Abstract:
An axial/radial three-channel diffuser is provided with two guide plates for dividing the diffuser into three partial diffusers that are distributed so that the distribution of the surface area over the three partial diffusers in the inlet surface area is uneven. The guide plates are oriented in accordance with the total pressure field after the last rotating blade row and are arranged at a minimum distance from the trailing edge of the last rotating blade row. Because of its long extension in relation to the channel heights of the partial diffusers, the three-channel diffuser brings about a gentle deflection of the diffuser flow. The diffuser according to the invention results in an improved pressure recovery and increased turbine performance.

Description:
FIELD OF THE INVENTION  
         [0001]    The invention relates to an axial-flow low-pressure steam turbines and to axial/radial multi-channel diffuser and waste steam housing for guiding the waste steam from the blades with few losses.  
         BACKGROUND OF THE INVENTION  
         [0002]    A diffuser of this type is described in DE 44 22 700. The diffuser disclosed in this document is provided after the last row of rotating blades of a low pressure steam turbine with an axial flow inlet and a radial flow outlet. The diffuser is designed with respect to optimized turbine performance by way of the greatest possible pressure recovery. For this purpose, the first partial pieces of the inner and outer diffuser ring each are oriented in relation to the hub or, respectively, the blade carrier, with an inflexion angle. This measure serves to homogenize the total pressure profile above the channel height of the diffuser in the area of the last row of rotating blades. The diffuser furthermore is provided with a radially outward curved guide plate that divides it into an inner and an outer channel. Hereby flow ribs impacted by the flow either radially or diagonally have been provided in the outer and inner channel. The guide plate is used both for deflecting and guiding the waste stream. The flow ribs have the purpose of supporting the guide plate and, in particular, reduce the spin in the delay zone, so that they also contribute to an optimization of the pressure recovery. However, realized flow ribs only are able to achieve optimum spin reduction with a specific operating load. At a different operating load, the spin reduction is not necessarily optimized. A diffuser with this kind of measure therefore only achieves optimum pressure recovery at a certain operating load. The flow ribs and their attachment to the guide plates furthermore are associated with relatively high construction expenditure. In addition, the supersonic gap flow interferes with the remaining subsonic flow.  
           [0003]    EP 581 978, especially in FIG. 4 of this publication, discloses a multi-channel waste gas diffuser for an axial-flow gas turbine with axial flow inlet and radial flow outlet. This multi-channel diffuser is provided with three zones along its length. The first zone is constructed in the manner of a bell diffuser and extends as one channel from the last row of rotating blades to the outlet plane of several flow ribs. Here also, the diffuser rings are provided with inflexion angles that have been established so that the total pressure profile is homogenized. Downstream from the flow ribs, the second zone has flow-guiding guide rings that form several channels. The third zone is used for a major deflection of the waste gas flow in radial direction and then merges with the chimney of the gas turbine. For this purpose, the guide rings of the second zone are extended across the length of the third zone, whereby they are curved there. The second zone has a minor deflection yet high diffuser effect; the third zone a major deflection, yet has a very moderate diffuser effect.  
         SUMMARY OF THE INVENTION  
         [0004]    It is the objective of the present invention to create, for a low-pressure steam turbine, an axial/radial multi-channel diffuser with waste steam housing that, in comparison to diffusers according to the state of the art, achieves an improved steam recovery, thus increasing the effectiveness of the low-pressure steam turbine. In addition, the multi-channel diffuser should be simultaneously optimized for as many operating conditions of the steam turbine as possible and should be associated with reduced construction expenditure. Finally, the waste steam housing should be adapted to the diffuser with respect to turbine performance.  
           [0005]    The three-channel diffuser is provided with three partial diffusers, i.e., an inner, middle, and outer partial diffuser, which are formed by an inner diffuser ring, and outer diffuser ring, and two guide plates provided between the diffuser rings. A first partial piece of the inner diffuser ring is hereby arranged in relation to the hub at an inflexion angle oriented inward, towards the rotor axis, and a first partial piece of the outer diffuser ring is arranged at an inflexion angle oriented outward in relation to the blade channel at the level of the last row of rotating blades, away from the rotor axis.  
           [0006]    In the axial/radial three-channel diffuser according to the invention, in particular, the two guide plates extend across the entire length of the diffuser. They are unevenly distributed between the inner and outer diffuser ring, so that the distribution of the surface area over the three partial diffusers in the inlet surface area of the diffuser is uneven. In the inlet plane, the majority of the inlet surface area hereby is part of the inner and middle partial diffuser, and a small part of the inlet surface area is part of the outer partial diffuser. Furthermore, the starting tangents of the two guide plates, together with the limits of the blade channel on the hub side and housing side, which approximate each other in a straight line, form an at least approximately common intersection point above the end stage of the low-pressure steam turbine in the meridian plane. Finally, the guide plates are located as close as possible to the last row of rotating blades, whereby the distance between the last rotating blade row and the leading edges of the guide plates are determined by the minimum distance that is permissible for all operating conditions.  
           [0007]    This describes the characteristics of the diffuser in its interaction zone with the last stage.  
           [0008]    The diffusion zone of the diffuser is characterized by the following characteristics.  
           [0009]    The ratio of the outlet surface area to the inlet surface area of the individual partial diffusers is greater than 2 for the middle partial diffuser and smaller than 2 for the outer partial diffuser. For the inner partial diffuser, the corresponding geometric surface area ratio ranges from 1.5 to 1.8.  
           [0010]    Furthermore, for the middle partial diffuser, the ratio of its length to its channel height in the inlet surface area is at least equal to 4. For the outer partial diffuser, the ratio of length to channel height in the inlet surface area is at least equal to 10, and for the inner partial diffuser, the corresponding ratio is at least equal to 2.5. Based on these relatively high length to channel height ratios, the deflections of the partial diffusers are accordingly relatively small.  
           [0011]    The ratio of the outlet surface area to the inlet surface area of the diffuser overall is approximately 2.  
           [0012]    Finally, the waste steam housing of the diffuser is designed so that the size of the surface area of the dividing plane between the top and bottom half of the waste steam housing is adapted to the size of the outlet surface areas of the partial diffusers.  
           [0013]    The two guide plates hereby are used to divide the diffuser channel into three partial diffusers in which the blade waste flow is guided. The resulting flow guidance is hereby the better, the more partial diffusers are present for the same overall diffuser. In contrast, the more guide plates are provided, the more friction losses and obstructions are created. The number chosen here, i.e., three partial diffusers and two guide plates, has the advantage that optimized flow guidance is achieved with justifiable friction losses at the guide plate surface areas and obstructions.  
           [0014]    The guide plates and partial diffusers bring about a guidance and stabilization of the blade waste flow as well as a deflection into a radial direction. Since the guide plates extend over the entire length of the diffuser, this guidance is further supported.  
           [0015]    The radial extension of the partial diffusers furthermore is used to naturally reduce the tangential speed. Because of this, the partial diffusers are optimized for all operating conditions with respect to a reduction of the tangential speed. The construction expenditure for the guide plates is also rather low, and the reduction of the tangential speed does not require any further constructive measures, such as deflection and flow ribs.  
           [0016]    The flow guidance and stabilization is further brought about, in particular, by distributing the diffuser inlet surface area over the three partial diffusers. A majority of the inlet surface area is part of the inner and middle channel, so that the majority of the flow is guided from the blades to the waste steam housing. The smaller part of the inlet surface area is part of the outer channel, through which the supersonic gap flow as well as the flow from the turbine influenced by the gap flow is taken up and is deflected meridionally and is guided, shielded from the majority flow, to the waste steam housing. This shielding prevents flow interferences between the majority flow and the high-energy gap flow that would interfere with the diffuser effect.  
           [0017]    The minimum distance between the last row of blades and the leading edges of the guide plates further promotes an optimal shielding of the gap flow and prevention of flow interferences and streamline convergences.  
           [0018]    The ratio of length to channel height of each partial diffuser of 2.5 or more enables a gentle deflection from the axial or diagonal to the radial flow direction, which prevents separation of the delayed flow even at a ratio of outlet surface area to inlet surface area of 1.6.  
           [0019]    The guidance and stabilization of the blade waste flow through the three partial diffusers, the shielding of the high-energy gap flow as well as the gentle deflection based on the length of the channels in relation to their channel heights overall achieve a homogenization and reduction of the total pressure profile at the level of the last row of rotating blades. The resulting added performance results in an increased efficiency of the low-pressure steam turbine.  
           [0020]    The design of the diffuser according to the invention is based on a reverse design process, during which the existing flow fields are determined first. Then the respective ideal flow fields are calculated from this, and the geometry of the diffuser is determined based on these ideal flow fields. In particular, this three-channel diffuser has been designed at limit load conditions. At the limit load, a flow field, for which a three-channel diffuser with an orientation of the starting tangent of its guide plates according to the invention achieves the highest pressure recovery, was determined. It was established experimentally, that the geometry resulting from this design is superior to the state of the art diffusers over the entire operating range. This design furthermore has the advantage that a higher turbine performance is achieved with the same condenser pressure, or that the same turbine performance is achieved with a higher condenser pressure, so that a smaller, cheaper cooling system is required for the steam turbine.  
           [0021]    Special embodiments of the invention below disclose additional, special characteristics of the interaction zone of the diffuser.  
           [0022]    In a first, special embodiment of the invention, the starting tangents of the guide plates are in an angle range around the first inflexion point of the guide plates and around a reference starting tangent that extend at least approximately through the first inflexion point of the guide plate and through the inflexion point of the blade channel limits that approximate each other in a straight line.  
           [0023]    In another special embodiment of the invention, the outer partial diffuser accounts for a part of the entire flow inlet surface area of the diffuser in the range from 10-12%. Of the remaining inlet surface area, 55-60% is distributed to the inner partial diffuser, 30-35% to the middle partial diffuser.  
           [0024]    In another embodiment, the distance between the leading edges of the guide plates and the trailing edge of the last rotating blade accounts for 4% of the entire height of the rotating blade row.  
           [0025]    In another embodiment, the leading edges of the guide plates are constructed with a profile at the flow inlet of the diffuser, resulting in a gentle acceleration at the inlet into the partial diffusers.  
           [0026]    In additional embodiments, the diffusion zone of the diffuser is characterized as follows.  
           [0027]    The guide plates each are carried by struts or supports extending from the inner and outer diffuser ring to the two guide plates. The middle partial diffuser remains free from any supports and therefore has minimal flow interference and losses.  
           [0028]    In another, special construction of the waste steam zone of the diffuser, a waste steam metal plate is arranged in a radial extension at the end of the guide plate between the inner and outer partial diffuser. This waste steam guide plate achieves a better flow distribution in the waste steam housing, so that flow losses are minimized and the condenser is supplied more evenly. 
       
    
    
     BRIEF DESCRIPTION OF DRAWINGS  
       [0029]    Preferred embodiments of the invention are described with reference to the accompanying drawings, in which  
         [0030]    [0030]FIG. 1 is a vertical cross-section of a diffuser with a waste steam housing according to the invention,  
         [0031]    [0031]FIG. 1 a  is a detail view of the interaction zone of the diffuser on the cylinder side,  
         [0032]    [0032]FIG. 1 b  is a detail view of the interaction zone of the diffuser on the hub side,  
         [0033]    [0033]FIG. 2 is a detail cross-section of the profiled leading edges of the guide plates at the diffuser inlet,  
         [0034]    [0034]FIG. 3 is a cross-section through a waste steam housing of the diffuser,  
         [0035]    [0035]FIG. 4 is a cross-sectional view along the dividing plane between the upper and lower half of the diffuser,  
         [0036]    [0036]FIG. 5 is a vertical cross-section of another embodiment of the diffuser with waste steam housing, according to the invention,  
         [0037]    [0037]FIG. 6 is a cross-sectional view along the dividing plane between the upper and lower half of the embodiment of FIG. 5. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0038]    [0038]FIG. 1 shows a three-channel diffuser as part of a low-pressure steam turbine. It guides the blade waste flow into a waste steam housing  20 . Of the low-pressure steam turbine, the rotor  1  with rotor axis  2  and a rotating blade  3  of the last row of rotating blades is shown. An inner diffuser ring  4  and an outer diffuser ring  5  limit the three-channel diffuser. The outer diffuser ring  4  is connected to the blade carrier  7 . The inner and outer diffuser rings  4  and  5  are provided in the surface area of the trailing edge of the rotating blade  3  with an inflexion angle N or, respectively, z, whereby, as shown in FIGS. 1 a  and  1   b , the angle N is formed by the first partial piece  4 ′ of the inner diffuser ring  4  and an extension of the hub  6 , and the angle Z is formed by the extension of the last partial piece  7 ′ of the blade carrier  7  and the first partial piece  5 ′ of the outer diffuser ring  5 . These inflexion angles are, for example, 10-20° and help to create the most homogeneous total pressure profile at the outlet of the last row of rotating blades.  
         [0039]    The diffuser is provided on its inside with two guide plates  8  and  9  that divide the diffuser into three partial channels: one inner partial diffuser  10 , one middle partial diffuser  11 , and one outer partial diffuser  12 . The guide plates are hereby carried by supports  13  that extend from the inner and outer diffuser rings  4  and  5  to the guide plates. For stability reasons, the supports  13  located first in the direction of the flow are thicker than the second supports and have been constructed with a round cross-section. The middle partial diffuser  10  is, in particular, free of any supports.  
         [0040]    The guide plates are distributed over the channel height of the diffuser with consideration of the total pressure profile in such a way that a surface area distribution over the three partial channels that is optimized with respect to flow mechanics is achieved. The first guide plate  8  is arranged so that the inner partial diffuser  10  has a flow inlet surface area that is, for example, approximately 60% of the flow inlet surface area of the diffuser overall. The second guide plate  9  is arranged furthermore so that the middle partial diffuser  11  has a flow inlet surface area that is, for example, approximately 30% of the flow inlet surface area overall. In this way, the majority of the total inlet surface area goes to the two first channels  10  and  11 . The outer partial diffuser  12  in contrast has a flow inlet surface area of, for example, approximately 10% of the flow inlet surface area overall.  
         [0041]    The diffuser outlet surface area has been designed so that the ratio of the outlet surface area to the inlet surface area of the diffuser overall, i.e., of its upper and lower half, is approximately 2.  
         [0042]    For the individual partial diffusers, the geometrical ratios of outlet to inlet surface area are as follows.  
         [0043]    For example, for the inner partial diffuser  10 , the ratio of outlet surface area S 12  in the upper half of the diffuser to the inlet surface area S 11  is approximately 1.3.  
         [0044]    The ratio of outlet surface area S 13  in the lower half of the diffuser is greater to the inlet surface area S 11  and is approximately 1.6. The outlet surface area S 13  of the inner partial diffuser  10  is therefore located further outward in the lower half of the diffuser than in the upper half. (It has been designated in this figure and in FIG. 4 with S 13 , even though it is actually located in the bottom half of the diffuser.)  
         [0045]    For the middle partial diffuser  11 , the ratio of the outlet surface area S 22  to inlet surface area S 21  is approximately 2.1.  
         [0046]    For the outer partial diffuser, the ratio of the outlet surface area S 32  to inlet surface area S 31  is approximately 3.3. Such surface area ratios are the condition for being able to significantly increase the effectiveness of the turbine.  
         [0047]    With respect to a gentle guidance of the flow, the diffuser has been designed with a slight curvature in relation to the channel height. For this reason, the three partial diffusers have a high length-to-channel height ratio. For the inner partial diffuser  10 , this is, for example, greater than 2.7 in the lower half of the diffuser. For the middle and outer partial diffuser  11  and  12 , the ratios in the shown example are greater than 4.4 or, respectively, greater than 12. Because of manufacturing technology, the inner and outer diffuser rings as well as the two guide plates have several straight partial pieces in their cross-section, which, because of the high length-to-channel height ratios, are located at slight tilt angles to each other. These slight tilt angles permit improved guidance of the flow coming from the blades. This prevents, in particular, flow interferences and flow separations. Because of the relatively large radial extension of the diffuser and partial diffusers, a natural reduction of the tangential speeds without help from additional flow ribs or other measures for reducing the tangential speeds is also achieved.  
         [0048]    Because of their radial extension, the three partial diffusers have a gentle deflection. The total deflection of each partial diffuser is designed with the angles 1, 2, and 3 in the center line  15  of the individual partial diffusers  10 ,  11  or, respectively,  12 . These angles are, for example, approximately 70°, 36°, or, respectively, 47°.  
         [0049]    The guide plates  8  and  9  are approximately constructed so that the extension of the starting tangents forms the intersection point A. Hereby the limits of the blade channel on the hub side and on the housing side, which approximate each other in a straight line, also runs through this intersection point A. In the shown exemplary embodiment, the starting tangents of guide plates  8  and  9  are oriented relative to the rotor axis  2  at angles 1 or, respectively, 2. In different embodiments of the invention, the intersection point A between the limits of the blade channel on the hub side and on the housing side, which approximate each other in a straight line, over the end stage of the turbine, and the starting tangents of the guide plates  8  and  9  form an at least approximately common intersection point. In the embodiments, the starting tangent of the guide plate  8  encloses an angle in the range from 1+8° with the limit on the hub side that is approximated in a straight line. The starting tangent of the guide plate  9  correspondingly forms an angle in the range of 2±4°  
         [0050]    This geometric design of the guide plates in relation to the limits of the blade channel also applies to other housing contours and blade types, for example, for completely conical, straight housing contours, for housing contours in which the partial piece above the last row of rotating blades extends cylindrically or almost cylindrically. This geometry furthermore not only can be used for rotating blades with tip seal, but also for rotating blades with cover bands. In this case, the housing-side limit of the blade channel runs through the intersection point of the trailing edge of the last rotating blade and the cover band.  
         [0051]    In a real design of the invention, the starting tangents of guide plates  8 ,  9  are in an angle range around the first intersection points B and C of the guide plates  8  or  9  and around the reference tangents that run through the intersection points B or, respectively, C, and through the intersection point A.  
         [0052]    In the shown example, the diffuser rings  4  and  5  and the guide plates  8  and  9  comprise several straight partial pieces that are placed together at small angles of tilt to each other. Instead of partial pieces, continuously curved guide plates and diffuser rings also can be realized.  
         [0053]    The partial diffusers  10  and  11  are arranged so that a main part of the flow flows off from the blades through these two partial diffusers into the waste steam housing  20 . A stable guidance of the main flow part is hereby the most susceptible to obstructions in the range of the middle partial diffuser because of the mach values occurring there. The middle partial diffuser  11  that is free from any supports therefore guides this part of the main flow without additional interference.  
         [0054]    In contrast, the high-energy, supersonic gap flow from the last row of rotating blades reaches the outer partial diffuser  12 , whereby the latter&#39;s channel height is determined in relation to the gap flow present. The gap flow is guided through the outer partial diffuser  12 , separately from the main part of the flow, into the waste steam housing  20 .  
         [0055]    The high length-to-channel height ratios bring about a stabilization of the diffuser flow and homogenization as well as reduction of the total pressure profile at the level of the last row of rotating blades. This increases the pressure recovery of the diffuser and achieves an increase in the efficiency of the low-pressure steam turbine overall.  
         [0056]    At the inlet to the diffuser, the guide plates  8  and  9  extend close to the row of rotating blades. Preferably, they are arranged as close as the axial, thermal movements of the rotating blade row and the safety distance necessary for the different operating conditions allow, without causing contact. For example, the distance a between the leading edges of the guide plates  8  and  9  and the trailing edge of the last rotating blades  3  accounts for 4% of the total height h W  of the last row of rotating blades.  
         [0057]    The leading edges of the guide plates  8  and  9  are also constructed with profiles in order to permit a gentle flow entrance with the smallest possible overspeeds into the partial diffusers. As shown in FIG. 2, the leading edges are, for example, shaped slightly tapered, for example according to the shape NACA  65 , whereby the profiling length e is three times the thickness . The guide plates are also constructed as thin as possible so that the mach numbers are increased slightly, if possible. To achieve this, their thickness is, for example, approximately 5% of the channel height of the middle partial diffuser  11 .  
         [0058]    The as small as possible distance between the leading edges of the guide plates  8  and  9  and the rotating blade row  3  as well as the gentle profiling of the leading edges are a decisive factor for increasing the pressure recovery. If the guide plates are arranged at a greater distance, sound fields and flow interferences may result that would make a pressure recovery in this surface area impossible.  
         [0059]    A waste steam guide plate  8 ′ is arranged in a radial extension at the guide plate  8  between the inner and middle partial diffuser in the shown embodiment. This waste steam guide plate  8 ′ achieves an improvement of the flow in the waste steam housing  20  and a homogenization of the flow in the condenser. The waste steam guide plate  8 ′ has a gentle total deflection L of approximately 50°. In this exemplary embodiment, this deflection is realized with two partial pieces whose ratio of total length to channel length in the outlet plane is approximately 0.7.  
         [0060]    [0060]FIG. 3 shows a cross-section through the waste steam housing  20  with an upper half  21  and lower half  22  that are separated from each other by a dividing plane  23 . The turbine steam that flows through the outlet surface area of the upper half of the diffuser into the upper half  21  of the waste steam housing  20  then flows down through the dividing plane  23  into the lower half  22 , and from there through the outlet surface area  24  of the waste steam housing into the condenser connected there.  
         [0061]    The waste steam housing has been adapted to the diffuser in such a way that the outlet surface area  24  of the waste steam housing  20  is approximately 15% greater than the total outlet surface area of the diffuser. This ensures a surface area reserve in the dividing plane for any obstructions of the outgoing flow.  
         [0062]    According to FIG. 4, the sum of the outlet surface areas of partial diffusers  11  and  12  of the upper half of the diffuser corresponds approximately to the surface area  25  in the dividing plane  23  that is formed between the waste steam housing and the waste steam guide plate  8 ′ of the guide plate  8  and that is shown striated with continuous lines in the figure. This means that half of the sum of the outlet surface areas S 22  and S 32  of the partial diffusers  11  or, respectively,  12  over the entire rotation of the diffuser equals the dividing plane surface area  25  that is striated in the figure. In addition, half of the outlet surface area S 12  of the inner guide plate  10  across the entire rotation of the diffuser equals the surface area  26  that is shown striated with broken lines. As a result of the adaptation of these surface areas, the outgoing diffuser flow of partial diffusers  11  and  12  has, if possible, an equal-sized flow-through surface area and no bottlenecks when flowing from the diffuser into the waste steam housing. This again has a positive effect on the pressure recovery.  
         [0063]    [0063]FIG. 5 shows an embodiment of the three-channel diffuser according to the invention with waste steam housing, which has been optimized in comparison with the configuration of FIG. 1. The optimized diffuser with waste steam housing has been designed, in particular, with respect to the inner partial diffuser, in such a manner that the outlet surface area S 12 ′ of the inner partial diffuser  10  has been defined further outward than in the configuration shown in FIG. 1. If the outlet surface area S 12 ′ is located further outward than indicated with the striated line, the ratio of outlet surface area to inlet surface area of the respective partial diffuser is increased, and the efficiency of the turbine correspondingly rises. For this purpose, the outlet surface area S 12 ′ is defined so that the ratio of its surface area to the inlet surface area S11 is increased to approximately 1.8, which is a significant increase compared to the ratio of approximately 1.3 in the embodiment shown in FIG. 1. In order to continue to ensure a flow-through surface area with the most equal size possible from the diffuser into the waste steam housing, the wall  21 ′ or hood of the upper half of the waste steam housing is placed radially further outward than the wall  21  of the waste steam housing in FIG. 1. At the same time, the impact wall  27 ′ of the waste steam housing is placed axially further outward. In comparison to the deflection angle in FIG. 1, the deflection angle 1 then is decreased to approximately 60°.  
         [0064]    [0064]FIG. 6 shows this embodiment in the dividing plane  23  between the upper and lower half of the diffuser. It also shows how the dimensions of the waste steam housing and the sizes of the outlet surface areas of the partial diffusers are adapted to each other. The diffuser is designed so that half of the outlet surface area S 12 ′ of the inner partial diffuser  10  approximately equals the surface area  28  shown striated with broken lines in the dividing plane  23  between the upper and lower half of the diffuser over the entire rotation of the diffuser. The surface area  28  is formed by the impact wall  27 ′ arranged axially further outward, the hood  21 ′ arranged radially further outward, a wall  31  facing the turbine, and the waste steam guide plate  8 ′. The surface area  28  then is closed by a fictitious, axially extending line  30  between the waste steam guide plate  8 ′ and wall  31 .  
         [0065]    The sum of the outlet surface areas S 22  and S 32  of the two other partial diffusers is furthermore approximately equal to the surface area  29  in the dividing plane that is striated with continuous lines. This surface area  29  is formed by the waste steam guide plate  8 ′, the line  30 , the wall  31 .  
         [0066]    In addition, the outlet surface area S 13 ′ in the lower half of the diffuser in this case coincides with the same point as the outlet surface area S 12 ′ for the upper half of the diffuser.