Abstract:
A radial-flow turbine wheel is provided. The radial-flow turbine wheel includes a hub having an outer radius gradually increasing from a front end to a rear end, a rear periphery of the hub being radially extended in a plane generally perpendicular to a center axis, and a plurality of turbine blades formed around the hub at constant intervals. A plurality of slots is formed by inward cuts at the rear periphery of the hub between the turbine blades of the hub. The turbine wheel restrains creation and propagation of cracks due to thermal stress, as well as improving a turbine efficiency.

Description:
BACKGROUND OF THE INVENTION 
   This application claims the priority of Korean Patent Application No. 2004-65881, filed on Aug. 20, 2004, in the Korean Intellectual Property Office, the disclosure of which is incorporated herein in its entirety by reference. 
   1. Field of the Invention 
   The present invention relates to a radial-flow turbine wheel, and more particularly, to a radial-flow turbine wheel capable of restraining creation and propagation of a crack due to thermal stress, as well as improving a turbine efficiency. 
   2. Description of the Related Art 
   In general, a gas turbine is powered by expansion of an operating fluid of high temperature and high pressure, which is generated from the combustion process of a combustor, to drive a compressor coupled coaxially to the gas turbine. In an internal combustion engine with a turbocharger, a high-pressure gas compressed by the compressor is supplied to a fuel cell or a combustion cylinder of the internal combustion engine. 
     FIG. 1  is a cross-sectional view of a common turbocharger driven by such a gas turbine. Referring to  FIG. 1 , during operation of an internal combustion engine (not shown) coupled to the turbocharger, an exhaust gas F firstly flows in a spiral inflow casing  6  of the turbine. The exhaust gas F is accelerated in the inflow casing  6 , and flows to turbine wheel  30 . The exhaust gas F is expanded in the turbine wheel section  30 , thereby generating an output to drive rotary shaft  5  and compressor wheel  4 . The compressor wheel  4  compresses air A and supplies the compressed air to a combustion cylinder (not shown). Reference numeral C indicates the center of the rotary shaft  5 . 
     FIG. 2  shows a conventional radial-flow turbine wheel  30  including a hub  10  and a plurality of turbine blades  20  formed around the hub  10  at constant intervals. The exhaust gas F flowing into the turbine wheel  30  flows along the turbine blades  20 . In this process, the turbine blades  20  are urged to move in a rotating direction by the flow of exhaust gas F, so as to rotate the turbine wheel  30 . According to the prior art, in order to reduce thermal stress and the weight of the gas turbine, a desired portion between the turbine blades  20  is cut away to form a scallop  60 . As, a result, an outermost rear periphery  10   a  of the hub between the adjacent turbine blades has an inwardly concave shape. 
   However, an excessive formation of such scallops  60  results in deterioration of turbine efficiency. In particular, referring to  FIG. 3 , when the scallops are excessively formed (i.e., an outer radius R 2  of the periphery  10   a  is remarkably reduced relative to the outer radius R 1  of the turbine blade  20 ), the exhaust gas flowing into the turbine wheel  30  via a flow path may collide against the periphery  10   a  (indicated by F 1 ) or may be leaked toward a back area B through a gap between the turbine wheel  30  and a wall  15  (indicated by F 2 ). Since the exhaust gas colliding against the periphery  10 a or leaked toward a back area B does not function as energy to drive the turbine wheel  30 , there is a driving loss, which deteriorates turbine efficiency. 
   SUMMARY OF THE INVENTION 
   The present invention provides a radial-flow turbine wheel capable of improving a turbine efficiency. 
   Also, the present invention provides a radial-flow turbine wheel capable of restraining creation and propagation of crack due to thermal stress. 
   According to one aspect of the present invention, a radial-flow turbine wheel comprises: a hub having a generally cylindrical front end, an intermediate portion with an outer radius generally increasing from the front end to a rear end, the rear end of the hub having an enlarged outer periphery; a plurality of turbine blades formed around the hub at constant intervals; and, a plurality of slots formed in a generally radial direction at the enlarged outer periphery of the hub between the turbine blades. 
   The slot may have a rounded inner surface. The slot preferably has a depth of at least 3 mm. 
   The rear periphery of the hub preferably has an inwardly-formed concavity between the turbine blades. An innermost outer radius of the periphery is greater than about 75% of an outer radius of the turbine blade. 

   
     BRIEF DESCRIPTION OF DRAWINGS 
     The above and other features and advantages of the present invention will become more apparent by describing in detail exemplary embodiments thereof with reference to the attached drawings in which: 
       FIG. 1  is a schematic cross-sectional view of a conventional turbocharger; 
       FIG. 2  is a partial and perspective view of a conventional turbine wheel; 
       FIG. 3  is a partial and schematic cross-sectional view of the turbine wheel in  FIG. 2 ; 
       FIG. 4  is a perspective view of a turbine wheel according to one embodiment of the present invention; 
       FIG. 5  is a rear view of the turbine wheel of  FIG. 4 ; 
       FIG. 6  is a graph of the variation of a stress intensity factor according to crack sizes; 
       FIG. 7  is a graph of the variation of a crack size according to the cycle of a turbine wheel; 
       FIG. 8  is a perspective view of a turbine wheel according to another embodiment of the present invention; and 
       FIG. 9  is a rear view of the turbine wheel in  FIG. 8 . 
   

   DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
   Reference will now be made in detail to describe a radial-flow turbine wheel according to preferred embodiments of the present invention. 
     FIG. 4  shows a turbine wheel  130  according to one embodiment of the present invention. Referring to  FIG. 4 , turbine wheel  130  includes a hub  110  and a plurality of turbine blades  120  formed around the hub  110  at constant intervals. 
   Hub  110  has an outer radius gradually increased from front to rear. The hub  110  includes a rear side periphery  110   a  (hereinafter, called a “rear periphery”) radially extending in a plane perpendicular to center axis C. A rotary shaft (not shown) supporting the turbine wheel  130  is inserted into the center of the hub  110 , and rotational energy is transferred from the turbine wheel  130  through the rotary shaft to a compressor wheel coaxially coupled to the rotary shaft. The hub  110  supports the plurality of turbine blades  120  formed-around the hub. 
   The turbine blades  120  convert pressure energy of an exhaust gas into rotational energy of the turbine wheel. In order to effectively transfer the pressure energy of the exhaust gas to the turbine wheel  130 , the turbine blade  120  has a desired curvature in a circumferential direction, as shown in the drawing. 
   A scallop  160  is formed between the turbine blades  120 , so that a rear periphery of the hub is formed in an inwardly concave shape. Such a scallop  160  may be formed by cutting a desired portion of a rear portion of the hub. Thermal stress can be reduced by cutting a portion of the rear portion of the hub directly contacting with the hot exhaust gas exited from a combustion chamber, thereby preventing a crack from being created due to thermal stress. 
   The rotary shaft supporting the turbine wheel  130  may be subject to bending deformation due to the weight of the turbine wheel  130 , or to bending vibration due to a centrifugal force (i.e., inertial moment) generated during rotation of the rotary shaft. The bending deformation or bending vibration causes stress to the rotary shaft. The weight of the turbine wheel  130  is reduced by the scallop  160  of this embodiment to decrease the stress applied to the rotary shaft. 
   It is preferable to restrict the size of the scallop  160  in a desired range. Referring to  FIG. 5 , the scallop  160  is preferably formed such that an innermost outer radius R 2  of the periphery is above 75% of an outer radius R 1  of the turbine blade  120 . If the scallop is excessively large, the gas flowing in the turbine wheel may be leaked toward a back area, or the exhaust gas may not smoothly flow in the turbine wheel. As such, the present invention can prevent the reduction of turbine efficiency. 
   As can be seen from  FIG. 4 , the turbine wheel  130  of the present invention is provided with a plurality of slots  150  formed inwardly at the rear periphery  110 a between the turbine blades  120 . The slots  150  are radially formed between the turbine blades  120  at constant intervals. As can be seen from  FIG. 5 , an inner tip  150   a  of the slot  150  is formed in a round shape, such that stress applied to the tip  150   a  is dispersed to prevent a crack from being generated due to a stress concentration. 
   If the slots  150  are formed on the periphery  110   a  at which combustion heat of the exhaust gas is concentrated, it can suppress creation and propagation of a crack due to the thermal stress, the function of which will now be described with reference to  FIG. 4 . 
   In a transitional period, such as acceleration of the turbine wheel  130  (i.e., start of the gas turbine) or deceleration of the turbine wheel (i.e., stop of the gas turbine), there is a large temperature difference between the rear periphery  110   a  of the turbine wheel  130  contacted directly with the exhaust gas and the hub  110  centered on the turbine wheel. Specifically, at the acceleration of the turbine wheel  130 , a temperature of the exhaust gas flowing in the turbine wheel  130  is raised up. As such, a temperature of the periphery  110   a  directly contacted with the exhaust gas is rapidly raised up, but a certain time is required until a temperature of the hub  110  at the center of the turbine wheel  130  is raised up. As a result, a transitional temperature difference occurs between the periphery  110   a  and the hub  110 . Also, at the deceleration of the turbine wheel  130 , the temperature of the exhaust gas flowing in the turbine wheel  130  is lowered down, and the temperature of the periphery  110   a  directly contacted with the exhaust gas is rapidly lowered down. Whereas, at the central hub  110  of the turbine wheel  130 , a lapse of time is required until the temperature of the hub  110  is lowered to a similar temperature. As a result, the transitional temperature difference happens between the periphery  110   a  and the hub  110 . 
   The transitional temperature difference results in a difference in thermal expansion, thereby applying the thermal stress (acting also as a hoop stress) to the periphery  110   a . Specifically, at the starting of the gas turbine, an undue compressive stress exceeding the elastic limit of the turbine wheel is applied to the periphery  110   a . At the stopping of the gas turbine, an undue tensile stress exceeding the elastic limit is applied to the periphery  110   a . Repetition of the starting and stopping of the gas turbine causes the thermal stress to be periodically applied to the turbine wheel  130 , thereby producing a crack and thus shortening the life span of the turbine wheel. If the turbine wheel  130  is provided with slots  150 , a resistance against a crack is increased, and a growth rate of the crack is slowed down. 
   According to one embodiment of the present invention, such a crack development and optimal condition of the slot formation can effectively be analyzed with the aid of a computer. One exemplary analysis result was illustrated in  FIGS. 6 and 7 . 
   For instance, such a computer-aided analysis can calculate a stress intensity factor at a crack tip by use of a finite element analysis. The stress intensity factor is a coefficient to define the stress distribution at the tip portion of the crack, in which the stress at one point adjacent to the crack tip is determined by a stress concentration factor and the position of the one point relative to the crack tip. The magnitude of the stress concentration factor is determined by the size and shape of the crack. 
   Although not shown in the figures, the computer analysis utilizes a finite element model with a scallop and a crack cut at the rear periphery of the hub formed toward the inside of the hub between turbine blades. For instance, the finite element analysis can calculate the stress intensity factor, without being restricted by the shape of the crack. The stress distribution of the turbine wheel under certain load conditions can be obtained from analyzing the results on a temperature distribution at the transitional state. In particular, the temperature distribution of the turbine wheel was obtained by analyzing the temperature distribution of the turbine wheel during one period from the start to the stop, and the stress distribution calculated from this result is applied to load conditions. 
     FIG. 6  shows a variation of the stress intensity factor according to the size of the crack. Referring to  FIG. 6 , if the crack size is below 3 mm, as the crack size increases, the stress intensity factor also increases. However, if the size of the crack is above 3 mm, as the crack size increases, the stress intensity factor decreases. The decrease of the stress intensity factor indicates decrease of the stress acting on the crack tip and thus slowdown of the growth rate of the crack. Accordingly, the preferable cut depth ‘d’ ( FIG. 5 ) of the slot from the outer periphery toward the inside is designed to have at least 3 mm based on the analysis result as illustrated in  FIG. 6 . 
   A propagation behavior of the crack can be calculated from the following Paris Equation, which is a differential equation (for example, see “Fatigue Design: Life Expectancy of Machine Parts” by Eliahu Zahavi, CRC Press, pp. 163-166, 1996): 
   
     
       
         
           
             
               ⅆ 
               a 
             
             
               ⅆ 
               N 
             
           
           = 
           
             C 
             × 
             
               ( 
               
                 Δ 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   K 
                   m 
                 
               
               ) 
             
           
         
       
     
   
   wherein, 
             ⅆ   a       ⅆ   N           
is a variation of a crack size for the cycle change, in which the cycle means a series of operating periods from the start to the stop of the turbine wheel. Also, ΔK is a variation of the stress intensity factor, and the variation value of the stress intensity factor corresponding to the crack size can be obtained from the results shown in  FIG. 6 . In addition, C and m are constants which can be experimentally obtained from test results.
 
   The crack size for every cycle can be calculated by integrating the Paris Equation, one result of which was shown in  FIG. 7 . Here, an initial condition was set to have an initial crack size of 0.5 mm after carrying out 300 cycles, which reflects a general condition in creating the crack according to one embodiment of the present invention. 
   The crack grows as the cycle increases, however, the growth rate of the crack slows down. In particular, according to one embodiment of the present invention as shown in  FIG. 7 , the crack was grown abruptly at the initial cycle of between about 300 cycles and about 900 cycles. The crack size became about 5 mm at 900 cycles. However, after reaching about 900 cycles (i.e., when the crack size becomes about 5 mm), the growth rate of the crack was slowed down. Thereafter, after reaching about 5000 cycles, when the crack size reaches about 8.6 mm, the growth rate of the crack was remarkably slowed down and the crack size was eventually maintained at a generally constant level. It will be apparent from the above analysis results that when the crack size becomes above a given level, the growth rate of the crack is slowed down rapidly. According to the present invention, an optimal cut-depth ‘d’ ( FIG. 5 ) of the slot can be determined based on the above described analysis results. Thus, it is more preferable to have the cut-depth ‘d’ of the slot greater than 5 mm because the growth rate of the crack slows down significantly after this point. 
     FIG. 8  shows the turbine wheel according to another embodiment of the present invention. Referring to  FIG. 8 , turbine wheel  230  includes hub  210  receiving a rotary shaft (not shown), and a plurality of turbine blades  220  formed around the hub  210  at certain intervals. The hub  210  includes a plurality of slots  250  formed inwardly (e.g., radially) at a rear periphery  210   a . A cut-depth ‘d’ ( FIG. 9 ) of the slot  250  and the round shape of slot tip  250   a  are substantially identical with those of the prior embodiment described above, and the description of which will be not repeated. 
   A distinctive feature of this embodiment is that the scallop is not formed at the rear periphery between the turbine blades, which is distinct from the first embodiment. In other words, the rear periphery  210   a  of the hub  210  is formed in a smooth shape, so that the exhaust gas flowing in the turbine wheel  230  is not leaked to a back area or disturbance of the exhaust gas inflow section is decreased (see  FIG. 3 ), thereby improving the operating efficiency of the turbine wheel  230 . 
   With the above description, the radial-flow turbine wheel of the present invention can obtain the following effects: 
   The radial-flow turbine wheel restricts the scallop in a desired size, so as to prevent leakage of the exhaust gas flowing into the turbine wheel or to limit the disturbance in the inflow section. Accordingly, it can prevent the decrease of the efficiency of the turbine and it can be expected to increase the operating efficiency thereof. 
   In addition, the radial-flow turbine wheel is provided with the inwardly cut slots, so as to suppress the creation and propagation of the crack due to the thermal stress. In addition, an optimal design specification of the cut-depth of the slot is also provided by the present invention to maximize the resistance against the crack. 
   Although the present invention is described with reference to the turbocharger, the features of the present invention are not limited thereto. The present invention may be applied to an air supplying unit for a fuel battery or auxiliary power unit. 
   While the present invention has been particularly shown and described with reference to exemplary embodiments described and depicted with the accompanying drawings, it will be understood by those of ordinary skill in the art that various changes and modifications in form and details may be made therein without departing from the spirit and scope of the present invention as disclosed in the accompanying claims.