to a HRSG design were compared and the optimal one studied in details. The study by means of CFD calculations of inlet duct flow distribution of a HRSG in a combined cycle working in partial by-pass mode is presented in [8]. The HRSG/by-pass system was modeled both in maximum open to HRSG position and minimum open to HRSG position and the recirculation flow observed in these two positions. Practical information on the design of the HRSG is instead more difficult to find. In [9], the main characteristics requested by an HRSG when used in single shaft combined cycle power generation systems are described. In [10], the various aspects that have to be analysed for an optimal HRSG design considering the thermodynamic issues as well as the structural and economical ones are depicted. An important feature in a HRSG design is represented by the exhaust gas system design, in particular when a by-pass system is present. However, this matter is often underestimated, even if the main and the by-pass stacks could be critical components in a power plant, since deficiencies in their design can have consequences on the entire system in terms of losses and incorrect operation [11]. Moreover, an exhaust gas system has to satisfy to several requirements and constraints, which include architectural and environmental impact, noise levels, structural resistance, thermodynamic efficiency, etc. To properly take into account all these features, the use of multidisciplinary tools (CAD solid modelling, FEM and CFD analysis, etc.) has begun to be also used for the design of the exhaust gas systems.
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Nomenclature C f D H k L _ m p P R Re T
g x U z
e q l
turbulence model constants dumping function diameter height turbulent kinetic energy geometric dimension mass flow rate pressure power gas constant Reynolds number temperature efficiency axial co-ordinate axial velocity component height co-ordinate dissipation rate of turbulent kinetic energy density viscosity
Acronyms C compressor CAD computer aided design
Only recently papers dealing with CFD simulations of exhaust gas systems have appeared in the open literature. In [12], practical issues about the use of fluid dynamic modelling to support the design of exhaust system are reported. In particular, they present CFD calculations used to optimise pressure losses. An experimental and computational study to investigate the effect of the flow at the inlet plane of the duct burner for a horizontal type of a supplemental-fired HRSG is presented in [13]. The application of CFD both for improved design and elimination of fouling inside an exhaust duct of a waste sludge incineration plant is demonstrated in [14]. Optimised solution was searched by simulating various solutions based on the installation of different vanes and swirl generators introduced to homogenise the exhaust gas flux. In this paper, the design of the exhaust gas system in a small size cogeneration plant based on a 4.2 MW gas turbine is performed numerically by means of an integrated three-dimensional numerical code. In the plant considered, a by-pass duct is present and a single stack for gases coming from both the utility heat exchangers and the by-pass at the gas turbine exit is used. The CFD simulations, together with some coupled FEM analyses, were first used to troubleshooting a defect in the original design and then to obtain an improved design. The improved design was chosen by considering, simulating and analysing different design solutions. The results in terms of flow field, temperature distribution and pressure losses are analysed and discussed in detail in order to highlight advantage and disadvantage of the different solutions. 2. Exhaust gas system design 2.1. Exhaust gas system and HRSG arrangements The exhaust gas system in a cogeneration or in a combined cycle plant is basically composed of two elements: a main stack, which collects the gases ejected from the HRSG and which is located at the HRSG exit, and a by-pass device, which is located at the GT exit and allows the extraction of part of the hot gases before they enter the HRSG. The by-pass device could be a by-pass stack, a by-pass duct connected to a stack or a discharge chimney. Depend-
CC CFD D FEM GT HRSG LHV
combustion chamber computational fluid dynamics diverter finite element method gas turbine heat recovery steam generator low heating value
Subscripts – yearly-averaged add additional amb ambient b by-pass el electric is isentropic loss power and efficiency loss o organic out turbine outlet s stack t turbine GT gas turbine w wall
ing on the type and on the size of the plant considered, it is possible to have either concrete or steel stacks. In cogeneration plants, the by-pass stack is an essential part of the plant since it allows the modulation of heat-to-power generation to follow variable daily demand and, thus, the optimal management of the heat and power production. This is particularly important in district heating plants in which the operating strategy is often dictated by the need to cover the heat load at minimum costs. In combined cycle power plants, the presence of a by-pass stack is also important, since, even if in this kind of plants the regulation usually follows the electric power demand, an as high as possible operation flexibility is required. Finally, in both cases, the by-pass stack is essential for preventing overall plant shutdown in case of HRSG failure or maintenance. Regarding the HRSG layout, the basic arrangements that have emerged [10,11,15] are the horizontal one, with the hot gases flowing horizontally over vertical tubes and the vertical, with the hot gases flowing vertically over horizontal tubes. Regarding the exhaust gas system, two types of solution can be adopted. The most common one is the use of two stacks (see for instance [8]). The main stack is located at the HRSG exit and collects gases which are usually at a low temperature (80 °C–200 °C). The by-pass stack is located between the gas turbine exit and the HRSG inlet; this stack collects gases, which can be at a quite high temperature (up to 600 °C–650 °C). To modulate the flow rate and, thus, the thermal energy demand, diverter valves are used. Another solution which can be found, even less frequently, is the use of a single stack (an interesting application out of the present work can be found in [16]). In this case, the hot diverted gases, instead of being exhausted separately, are conveyed in a duct which is connected to the main stack, still located at the HRSG exit. In this manner, the hot (GT exit) and cold (HRSG exit) gases are mixed together and ejected through the same stack. In Fig. 1a schematic layout of three different combination of HRSG and exhaust system arrangements is presented. It is possible to notice that the vertical arrangement is more space-saving, case (a), and that the use of only one stack reduces the plant complexity, case (c).
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a
b
c
HRSG HRSG
HRSG D
GT
D
GT
D
GT
Fig. 1. Different stack arrangements: (a) vertical HRSG, two stacks; (b) horizontal HRSG, two stacks; (c) horizontal HRSG, one stack.
2.2. Requirements for stack design In the case of small size plants, usually steel stacks are used. The design of these kind of stacks have to undergo to a high number of requirements and constraints, which essentially are: Architectural constraints. The power plant building, in particular in distributed power generation applications, can be located inside or nearby an urban area to minimise distribution and transmission losses. Hence, the stack visual impact has to be taken into consideration, in particular considering that the additional by-pass stack can considerably get the situation worse. Pollutant emission dispersion. The stack height should be accurately chosen to ensure ground level concentration of pollutant emission discharged from the stacks, which must be inside the limits specified by the local regulations. Hence, to accurately evaluate exhaust and intake designs to ensure acceptable air quality inside and around buildings, careful design is needed [17]. Furthermore, this task is even more critical when a by-pass stack is present, as clearly highlighted in [18]. Noise levels. Lack of sound attenuation can cause objectionable noise levels. Thus, exhaust silencers inside the stacks have to be considered in the design in order to mitigate sound emissions deriving from the gas turbine exit. In particular, differences arise whether the two stacks solution is used or not. If two stacks are present, one silencer for each stack has to be used. Moreover, the silencer in the by-pass stack should be larger than that in the main stack since the noise reduction due to the passage of the fluid through the tube banks of the HRSG is absent. If the one stack solution is instead adopted, only one silencer in the main stack could be sufficient to ensure acceptable noise abatement. However, if necessary, an additional silencer can be added in the by-pass duct which, anyway, could be considerably smaller than the main one. A comprehensive study regarding the interaction between fluid dynamic and acoustic noise in gas turbine exhaust systems can be found in [12]. Thermodynamic optimisation. An incorrect fluid dynamic and thermal design can result in excessive pressure drops, efficiency loss and/or in incorrect operation. Structural design. The stack is subjected to stresses deriving from dead loads, live loads and from temperature non-uniformity. In the first kind are included the structure self-weight. The second kind of stresses is typically originated by aerodynamically induced vibration due to vortex shedding caused by wind and/or by internal fluid dynamics effects such as sudden changes of the direction of the gas stream. Finally, the third source can be originated if non-homogeneous temperature distribution along the stack walls is present. Hence, poorly designed sections of the stack can result in an unbalanced system, in an incorrect operation and, in the worst case, in structure failure. Economical issues. Initial investment, system operating and maintenance costs as a part of the overall plant business plan are obviously a key parameter to keep under control by the stack
designer. Moreover, a wrongly designed stack can cause high pressure drops, which cause loss of production and, thus, loss of plant profitability. Both the two stacks and the single stack arrangements have advantages and disadvantages. However, the second solution seems to have some winning advantages at least in terms of costs and environmental impact. In fact, the presence of only one stack instead of two can reduce emission dispersion problems, can have a lower impact on architectural landscape and could be economically convenient. On the other side, problems related to the design of the by-pass/stack junction (mixing of two gases with a high temperature difference, additional pressure drops) can arise. To properly take into account all the features outlined, an integrated multidisciplinary analysis can be the right approach for an optimal system design. In power plant design, usually the structural (FEM) and fluid dynamic (CFD) numerical analyses are dealt separately, with only minor and simplified reciprocal integration. In this paper, the analysis of the exhaust gas system of a cogeneration plant is performed with a CAD/CFD/FEM integrated procedure, outlined in Fig. 2. The procedure was performed through the EFDLab software, which is a three-dimensional CFD numerical code fully embedded with a CAD solid modeller based on SolidWorks engine. At the time of the work, the EFDLab software did not still have the FEM solver integrated with the CAD and CFD modules. Hence, the structural analysis was performed by using the CosmosWork software. 2.3. Numerical models and gridding issues The EFDLab solver [19] uses a rectangular mesh automatically distinguishing the fluid and solid domains in the computational domain. The algorithm to generate the mesh is based on the geometrical discontinuity or ‘‘gap size” and it increases the number of cells in proximity of narrow channels, corners gaps, etc. Mesh cell sides are orthogonal to the specified cartesian co-ordinate system axes and are not fitted to the solid/fluid interface. Hence, a partial cell approach is used, in which the solid/fluid interface cuts the near-wall mesh cells and the mass and heat fluxes are treated properly with a special algorithm. The code solves the Navier–Stokes equations through a Reynolds averaged approach and uses a finite volume method for the equation discretisation. A second-order upwind approximation is used for the advection terms. Following the SIMPLE approach, an elliptic type discrete pressure equation is derived by algebraic transformations of the originally derived discrete equations for mass and momentum. A multigrid method is then used to accelerate the solution convergence. For turbulence modelling, the low Reynolds number k–e model as in the Lam–Bremhorst formulation is used [20]. In this model, the turbulent eddy viscosity is given by
lt ¼ qC l fl k2 =e
ð1Þ
and, while the equation for the turbulent kinetic energy k is in the usual form, the equation for its dissipation e is modified as follows.
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Geometry exchange [standard (IGES,STL), integrated ]
CAD
Grid generator Post-processing and result analysis
Mesh optimisation surface FEM volume CFD
Fig. 2. CAD/CFD/FEM integrated procedure.
De o ¼ Dt oxj
lþ
lt o e e oU i oU j oU i e2 þ q C 2 f2 þ C 1 f1 re oxj k oxj oxi oxj k
duce thermal power through the HRSG, which is used to produce heat for district heating during winter and to feed an absorption chiller during summer. The plant is based on a thermal-following management, i.e. the plant was designed to meet the thermal demand of the site in which it was located. Hence, a first-level regulation of the thermal demand is performed by regulating the GT load (through the combined action of the IGV and of the fuel mass flow rate). Then, when the heat requested by the users (district heating or absorption chiller) is lowered below the minimum acceptable working condition of the GT (imposed by the maximum allowable emission levels), a second-level regulation of the heat is performed in a dissipative way by acting on the by-pass valve and exhausting the hot gases to the atmosphere. This allows the plant owner to keep the GT turbine working and, thus, generating profit by selling the electric energy. In any case, the wasted thermal power has to be controlled in order to keep the primary energy saving (PES) index above the value fixed by the local regulation; if this limit value is passed, the plant is forced to be shut down. Since the plant is located in a high-density urban area, a single stack configuration was adopted for the by-pass of gases. In the plant lay out, the by-pass duct (inside which a silencer was positioned) was joined to the stack through a 135° junction located
ð2Þ
Following [20], the parameters f1, f2 and fl for near-wall resolution are defined as
f1 ¼ 1 þ
3 2 0:05 and f 2 ¼ 1 eRt fl
fl ¼ 1 e0:0165Rk
2
ð3Þ
20:5 1þ Rt
ð4Þ
where and Rt = q k2/(l e) and Rk = q k0.5 y/l are turbulence Reynolds numbers. 3. Problem statement The problem under investigation refers to the design of an exhaust system of a cogeneration plant (Fig. 3a) composed of a single shaft 4.2 MW gas turbine, used for power generation, followed by a horizontal type HRSG for heat production. Between the GT and the HRSG a by-pass system, guided by a diverter valve, is present. The cogeneration plant under investigation was conceived to produce electric power with the GT, which is sold to the grid, and to pro-
a b
C
Db = 1.3 m
Hs = 30 m
T Main stack silencer
F
CC
Ds = 1.4 m
Main stack silencer
By-pass duct
By-pass silencer
inlet 2 (from GT)
HRSG
D
GT
inlet 1 (from HRSG)
Fig. 3. Cogeneration plant under consideration (a) and stack solid model (b).
M. Pinelli, G. Bucci / Applied Energy 86 (2009) 857–866
at 25% of the total stack height, while the HRSG exit gases entered into the stack at its base after a 90° bend. Over the by-pass junction, a main silencer is present. The necessity of re-design of the stack/by-pass system arose since during the first part of the plant life a relevant deflection of the stack vertical axis was noticed which caused more than one stop of the entire plant. Subsequently, some displacement measurements were performed on the structure in correspondence of the roof of the silencer (z = 15 m). At this height, a deviation from the vertical axis of the stack as equal to 0.24 m was measured, which, in turn, caused a calculated deflection of the stack top of about 0.60 m. Hence, the fluid dynamic and structural numerical calculations were performed to detect the source of this deflection and to search for a suitable solution in terms of fluid dynamic optimisation and economic impact. 3.1. Numerical approach The solid model of the stack is reported in Fig. 3b. The domain considered during the numerical simulation was only the exhaust duct geometry. The two gas streams arriving from the HRSG and from the GT, which are at different temperature, enters the domain considered through the openings at the stack base and at definite section along the by-pass (inlet 1 and inlet 2 in Fig. 3b). Since the aim of the paper is to compare different design solutions rather than obtaining accurate results in terms of absolute values, the two gases entering the domain were considered as standard air. Moreover, the problem was considered incompressible. This hypothesis was considered acceptable since the pressure differences inside the entire domain remains very small with respect to the absolute pressure of the fluid. Thus, fluid density was considered dependent only from temperature. For the molecular viscosity and the specific heat, a second-order dependency from temperature was considered. 3.2. Boundary conditions The most robust boundary conditions were found to be imposed temperature and mass flow rate at the inlet for both the gas streams and an outlet average static pressure at the stack exit. The temperature, pressure and mass flow rate values adopted are referred to a representative working condition of the plant. The working condition considered is characterised by gas turbine at full load (Pel = 4.2 MW) and standard ambient conditions (Tamb = 15 °C, pamb = 101,325 Pa, RH = 60%). The values of the imposed boundary conditions were obtained by experiments. The total mass flow rate entering the stack was set equal to 17.3 kg/s. Different ratio between the main gas stream mass flow rate (from HRSG) and the by-passed gas stream mass flow rate (directly from the GT) have been considered. However, a series of trials on the plant showed that the most critical condition for temperature non-uniformity is when the by-passed gases are the 50% of total mass flow rate exiting the gas turbine. Regarding the thermal boundary conditions, two different imposed temperatures were set. In particular, the temperature of the gas from the HRSG (inlet 1) was set as equal to 120 °C and the temperature of the gas from the gas turbine (inlet 2) was set as equal to 537 °C. These values remained the same for all the cases considered. No heat flux was considered at the stack walls since the walls are externally insulated. This hypothesis can be considered acceptable considering that the global heat transfer coefficient between internal gas flow and ambient air was estimated to be always less than 1.0 W/(m2 °C). Therefore, the coupling with the environment can be neglected. Finally, at the stack exit, the standard value of atmospheric pressure was used (pamb = 101,325 Pa).
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3.3. Grids The domain region was divided in sub-regions separately gridded in order to generate a regular mesh. In this manner it was possible to obtain a good quality grid with refinement in areas of most concern in the simulation. The number of grid cells was different for each calculation. Grid independence issues were carried out separately: the number of cells used within each calculation was chosen accordingly. 4. Results and discussion 4.1. Case (a). Baseline configuration The baseline configuration of the stack of the plant (for which the main geometric characteristics are reported in Table 1) has been initially studied. The following numerical procedure was carried out: 1. The actual geometry of the stack/by-pass system was modelled through the three-dimensional CAD (in Fig. 4a, a particular of the stack/by-pass junction geometry is reported). 2. The geometry was then gridded. The total number of grid cells resulted equal to 70,825. This amount was considered acceptable to balance between calculation accuracy and computational time. 3. The CFD simulation was performed through the fluid dynamic module. As inlet mass flow boundary conditions, the mass flow rate was considered equally distributed between the two inlets of the stack (50% from HRSG and 50% from GT). 4. The numerical results were analysed. In Fig. 4b, the temperature distribution near the by-pass region is reported on a longitudinal mid-plane. It can be seen that when the hot gas stream enters inside the stack, it tends to ‘‘stick” on one side of the stack wall (Zone 2) greatly enhancing its temperature. On the diametrically opposite side located at the same height (Zone 1), instead, the stack walls are ‘‘cooled” by the cold gas stream arriving from the bottom and, consequently, the temperature in these zones remains low. Thus, the temperature field inside the stack walls results highly non-uniform. A temperature difference DTw of nearly 400 °C between Zone 1 and Zone 2 was calculated. This analysis suggested that the possible cause of the stack deformation could effectively be the temperature nonuniformity inside the stack walls. In fact, a consequent non-uniformity of the strain field is originated, which, in turn, causes a different elongation of the material (steel) in Zone 1 and Zone 2 and, in turn, the deformation of the stack. 5. To confirm the observation made in the previous step, the calculated temperature distribution was used as a boundary condition for the FEM simulation, through which a numerical structural analysis was performed. The FEM calculations confirmed the hypothesis that the non-uniform temperature distribution was the cause of the stack deflection. In fact, the deflection of the stack in correspondence of the silencer roof (z = 15 m) was calculated equal to 220 mm, which is a value in very good agreement with the available experimental data (Table 2).
Table 1 Stack geometric characteristics Total height Silencer width By-pass junction height Main stack diameter By-pass duct diameter
32.0 m 4.5 m 8.0 m 1.4 m 1.3 m
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Fig. 4. Baseline stack-by-pass geometry (a) and temperature distribution (b).
Table 2 Numerical and experimental stack deformation at z = 15 m Deviation from stack vertical axis Numerical result Experimental data
0.22 m 0.24 m
In conclusion, through the integrated CFD/FEM calculation, it was possible to individuate the cause of the stack distortion. Moreover, this result was considered as a good validation of the code and, more in general, of the entire calculation procedure. Once the problem has been detected and the code has been validated, other possible stack/by-pass junction design solutions have been considered and analysed numerically. The most interesting are presented in the following and discussed in detail. 4.2. Case (b). Single-pipe configuration In order to overcome the structural problems outlined above, the solution presented in Fig. 5a was evaluated. The by-pass proposed is composed of a circular duct which enters the main stack perpendicularly. Then, the hot gas stream is forced to change its direction through a 90° pipe-shaped duct concentrically located inside the stack. In the stack zone in which the by-pass duct enters, the stack transversal section has been augmented from 1.4 m to 2.0 m to properly locate the pipe. The computational strategy to perform the simulation was the same used in Case (a). The mass flow was considered equally distributed between the two inlets. The final mesh consisted of 71,356 cells. The temperature distribution in a longitudinal mid section obtained from the CFD calculation is reported in Fig. 5b. The temperature field shows that the hot stream is now detached from the wall near the by-pass duct junction but, at the same time, this hot stream is brought closer to the opposite wall. It is possible to notice that, even if in a lesser degree, high temperature differences between different zone at equal height are still present, and, thus, the risk of thermally-induced structural problems are not completely avoided. As can be seen from Fig. 5c, which reports the temperature profile along a radius located at a stack height of z = 12.5 m (just upstream the silencer), the maximum calculated temperature difference between opposite-located zones is considerably reduced (DTw = 228 °C). In Fig. 6 the temperature distribution in three transversal sections at different stack heights (z = 10.5 m, 11.5 m and 12.5 m, respectively) are reported. By analysing in detail this three-dimensional pattern of the temperature field, the hot core inside gas stream is still noticeable near stack walls, also in the zones located just upstream the silencer.
Moreover, from the analysis of the figure, it can be seen that the hot core of the stream is rotated of about 45° anticlockwise going from the lower to the upper section, thus suggesting that, after the by-pass duct, a swirling velocity component is present. As a first modification of this arrangement, the pipe was positioned eccentrically with respect to the stack axis. In particular, the pipe vertical axis was brought closer to the wall in which the stack/by-pass junction is located. Moreover, the convergent between the pipe and the silencer was eliminated. The analysis of the results shows that the new configuration did not allow a significant improvement neither regarding the temperature differences nor the swirling pattern of the stream. 4.3. Case (c). Three-pipe configuration To minimise the wall temperature differences and the swirling pattern of the flow, which can cause additional pressure drops and flow instabilities, a three-pipe configuration has been studied. In Fig. 7a, the geometry of the proposed by-pass duct is presented. It consists of three concentric ducts, eccentrically set with respect to the stack axis, which guide the fluid toward the stack axis. Also in this case, in the zone in which the by-pass duct enters, the stack transversal section has been augmented from 1.4 m to 2.0 m. The generated mesh consisted of a total number of 74,897 cells. The mass flow was considered equally distributed between the two inlets. In Fig. 7b, the temperature distribution in a longitudinal mid section along the stack vertical axis is presented. It can be noticed that the hot core of the stream is distant from the walls and it is well confined in the inner zone of the stack. The hot core of the stream moves through the stack in a very regular way and remains detached from the walls also away from the pipe. In Fig. 7c, the temperature profiles along two different radius (located at a stack height of z = 9 m and z = 13.5 m, respectively) are reported. It can be noticed that immediately after the stack/ by-pass junction there is not temperature difference between opposite-located zones. Moreover, the temperature difference in the most critical zone, which is at z = 13.5 m and was detected after the post-processing of the results, the calculated maximum temperature DTw is dropped down to 137 °C. In Fig. 8, the temperature fields in four sections at different stack heights are reported. The gas stream coming from the bypass presents a regular structure and a well-defined vertical direction, which allow a regular flow pattern in terms of both velocity distribution and temperature. The hot core of the stream remains detached from the walls also away from the pipe. Moreover, the swirling characteristic seems to be completely suppressed.
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a
b
c
600
T [˚C]
400
200
0 -1.00
-0.50
0.00
0.50
1.00
r/r max Fig. 5. Single-pipe configuration: (a) geometry; (b) temperature distribution at midsection and (c) temperature profile at midsection and at z = 12.5 m.
Fig. 6. Single-pipe configuration: temperature distribution at different height.
4.4. Economic considerations Both the two configurations proposed since now showed good thermal and fluid dynamic characteristics, as highlighted by the CFD calculation. However, it must also be considered that the stack/by-pass configuration is to be seen as a part of the GT/HRSG system, and, thus, the consequences of these modifications have to be investigated also considering their inclusion in the entire plant lay-out. In particular, a very important issue is represented by the
additional pressure drops which may occur along the gas path. In fact, pressure drops at the turbine exhaust negatively influence the gas turbine efficiency and power output and, thus, their increase can have relevant influence on the profitability of the power plant. Indeed, minimisation of the gas-side pressure drop is a relevant issue in HRSG optimisation [5]. For these reasons, the pressure drops between the base and the top of the stack have been calculated for the baseline configuration and for the two new solutions (single-pipe and three-pipe
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a
b
c
600
T [˚C]
400
z=9m
200
z = 13.5 m
0 -1.00
-0.50
0.00
r/r
0.50
1.00
max
Fig. 7. Three-pipe configuration: (a) geometry; (b) temperature distribution at midsection and (c) temperature profile at midsection and at different heights.
Fig. 8. Three-pipe configuration: temperature distribution at different heights.
configuration). The calculations were performed by considering the flow entirely coming from the HRSG exit, which is the most frequent and, in terms of total stack pressure drop, the most penalising working condition. To obtain the magnitude of the power output DPloss and efficiency loss Dgloss due to the additional stack pressure drop Dpadd, it is possible to use: (i) the correction curves supplied by the manufacturer, which reports the power loss magnifying factors as a function of the exhaust pressure loss; (ii) analytical relations based on thermodynamic considerations. The first are more accurate but not always available while the second are simplified but general. In this case, the second method was adopted by using an equation proposed by Lozza [11] for DPloss, valid for single shaft gas turbines:
DPloss ¼
_ out ðgel go gis Þt mRT Dpadd pamb
Since the exhaust pressure drop does not influence the fuel consumption, the value of Dgloss is directly related to the value of DPloss. The results are reported in Table 3. The percentage efficiency loss is evaluated referring to a yearly-averaged efficiency of the GT = 0.25. As gas turbine, which, in this case, was estimated as g can be seen, the additional pressure drops caused by the singleand the three-pipe configurations are practically equal, as expected, and the power output decrease and the efficiency loss are rather low in both cases.
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M. Pinelli, G. Bucci / Applied Energy 86 (2009) 857–866 Table 3 Calculated pressure drop due to stack and additional power output and efficiency losses
Case (a). Baseline configuration Case (b). Single-pipe configuration Case (a). Three-pipe configuration
Dps (Pa)
Dpadd (Pa)
DPloss (kW)
Dgloss (%)
238 460 465
– 222 227
– 7.38 7.55
– 0.308 0.315
However, if an economic evaluation on the basis of the plant entire life is performed, the adoption of these solution can cause profitability losses which can be significant. In fact, assuming that (i) the working hours per year of the plant are 7000 h, (ii) even if the cost of the fuel (natural gas) for a 4.2 MW cogeneration plant located in Italy can vary significantly, a reference illustrative value can be set at 0.40 €/Sm3, (iii) the plant is managed as to achieve in the following years the same electric energy production and (iv) an yearly-averaged natural gas LHV equal to 48,000 kJ/kg; hence, with the figures stated above, which are illustrative but realistic, the total profitability loss of the plant would be roughly equal to 8800 €/year and to 9000 €/year for the single- and the three-pipe configurations, respectively. Then, if the expected working life of the plant (more than 20 years) is included in this evaluation, it is evident the importance of evaluating the criticality of the action that has to performed on the stack.
a
4.5. Case (d). Baffle configuration As a result of the analysis performed above in terms of both thermodynamic and economical point of view, another by-pass junction was designed and analysed. The objective of this new design was the effort to obtain a compromise between minimal pressure drops, and thus minimal profitability losses, and avoidance of structural stresses. The new geometry has the same configuration of the baseline design with the by-pass/stack junction performed through a 135° connection. To avoid the direct contact of the hot stream coming from the by-pass with the stack walls, the by-pass duct has been extended inside the stack by adding an appropriately shaped baffle which drives the hot stream towards the stack axis. In the numerical calculation, the mesh used consisted of 80,000 cells. The baffle geometry and a particular of the mesh refinement near the baffle is shown in Fig. 9a. The mass flow was considered equally distributed between the two inlets.
b
c
600
T[˚C]
400
200
0 -1.00
-0.50
0.00
0.50
1.00
r/r max Fig. 9. Baffle configuration: (a) geometry and grid; (b) temperature distribution at midsection and (c) temperature profile at z = 13.5 m.
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In Fig. 9b the temperature distribution in a longitudinal mid section inside the stack is presented. It is clearly noticeable that the hot stream of the core is correctly driven to occupy the central region of the stack, and it is sufficiently detached from the stack walls. In the region near the by-pass/stack junction, the calculated wall temperature difference DTw is almost equal to 250 °C. In addition, in Fig. 9c it is possible to notice that the temperature field on the stack walls surface presents an acceptable uniformity. Finally, the analysis of the pressure distribution revealed that the pressure drop is almost equal to the baseline configuration. Hence, this geometry, even if does not allow a regularity of the temperature and flow field distribution as good as the one obtained with the three-pipe configuration, has some advantageous features, which are: (i) it does not introduce additional pressure drops which, as demonstrated, can cause power output and, thus, profitability losses; (ii) it allow the obtaining of reasonable temperature differences between different zones of the stack walls; (iii) it is the solution which implies reduced actions on the baseline structure and, thus, very low additional costs. For these reasons, this solution was considered for the stack modification. The FEM analysis was performed in order to verify if the structure could effectively originate a benefit in terms of stresses and strains. Hence, following the procedure outlined in the previous paragraphs, the temperature field inside the stack walls obtained with the CFD calculation were used as boundary condition in the FEM calculation. The calculation confirmed that the stresses on the structure should have values well below the resistance limits imposed by the materials adopted. 5. Conclusions The analysis of different stack design solutions in a cogeneration power plant has been performed by using a multidisciplinary analysis. In particular, in the plant considered the exhaust gas system consists of a single steel stack through which both the main and the by-passed gas streams are ejected. This solution, which can have advantages in terms of costs, presents some design difficulties due to the mixing of two gas streams with a high temperature difference. In particular, a thermal-induced stresses appeared, which originated a deflection of the stack. The developed CAD/CFD/FEM integrated procedure demonstrated the effectiveness of these kind of analyses in the optimised design of the exhaust system of the plant considered. The coupled CFD/FEM numerical calculation allowed the detection of the struc-
tural problem of the analysed stack. Regarding economical issue, the calculation of the pressure drops along the stack showed that a wrongly designed duct lead to profitability losses which, in a long-period time frame, can be significant. Acknowledgement The Authors gratefully acknowledge: Prof. R. Bettocchi and Prof. P.R. Spina for the helpful discussions and suggestions; Ing. L. Begani and P.i. S. Tassoni for the information provided. References [1] Pilavachi M. Power generation with gas turbine systems and combined heat and power. Appl Therm Eng 2000;20:1421–9. [2] Zachary JJ. Strategies for integration of advanced gas and steam turbines in power generation applications. ASME Paper GT2007-27978. [3] Franco A, Russo A. Combined cycle plant efficiency increase based on the optimization of the heat recovery steam generator operating parameters. Int J Therm Sci 2002;41:843–59. [4] Franco A, Giannini N. A general method for the optimum design of heat recovery steam generators. Energy 2006;31:3342–61. [5] Torresi M, Saponaro A, Camporeale SM, Fortunato B. CFD analysis of the flow through tube banks of HRSG, ASME Paper GT2008-51300; 2008. [6] Sunil Kumar Vylta VV, Huang GPG. CFD modeling of heat recovery steam generators using fluent. 30th annual dayton-cincinnati aerospace science symposium; 2000. [7] Hegde N, Han I, Lee TW, Roy RP. Flow and heat transfer in heat recovery steam generators. J Energy Res Tech 2007;129(3):232–42. [8] Bell MB, Nitzken JA. Controlling steam production in heat recovery steam generators for combined cycle and enhanced oil recovery operations. Las Vegas, Nevada: Proceedings of POWER-GEN International; 2003. [9] Tomlinson LO, Mc Cullough S. Single-shaft combined-cycle power generation systems. Technical Report No. GER-3767 B GE Power Systems; 1996. [10] Nestianu D, Larson T, Lynch L, Zachary J. Vertical or horizontal? An EPC contractor’s angle. Modern Power Syst 2003;23(3):19–22. [11] Lozza G. Turbine a gas e cicli combinati. Bologna: Società Editrice Esculapio; 1996. [12] Rieckmann J, Laquinnia L, Alexander A, Graham J. Acoustic considerations for gas turbine: intake and exhaust systems. Cogeneration and on-site power production 2004;5(2):35–42. [13] Lee BE, Kwon SB, Lee CS. On the effect of swirl flow of gas turbine exhaust gas in an inlet duct of heat recovery steam generator. J Gas Turb Power 2002;124:496–502. [14] Stehlik P. Heat transfer as an important subject in waste-to-energy systems. Appl Thermal Eng 2007;27:1658–70. [15] Horlock JH. Combined power plants including combined cycle gas turbine (CCGT) plants. Oxford: Pergamon Press; 1992. [16] Brandstetter G, Daublebsky C. Investigations on dynamic behaviour of heat recovery steam generators carried out with a commercial software program. ASME Paper GT2007-27380; 2007. [17] Petersen RL, Cochran BC, Carter JJ. Specifying exhaust and intake systems. ASHRAE J 2000;8:12–8. [18] Bell B. Air dispersion modelling – cockburn power project gas turbine bypass stacks proposal. Technical Report Western Power Corporation ENVIRON, Australia; 2002. [19] EFDLab. User Manual. Germany; 2006. [20] Lam CKG, Bremhorst K. A modified form of the k–e model for predicting wall turbulence. J Fluids Eng 1981;103:456–60.
Contents lists available at ScienceDirect
Applied Energy journal homepage: www.elsevier.com/locate/apenergy
Numerical based design of exhaust gas system in a cogeneration power plant M. Pinelli a,*, G. Bucci b a b
Dipartimento di Ingegneria, Università di Ferrara, Via Saragat, 1, 44100 Ferrara, Italy Sinapsi Innotec Srl, Via Trevisago 35, 25080 Manerba del Garda (BS), Italy
a r t i c l e
i n f o
Article history: Received 21 May 2008 Received in revised form 4 August 2008 Accepted 15 August 2008 Available online 26 October 2008 Keywords: Stack Cogeneration power plant Multidisciplinary design CFD
a b s t r a c t Among the various aspects that have to be analysed in a cogeneration and combined cycle plant design, the exhaust gas stack design can represent a critical aspect, in particular when a by-pass stack, which allows the modulation of heat-to-power generation, is present, since it may influence the entire system working condition. To properly take into account the large number of the different requirements which enter in an exhaust gas system design, a multidisciplinary analysis involving numerical integrated approaches can be adopted in order to obtain an optimally designed stack system. In this paper, the design of the exhaust gas system in a cogeneration plant is analysed. The design is performed numerically through a three-dimensional integrated numerical code. Different design solutions are simulated and the results discussed in detail. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction The use of gas turbines for power generation has increased in recent years and is likely to continue to increase particularly for distributed power and heat production, either for large-sized or for small-sized (<5 MW) plants [1]. The optimal thermodynamic and economical design of this kind of plants requires the study of their main components, which essentially are the gas turbine (GT), the steam turbine (if present) and the Heat recovery steam generator (HRSG), which is used to produce steam and/or hot water, either to be used in a steam cycle or to feed industrial/civil utilities. The HRSG performances and its matching with other components of the plant are crucial issues for the optimisation of cogeneration and combined cycle plants [2]. Many authors have dealt theoretically with the HRSG thermodynamic optimisation in terms of heat transfer area, heat exchanger tube displacement, steam circulation, mode operation, etc. In this field, interesting models and optimisation strategies are presented in [3] and [4]. Recently, the design of HRSG has also taken advantage of the development and of the extensive use of CFD calculations. In [5], the simulation of an existing entire fired HRSG of the horizontal type has been performed and the results have been compared with experimental data. In particular, emphasis has been given to experimental and numerical pressure drop evaluation through the HRSG and the exhaust duct. CFD analysis of the gas-side flow path of the HRSG as an integral tool in the design process is presented in [6]. * Corresponding author. Tel.: +39 0532 974889; fax: +39 0532 974870. E-mail address: [email protected] (M. Pinelli). 0306-2619/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2008.08.016
The work focuses on how CFD analysis can be used to assess the impact of the gas-side flow on the HRSG performance and identify design modifications. CFD simulations of flow and heat transfer in HRSG of vertical- and horizontal-tube designs were also used in [7], in which two modifications to a HRSG design were compared and the optimal one studied in details. The study by means of CFD calculations of inlet duct flow distribution of a HRSG in a combined cycle working in partial by-pass mode is presented in [8]. The HRSG/by-pass system was modeled both in maximum open to HRSG position and minimum open to HRSG position and the recirculation flow observed in these two positions. Practical information on the design of the HRSG is instead more difficult to find. In [9], the main characteristics requested by an HRSG when used in single shaft combined cycle power generation systems are described. In [10], the various aspects that have to be analysed for an optimal HRSG design considering the thermodynamic issues as well as the structural and economical ones are depicted. An important feature in a HRSG design is represented by the exhaust gas system design, in particular when a by-pass system is present. However, this matter is often underestimated, even if the main and the by-pass stacks could be critical components in a power plant, since deficiencies in their design can have consequences on the entire system in terms of losses and incorrect operation [11]. Moreover, an exhaust gas system has to satisfy to several requirements and constraints, which include architectural and environmental impact, noise levels, structural resistance, thermodynamic efficiency, etc. To properly take into account all these features, the use of multidisciplinary tools (CAD solid modelling, FEM and CFD analysis, etc.) has begun to be also used for the design of the exhaust gas systems.
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Nomenclature C f D H k L _ m p P R Re T
g x U z
e q l
turbulence model constants dumping function diameter height turbulent kinetic energy geometric dimension mass flow rate pressure power gas constant Reynolds number temperature efficiency axial co-ordinate axial velocity component height co-ordinate dissipation rate of turbulent kinetic energy density viscosity
Acronyms C compressor CAD computer aided design
Only recently papers dealing with CFD simulations of exhaust gas systems have appeared in the open literature. In [12], practical issues about the use of fluid dynamic modelling to support the design of exhaust system are reported. In particular, they present CFD calculations used to optimise pressure losses. An experimental and computational study to investigate the effect of the flow at the inlet plane of the duct burner for a horizontal type of a supplemental-fired HRSG is presented in [13]. The application of CFD both for improved design and elimination of fouling inside an exhaust duct of a waste sludge incineration plant is demonstrated in [14]. Optimised solution was searched by simulating various solutions based on the installation of different vanes and swirl generators introduced to homogenise the exhaust gas flux. In this paper, the design of the exhaust gas system in a small size cogeneration plant based on a 4.2 MW gas turbine is performed numerically by means of an integrated three-dimensional numerical code. In the plant considered, a by-pass duct is present and a single stack for gases coming from both the utility heat exchangers and the by-pass at the gas turbine exit is used. The CFD simulations, together with some coupled FEM analyses, were first used to troubleshooting a defect in the original design and then to obtain an improved design. The improved design was chosen by considering, simulating and analysing different design solutions. The results in terms of flow field, temperature distribution and pressure losses are analysed and discussed in detail in order to highlight advantage and disadvantage of the different solutions. 2. Exhaust gas system design 2.1. Exhaust gas system and HRSG arrangements The exhaust gas system in a cogeneration or in a combined cycle plant is basically composed of two elements: a main stack, which collects the gases ejected from the HRSG and which is located at the HRSG exit, and a by-pass device, which is located at the GT exit and allows the extraction of part of the hot gases before they enter the HRSG. The by-pass device could be a by-pass stack, a by-pass duct connected to a stack or a discharge chimney. Depend-
CC CFD D FEM GT HRSG LHV
combustion chamber computational fluid dynamics diverter finite element method gas turbine heat recovery steam generator low heating value
Subscripts – yearly-averaged add additional amb ambient b by-pass el electric is isentropic loss power and efficiency loss o organic out turbine outlet s stack t turbine GT gas turbine w wall
ing on the type and on the size of the plant considered, it is possible to have either concrete or steel stacks. In cogeneration plants, the by-pass stack is an essential part of the plant since it allows the modulation of heat-to-power generation to follow variable daily demand and, thus, the optimal management of the heat and power production. This is particularly important in district heating plants in which the operating strategy is often dictated by the need to cover the heat load at minimum costs. In combined cycle power plants, the presence of a by-pass stack is also important, since, even if in this kind of plants the regulation usually follows the electric power demand, an as high as possible operation flexibility is required. Finally, in both cases, the by-pass stack is essential for preventing overall plant shutdown in case of HRSG failure or maintenance. Regarding the HRSG layout, the basic arrangements that have emerged [10,11,15] are the horizontal one, with the hot gases flowing horizontally over vertical tubes and the vertical, with the hot gases flowing vertically over horizontal tubes. Regarding the exhaust gas system, two types of solution can be adopted. The most common one is the use of two stacks (see for instance [8]). The main stack is located at the HRSG exit and collects gases which are usually at a low temperature (80 °C–200 °C). The by-pass stack is located between the gas turbine exit and the HRSG inlet; this stack collects gases, which can be at a quite high temperature (up to 600 °C–650 °C). To modulate the flow rate and, thus, the thermal energy demand, diverter valves are used. Another solution which can be found, even less frequently, is the use of a single stack (an interesting application out of the present work can be found in [16]). In this case, the hot diverted gases, instead of being exhausted separately, are conveyed in a duct which is connected to the main stack, still located at the HRSG exit. In this manner, the hot (GT exit) and cold (HRSG exit) gases are mixed together and ejected through the same stack. In Fig. 1a schematic layout of three different combination of HRSG and exhaust system arrangements is presented. It is possible to notice that the vertical arrangement is more space-saving, case (a), and that the use of only one stack reduces the plant complexity, case (c).
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a
b
c
HRSG HRSG
HRSG D
GT
D
GT
D
GT
Fig. 1. Different stack arrangements: (a) vertical HRSG, two stacks; (b) horizontal HRSG, two stacks; (c) horizontal HRSG, one stack.
2.2. Requirements for stack design In the case of small size plants, usually steel stacks are used. The design of these kind of stacks have to undergo to a high number of requirements and constraints, which essentially are: Architectural constraints. The power plant building, in particular in distributed power generation applications, can be located inside or nearby an urban area to minimise distribution and transmission losses. Hence, the stack visual impact has to be taken into consideration, in particular considering that the additional by-pass stack can considerably get the situation worse. Pollutant emission dispersion. The stack height should be accurately chosen to ensure ground level concentration of pollutant emission discharged from the stacks, which must be inside the limits specified by the local regulations. Hence, to accurately evaluate exhaust and intake designs to ensure acceptable air quality inside and around buildings, careful design is needed [17]. Furthermore, this task is even more critical when a by-pass stack is present, as clearly highlighted in [18]. Noise levels. Lack of sound attenuation can cause objectionable noise levels. Thus, exhaust silencers inside the stacks have to be considered in the design in order to mitigate sound emissions deriving from the gas turbine exit. In particular, differences arise whether the two stacks solution is used or not. If two stacks are present, one silencer for each stack has to be used. Moreover, the silencer in the by-pass stack should be larger than that in the main stack since the noise reduction due to the passage of the fluid through the tube banks of the HRSG is absent. If the one stack solution is instead adopted, only one silencer in the main stack could be sufficient to ensure acceptable noise abatement. However, if necessary, an additional silencer can be added in the by-pass duct which, anyway, could be considerably smaller than the main one. A comprehensive study regarding the interaction between fluid dynamic and acoustic noise in gas turbine exhaust systems can be found in [12]. Thermodynamic optimisation. An incorrect fluid dynamic and thermal design can result in excessive pressure drops, efficiency loss and/or in incorrect operation. Structural design. The stack is subjected to stresses deriving from dead loads, live loads and from temperature non-uniformity. In the first kind are included the structure self-weight. The second kind of stresses is typically originated by aerodynamically induced vibration due to vortex shedding caused by wind and/or by internal fluid dynamics effects such as sudden changes of the direction of the gas stream. Finally, the third source can be originated if non-homogeneous temperature distribution along the stack walls is present. Hence, poorly designed sections of the stack can result in an unbalanced system, in an incorrect operation and, in the worst case, in structure failure. Economical issues. Initial investment, system operating and maintenance costs as a part of the overall plant business plan are obviously a key parameter to keep under control by the stack
designer. Moreover, a wrongly designed stack can cause high pressure drops, which cause loss of production and, thus, loss of plant profitability. Both the two stacks and the single stack arrangements have advantages and disadvantages. However, the second solution seems to have some winning advantages at least in terms of costs and environmental impact. In fact, the presence of only one stack instead of two can reduce emission dispersion problems, can have a lower impact on architectural landscape and could be economically convenient. On the other side, problems related to the design of the by-pass/stack junction (mixing of two gases with a high temperature difference, additional pressure drops) can arise. To properly take into account all the features outlined, an integrated multidisciplinary analysis can be the right approach for an optimal system design. In power plant design, usually the structural (FEM) and fluid dynamic (CFD) numerical analyses are dealt separately, with only minor and simplified reciprocal integration. In this paper, the analysis of the exhaust gas system of a cogeneration plant is performed with a CAD/CFD/FEM integrated procedure, outlined in Fig. 2. The procedure was performed through the EFDLab software, which is a three-dimensional CFD numerical code fully embedded with a CAD solid modeller based on SolidWorks engine. At the time of the work, the EFDLab software did not still have the FEM solver integrated with the CAD and CFD modules. Hence, the structural analysis was performed by using the CosmosWork software. 2.3. Numerical models and gridding issues The EFDLab solver [19] uses a rectangular mesh automatically distinguishing the fluid and solid domains in the computational domain. The algorithm to generate the mesh is based on the geometrical discontinuity or ‘‘gap size” and it increases the number of cells in proximity of narrow channels, corners gaps, etc. Mesh cell sides are orthogonal to the specified cartesian co-ordinate system axes and are not fitted to the solid/fluid interface. Hence, a partial cell approach is used, in which the solid/fluid interface cuts the near-wall mesh cells and the mass and heat fluxes are treated properly with a special algorithm. The code solves the Navier–Stokes equations through a Reynolds averaged approach and uses a finite volume method for the equation discretisation. A second-order upwind approximation is used for the advection terms. Following the SIMPLE approach, an elliptic type discrete pressure equation is derived by algebraic transformations of the originally derived discrete equations for mass and momentum. A multigrid method is then used to accelerate the solution convergence. For turbulence modelling, the low Reynolds number k–e model as in the Lam–Bremhorst formulation is used [20]. In this model, the turbulent eddy viscosity is given by
lt ¼ qC l fl k2 =e
ð1Þ
and, while the equation for the turbulent kinetic energy k is in the usual form, the equation for its dissipation e is modified as follows.
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Geometry exchange [standard (IGES,STL), integrated ]
CAD
Grid generator Post-processing and result analysis
Mesh optimisation surface FEM volume CFD
Fig. 2. CAD/CFD/FEM integrated procedure.
De o ¼ Dt oxj
lþ
lt o e e oU i oU j oU i e2 þ q C 2 f2 þ C 1 f1 re oxj k oxj oxi oxj k
duce thermal power through the HRSG, which is used to produce heat for district heating during winter and to feed an absorption chiller during summer. The plant is based on a thermal-following management, i.e. the plant was designed to meet the thermal demand of the site in which it was located. Hence, a first-level regulation of the thermal demand is performed by regulating the GT load (through the combined action of the IGV and of the fuel mass flow rate). Then, when the heat requested by the users (district heating or absorption chiller) is lowered below the minimum acceptable working condition of the GT (imposed by the maximum allowable emission levels), a second-level regulation of the heat is performed in a dissipative way by acting on the by-pass valve and exhausting the hot gases to the atmosphere. This allows the plant owner to keep the GT turbine working and, thus, generating profit by selling the electric energy. In any case, the wasted thermal power has to be controlled in order to keep the primary energy saving (PES) index above the value fixed by the local regulation; if this limit value is passed, the plant is forced to be shut down. Since the plant is located in a high-density urban area, a single stack configuration was adopted for the by-pass of gases. In the plant lay out, the by-pass duct (inside which a silencer was positioned) was joined to the stack through a 135° junction located
ð2Þ
Following [20], the parameters f1, f2 and fl for near-wall resolution are defined as
f1 ¼ 1 þ
3 2 0:05 and f 2 ¼ 1 eRt fl
fl ¼ 1 e0:0165Rk
2
ð3Þ
20:5 1þ Rt
ð4Þ
where and Rt = q k2/(l e) and Rk = q k0.5 y/l are turbulence Reynolds numbers. 3. Problem statement The problem under investigation refers to the design of an exhaust system of a cogeneration plant (Fig. 3a) composed of a single shaft 4.2 MW gas turbine, used for power generation, followed by a horizontal type HRSG for heat production. Between the GT and the HRSG a by-pass system, guided by a diverter valve, is present. The cogeneration plant under investigation was conceived to produce electric power with the GT, which is sold to the grid, and to pro-
a b
C
Db = 1.3 m
Hs = 30 m
T Main stack silencer
F
CC
Ds = 1.4 m
Main stack silencer
By-pass duct
By-pass silencer
inlet 2 (from GT)
HRSG
D
GT
inlet 1 (from HRSG)
Fig. 3. Cogeneration plant under consideration (a) and stack solid model (b).
M. Pinelli, G. Bucci / Applied Energy 86 (2009) 857–866
at 25% of the total stack height, while the HRSG exit gases entered into the stack at its base after a 90° bend. Over the by-pass junction, a main silencer is present. The necessity of re-design of the stack/by-pass system arose since during the first part of the plant life a relevant deflection of the stack vertical axis was noticed which caused more than one stop of the entire plant. Subsequently, some displacement measurements were performed on the structure in correspondence of the roof of the silencer (z = 15 m). At this height, a deviation from the vertical axis of the stack as equal to 0.24 m was measured, which, in turn, caused a calculated deflection of the stack top of about 0.60 m. Hence, the fluid dynamic and structural numerical calculations were performed to detect the source of this deflection and to search for a suitable solution in terms of fluid dynamic optimisation and economic impact. 3.1. Numerical approach The solid model of the stack is reported in Fig. 3b. The domain considered during the numerical simulation was only the exhaust duct geometry. The two gas streams arriving from the HRSG and from the GT, which are at different temperature, enters the domain considered through the openings at the stack base and at definite section along the by-pass (inlet 1 and inlet 2 in Fig. 3b). Since the aim of the paper is to compare different design solutions rather than obtaining accurate results in terms of absolute values, the two gases entering the domain were considered as standard air. Moreover, the problem was considered incompressible. This hypothesis was considered acceptable since the pressure differences inside the entire domain remains very small with respect to the absolute pressure of the fluid. Thus, fluid density was considered dependent only from temperature. For the molecular viscosity and the specific heat, a second-order dependency from temperature was considered. 3.2. Boundary conditions The most robust boundary conditions were found to be imposed temperature and mass flow rate at the inlet for both the gas streams and an outlet average static pressure at the stack exit. The temperature, pressure and mass flow rate values adopted are referred to a representative working condition of the plant. The working condition considered is characterised by gas turbine at full load (Pel = 4.2 MW) and standard ambient conditions (Tamb = 15 °C, pamb = 101,325 Pa, RH = 60%). The values of the imposed boundary conditions were obtained by experiments. The total mass flow rate entering the stack was set equal to 17.3 kg/s. Different ratio between the main gas stream mass flow rate (from HRSG) and the by-passed gas stream mass flow rate (directly from the GT) have been considered. However, a series of trials on the plant showed that the most critical condition for temperature non-uniformity is when the by-passed gases are the 50% of total mass flow rate exiting the gas turbine. Regarding the thermal boundary conditions, two different imposed temperatures were set. In particular, the temperature of the gas from the HRSG (inlet 1) was set as equal to 120 °C and the temperature of the gas from the gas turbine (inlet 2) was set as equal to 537 °C. These values remained the same for all the cases considered. No heat flux was considered at the stack walls since the walls are externally insulated. This hypothesis can be considered acceptable considering that the global heat transfer coefficient between internal gas flow and ambient air was estimated to be always less than 1.0 W/(m2 °C). Therefore, the coupling with the environment can be neglected. Finally, at the stack exit, the standard value of atmospheric pressure was used (pamb = 101,325 Pa).
861
3.3. Grids The domain region was divided in sub-regions separately gridded in order to generate a regular mesh. In this manner it was possible to obtain a good quality grid with refinement in areas of most concern in the simulation. The number of grid cells was different for each calculation. Grid independence issues were carried out separately: the number of cells used within each calculation was chosen accordingly. 4. Results and discussion 4.1. Case (a). Baseline configuration The baseline configuration of the stack of the plant (for which the main geometric characteristics are reported in Table 1) has been initially studied. The following numerical procedure was carried out: 1. The actual geometry of the stack/by-pass system was modelled through the three-dimensional CAD (in Fig. 4a, a particular of the stack/by-pass junction geometry is reported). 2. The geometry was then gridded. The total number of grid cells resulted equal to 70,825. This amount was considered acceptable to balance between calculation accuracy and computational time. 3. The CFD simulation was performed through the fluid dynamic module. As inlet mass flow boundary conditions, the mass flow rate was considered equally distributed between the two inlets of the stack (50% from HRSG and 50% from GT). 4. The numerical results were analysed. In Fig. 4b, the temperature distribution near the by-pass region is reported on a longitudinal mid-plane. It can be seen that when the hot gas stream enters inside the stack, it tends to ‘‘stick” on one side of the stack wall (Zone 2) greatly enhancing its temperature. On the diametrically opposite side located at the same height (Zone 1), instead, the stack walls are ‘‘cooled” by the cold gas stream arriving from the bottom and, consequently, the temperature in these zones remains low. Thus, the temperature field inside the stack walls results highly non-uniform. A temperature difference DTw of nearly 400 °C between Zone 1 and Zone 2 was calculated. This analysis suggested that the possible cause of the stack deformation could effectively be the temperature nonuniformity inside the stack walls. In fact, a consequent non-uniformity of the strain field is originated, which, in turn, causes a different elongation of the material (steel) in Zone 1 and Zone 2 and, in turn, the deformation of the stack. 5. To confirm the observation made in the previous step, the calculated temperature distribution was used as a boundary condition for the FEM simulation, through which a numerical structural analysis was performed. The FEM calculations confirmed the hypothesis that the non-uniform temperature distribution was the cause of the stack deflection. In fact, the deflection of the stack in correspondence of the silencer roof (z = 15 m) was calculated equal to 220 mm, which is a value in very good agreement with the available experimental data (Table 2).
Table 1 Stack geometric characteristics Total height Silencer width By-pass junction height Main stack diameter By-pass duct diameter
32.0 m 4.5 m 8.0 m 1.4 m 1.3 m
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Fig. 4. Baseline stack-by-pass geometry (a) and temperature distribution (b).
Table 2 Numerical and experimental stack deformation at z = 15 m Deviation from stack vertical axis Numerical result Experimental data
0.22 m 0.24 m
In conclusion, through the integrated CFD/FEM calculation, it was possible to individuate the cause of the stack distortion. Moreover, this result was considered as a good validation of the code and, more in general, of the entire calculation procedure. Once the problem has been detected and the code has been validated, other possible stack/by-pass junction design solutions have been considered and analysed numerically. The most interesting are presented in the following and discussed in detail. 4.2. Case (b). Single-pipe configuration In order to overcome the structural problems outlined above, the solution presented in Fig. 5a was evaluated. The by-pass proposed is composed of a circular duct which enters the main stack perpendicularly. Then, the hot gas stream is forced to change its direction through a 90° pipe-shaped duct concentrically located inside the stack. In the stack zone in which the by-pass duct enters, the stack transversal section has been augmented from 1.4 m to 2.0 m to properly locate the pipe. The computational strategy to perform the simulation was the same used in Case (a). The mass flow was considered equally distributed between the two inlets. The final mesh consisted of 71,356 cells. The temperature distribution in a longitudinal mid section obtained from the CFD calculation is reported in Fig. 5b. The temperature field shows that the hot stream is now detached from the wall near the by-pass duct junction but, at the same time, this hot stream is brought closer to the opposite wall. It is possible to notice that, even if in a lesser degree, high temperature differences between different zone at equal height are still present, and, thus, the risk of thermally-induced structural problems are not completely avoided. As can be seen from Fig. 5c, which reports the temperature profile along a radius located at a stack height of z = 12.5 m (just upstream the silencer), the maximum calculated temperature difference between opposite-located zones is considerably reduced (DTw = 228 °C). In Fig. 6 the temperature distribution in three transversal sections at different stack heights (z = 10.5 m, 11.5 m and 12.5 m, respectively) are reported. By analysing in detail this three-dimensional pattern of the temperature field, the hot core inside gas stream is still noticeable near stack walls, also in the zones located just upstream the silencer.
Moreover, from the analysis of the figure, it can be seen that the hot core of the stream is rotated of about 45° anticlockwise going from the lower to the upper section, thus suggesting that, after the by-pass duct, a swirling velocity component is present. As a first modification of this arrangement, the pipe was positioned eccentrically with respect to the stack axis. In particular, the pipe vertical axis was brought closer to the wall in which the stack/by-pass junction is located. Moreover, the convergent between the pipe and the silencer was eliminated. The analysis of the results shows that the new configuration did not allow a significant improvement neither regarding the temperature differences nor the swirling pattern of the stream. 4.3. Case (c). Three-pipe configuration To minimise the wall temperature differences and the swirling pattern of the flow, which can cause additional pressure drops and flow instabilities, a three-pipe configuration has been studied. In Fig. 7a, the geometry of the proposed by-pass duct is presented. It consists of three concentric ducts, eccentrically set with respect to the stack axis, which guide the fluid toward the stack axis. Also in this case, in the zone in which the by-pass duct enters, the stack transversal section has been augmented from 1.4 m to 2.0 m. The generated mesh consisted of a total number of 74,897 cells. The mass flow was considered equally distributed between the two inlets. In Fig. 7b, the temperature distribution in a longitudinal mid section along the stack vertical axis is presented. It can be noticed that the hot core of the stream is distant from the walls and it is well confined in the inner zone of the stack. The hot core of the stream moves through the stack in a very regular way and remains detached from the walls also away from the pipe. In Fig. 7c, the temperature profiles along two different radius (located at a stack height of z = 9 m and z = 13.5 m, respectively) are reported. It can be noticed that immediately after the stack/ by-pass junction there is not temperature difference between opposite-located zones. Moreover, the temperature difference in the most critical zone, which is at z = 13.5 m and was detected after the post-processing of the results, the calculated maximum temperature DTw is dropped down to 137 °C. In Fig. 8, the temperature fields in four sections at different stack heights are reported. The gas stream coming from the bypass presents a regular structure and a well-defined vertical direction, which allow a regular flow pattern in terms of both velocity distribution and temperature. The hot core of the stream remains detached from the walls also away from the pipe. Moreover, the swirling characteristic seems to be completely suppressed.
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Fig. 6. Single-pipe configuration: temperature distribution at different height.
4.4. Economic considerations Both the two configurations proposed since now showed good thermal and fluid dynamic characteristics, as highlighted by the CFD calculation. However, it must also be considered that the stack/by-pass configuration is to be seen as a part of the GT/HRSG system, and, thus, the consequences of these modifications have to be investigated also considering their inclusion in the entire plant lay-out. In particular, a very important issue is represented by the
additional pressure drops which may occur along the gas path. In fact, pressure drops at the turbine exhaust negatively influence the gas turbine efficiency and power output and, thus, their increase can have relevant influence on the profitability of the power plant. Indeed, minimisation of the gas-side pressure drop is a relevant issue in HRSG optimisation [5]. For these reasons, the pressure drops between the base and the top of the stack have been calculated for the baseline configuration and for the two new solutions (single-pipe and three-pipe
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Fig. 7. Three-pipe configuration: (a) geometry; (b) temperature distribution at midsection and (c) temperature profile at midsection and at different heights.
Fig. 8. Three-pipe configuration: temperature distribution at different heights.
configuration). The calculations were performed by considering the flow entirely coming from the HRSG exit, which is the most frequent and, in terms of total stack pressure drop, the most penalising working condition. To obtain the magnitude of the power output DPloss and efficiency loss Dgloss due to the additional stack pressure drop Dpadd, it is possible to use: (i) the correction curves supplied by the manufacturer, which reports the power loss magnifying factors as a function of the exhaust pressure loss; (ii) analytical relations based on thermodynamic considerations. The first are more accurate but not always available while the second are simplified but general. In this case, the second method was adopted by using an equation proposed by Lozza [11] for DPloss, valid for single shaft gas turbines:
DPloss ¼
_ out ðgel go gis Þt mRT Dpadd pamb
Since the exhaust pressure drop does not influence the fuel consumption, the value of Dgloss is directly related to the value of DPloss. The results are reported in Table 3. The percentage efficiency loss is evaluated referring to a yearly-averaged efficiency of the GT = 0.25. As gas turbine, which, in this case, was estimated as g can be seen, the additional pressure drops caused by the singleand the three-pipe configurations are practically equal, as expected, and the power output decrease and the efficiency loss are rather low in both cases.
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M. Pinelli, G. Bucci / Applied Energy 86 (2009) 857–866 Table 3 Calculated pressure drop due to stack and additional power output and efficiency losses
Case (a). Baseline configuration Case (b). Single-pipe configuration Case (a). Three-pipe configuration
Dps (Pa)
Dpadd (Pa)
DPloss (kW)
Dgloss (%)
238 460 465
– 222 227
– 7.38 7.55
– 0.308 0.315
However, if an economic evaluation on the basis of the plant entire life is performed, the adoption of these solution can cause profitability losses which can be significant. In fact, assuming that (i) the working hours per year of the plant are 7000 h, (ii) even if the cost of the fuel (natural gas) for a 4.2 MW cogeneration plant located in Italy can vary significantly, a reference illustrative value can be set at 0.40 €/Sm3, (iii) the plant is managed as to achieve in the following years the same electric energy production and (iv) an yearly-averaged natural gas LHV equal to 48,000 kJ/kg; hence, with the figures stated above, which are illustrative but realistic, the total profitability loss of the plant would be roughly equal to 8800 €/year and to 9000 €/year for the single- and the three-pipe configurations, respectively. Then, if the expected working life of the plant (more than 20 years) is included in this evaluation, it is evident the importance of evaluating the criticality of the action that has to performed on the stack.
a
4.5. Case (d). Baffle configuration As a result of the analysis performed above in terms of both thermodynamic and economical point of view, another by-pass junction was designed and analysed. The objective of this new design was the effort to obtain a compromise between minimal pressure drops, and thus minimal profitability losses, and avoidance of structural stresses. The new geometry has the same configuration of the baseline design with the by-pass/stack junction performed through a 135° connection. To avoid the direct contact of the hot stream coming from the by-pass with the stack walls, the by-pass duct has been extended inside the stack by adding an appropriately shaped baffle which drives the hot stream towards the stack axis. In the numerical calculation, the mesh used consisted of 80,000 cells. The baffle geometry and a particular of the mesh refinement near the baffle is shown in Fig. 9a. The mass flow was considered equally distributed between the two inlets.
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In Fig. 9b the temperature distribution in a longitudinal mid section inside the stack is presented. It is clearly noticeable that the hot stream of the core is correctly driven to occupy the central region of the stack, and it is sufficiently detached from the stack walls. In the region near the by-pass/stack junction, the calculated wall temperature difference DTw is almost equal to 250 °C. In addition, in Fig. 9c it is possible to notice that the temperature field on the stack walls surface presents an acceptable uniformity. Finally, the analysis of the pressure distribution revealed that the pressure drop is almost equal to the baseline configuration. Hence, this geometry, even if does not allow a regularity of the temperature and flow field distribution as good as the one obtained with the three-pipe configuration, has some advantageous features, which are: (i) it does not introduce additional pressure drops which, as demonstrated, can cause power output and, thus, profitability losses; (ii) it allow the obtaining of reasonable temperature differences between different zones of the stack walls; (iii) it is the solution which implies reduced actions on the baseline structure and, thus, very low additional costs. For these reasons, this solution was considered for the stack modification. The FEM analysis was performed in order to verify if the structure could effectively originate a benefit in terms of stresses and strains. Hence, following the procedure outlined in the previous paragraphs, the temperature field inside the stack walls obtained with the CFD calculation were used as boundary condition in the FEM calculation. The calculation confirmed that the stresses on the structure should have values well below the resistance limits imposed by the materials adopted. 5. Conclusions The analysis of different stack design solutions in a cogeneration power plant has been performed by using a multidisciplinary analysis. In particular, in the plant considered the exhaust gas system consists of a single steel stack through which both the main and the by-passed gas streams are ejected. This solution, which can have advantages in terms of costs, presents some design difficulties due to the mixing of two gas streams with a high temperature difference. In particular, a thermal-induced stresses appeared, which originated a deflection of the stack. The developed CAD/CFD/FEM integrated procedure demonstrated the effectiveness of these kind of analyses in the optimised design of the exhaust system of the plant considered. The coupled CFD/FEM numerical calculation allowed the detection of the struc-
tural problem of the analysed stack. Regarding economical issue, the calculation of the pressure drops along the stack showed that a wrongly designed duct lead to profitability losses which, in a long-period time frame, can be significant. Acknowledgement The Authors gratefully acknowledge: Prof. R. Bettocchi and Prof. P.R. Spina for the helpful discussions and suggestions; Ing. L. Begani and P.i. S. Tassoni for the information provided. References [1] Pilavachi M. Power generation with gas turbine systems and combined heat and power. Appl Therm Eng 2000;20:1421–9. [2] Zachary JJ. Strategies for integration of advanced gas and steam turbines in power generation applications. ASME Paper GT2007-27978. [3] Franco A, Russo A. Combined cycle plant efficiency increase based on the optimization of the heat recovery steam generator operating parameters. Int J Therm Sci 2002;41:843–59. [4] Franco A, Giannini N. A general method for the optimum design of heat recovery steam generators. Energy 2006;31:3342–61. [5] Torresi M, Saponaro A, Camporeale SM, Fortunato B. CFD analysis of the flow through tube banks of HRSG, ASME Paper GT2008-51300; 2008. [6] Sunil Kumar Vylta VV, Huang GPG. CFD modeling of heat recovery steam generators using fluent. 30th annual dayton-cincinnati aerospace science symposium; 2000. [7] Hegde N, Han I, Lee TW, Roy RP. Flow and heat transfer in heat recovery steam generators. J Energy Res Tech 2007;129(3):232–42. [8] Bell MB, Nitzken JA. Controlling steam production in heat recovery steam generators for combined cycle and enhanced oil recovery operations. Las Vegas, Nevada: Proceedings of POWER-GEN International; 2003. [9] Tomlinson LO, Mc Cullough S. Single-shaft combined-cycle power generation systems. Technical Report No. GER-3767 B GE Power Systems; 1996. [10] Nestianu D, Larson T, Lynch L, Zachary J. Vertical or horizontal? An EPC contractor’s angle. Modern Power Syst 2003;23(3):19–22. [11] Lozza G. Turbine a gas e cicli combinati. Bologna: Società Editrice Esculapio; 1996. [12] Rieckmann J, Laquinnia L, Alexander A, Graham J. Acoustic considerations for gas turbine: intake and exhaust systems. Cogeneration and on-site power production 2004;5(2):35–42. [13] Lee BE, Kwon SB, Lee CS. On the effect of swirl flow of gas turbine exhaust gas in an inlet duct of heat recovery steam generator. J Gas Turb Power 2002;124:496–502. [14] Stehlik P. Heat transfer as an important subject in waste-to-energy systems. Appl Thermal Eng 2007;27:1658–70. [15] Horlock JH. Combined power plants including combined cycle gas turbine (CCGT) plants. Oxford: Pergamon Press; 1992. [16] Brandstetter G, Daublebsky C. Investigations on dynamic behaviour of heat recovery steam generators carried out with a commercial software program. ASME Paper GT2007-27380; 2007. [17] Petersen RL, Cochran BC, Carter JJ. Specifying exhaust and intake systems. ASHRAE J 2000;8:12–8. [18] Bell B. Air dispersion modelling – cockburn power project gas turbine bypass stacks proposal. Technical Report Western Power Corporation ENVIRON, Australia; 2002. [19] EFDLab. User Manual. Germany; 2006. [20] Lam CKG, Bremhorst K. A modified form of the k–e model for predicting wall turbulence. J Fluids Eng 1981;103:456–60.