DESIGN METHOD FOR A MULTI-BLADE RADIAL FAN AND MULTI-BLADE RADIAL FAN

Abstract: In a multi-blade radial fan comprising an impeller having a multiplicity of radial blades disposed in a circumferential direction such that a divergent angle of a scroll type casing and a divergent angle of a free vortex formed by air flow from the impeller substantially coincide with each other and a scroll type casing for receiving the impeller, a method for deciding specifications of the impeller and the scroll type casing.

Description: The present invention relates to a method for designing a multiblade centrifugal fan according to the preamble of claim 1. The radial fan, one type of centrifugal fan, has both its blades and interblade channels directed radially and is thus simpler than other types of centrifugal fans such as the sirocco fan, which has forward-curved blades, and the turbo fan, which has backward-curved blades. The radial fan is expected to come into wide use as a component of various kinds of household appliances. Such a centrifuga fan is known e.g. from the patent application EP 0 529 099 A1. . Quietness of the multiblade radial fan, which has numerous radially directed blades disposed at equal circumferential distance from each other, is heavily affected by the impeller of the multiblade radial fan, compatibility between the impeller and the scroll type casing for accommodating the impeller, and interference between the tongue of the scroll type casing and the blades of the impeller. The inventors of the present invention proposed design criteria for enhancing the quietness of the impeller of the multiblade radial fan in international application PCT/JP95/00789. No one has ever proposed design criteria for achieving compatibility between the impeller and the scroll type casing accommodating the impeller of the multiblade radial fan, or design criteria for decreasing sound caused by interference between the tongue of the scroll type casing and the blades of the impeller. [II] Provision of design criteria for decreasing sound level caused by interference between the tongue of the scroll type casing and the impeller of the multiblade radial fan, thereby enhancing quietness of the multiblade radial fan, and provision of design criteria for decreasing sound level caused by interference between the tongue of the scroll type casing and the impeller of the multiblade centrifugal fan as generally defined to include the multiblade radial fan, thereby enhancing quietness of multiblade centrifugal fans in general. Sound caused by interference between the tongue of the scroll type casing and the blades of the impeller (hereinafter called tongue interference sound) is, as shown in Figure 21, caused by the periodical collision of the air discharged from the interblade channels of the impeller and having uneven circumferential velocity distribution with the tongue of the scroll type casing. Frequency f of the tongue interference sound is expressed by the formula f = n× z (where n : number of the blades of the impeller, Z : revolution speed of the impeller). As shown in Figure 22, the circumferential velocity distribution of the air discharged from the interblade channels becomes more uniform as the distance from the impeller increases. It is thought that the manner in which the circumferential velocity distribution of the air discharged from the interblade channels becomes uniform varies with the specifications of the impeller. The inventors of the present invention conducted an extensive study and found that there is a definite correlation between the manner in which the circumferential velocity distribution of the air discharged from the interblade channels becomes uniform and the specifications of the impeller. The present invention was accomplished based on this finding. An object of the present invention is therefore to determine the specifications of the impeller and the scroll type casing so as to make the air discharged from the interblade channels collide with the tongue of the scroll type casing after the circumferential velocity distribution of the air has become fairly uniform, thereby decreasing the tongue interference sound of the multiblade centrifugal fan as generally defined to include the multiblade radial fan. In order to achieve the aforementioned objects according to the present invention, there is provided a method for designing a multiblade centrifugal fan in accordance with claim 1 and a multiblade centrifugal fan in accordance with claim 5. Preferred embodiments are claimed in the dependent claims. According to the present invention, there is provided a method for designing a multiblade centrifugal fan comprising an impeller having numerous blades circumferentially spaced from each other and a scroll type casing accommodating the impeller, wherein the tongue of the scroll type casing is located the radial position where the ratio of the half band width of a jet flow discharge from an interblade channel to the virtual interblade pitch is a value in the range of greater than 0,866 and smaller than or, equal to, 2,92,. It is possible to make the air discharged from the interblade channels collide with the tongue of the scroll type casing after the circumferential velocity distribution of the air has become fairly uniform by locating the tongue of the scroll type casing at the radial position where the ratio of the half band width of a jet flow discharged from an interblade channel to the virtual interblade pitch is a value in the range of greater than 0,866 and smaller than or, equal to, 2,92. Thus, the tongue interference sound of the multiblade centrifugal fan decreases. According to the present invention, there is provided a method for designing a multiblade centrifugal fan comprising an impeller having numerous blades circumferentially spaced from each other and a scroll type casing accommodating the impeller, wherein the tongue of the scroll type casing is located at the radial position where the ratio of the half band width of a jet flow discharged from an interblade channel to the virtual interblade pitch at a radial position where the half band widths of two adjacent jet flows discharged from two adjacent interblade channels are equal to the virtual interblade pitch is a value in the range of greater than 0,866 and smaller than or, equal to, 2,92. It is possible to make the air discharged from the interblade channels collide with the tongue of the scroll type casing after the circumferential velocity distribution of the air has become fairly uniform by locating the tongue of the scroll type casing at the radial position where the ratio of the half band width of a jet flow discharged from an interblade channel to the virtual interblade pitch at a radial position where the half band widths of two adjacent jet flows discharged from two adjacent interblade channels are equal to the virtual interblade pitch is a value in the range of greater than 0,866 and smaller than or, equal to, 2,92. Thus, tongue interference sound of the multiblade centrifugal fan decreases. According to the present invention, there is provided a method for designing a multiblade centrifugal fan comprising an impeller having numerous blades circumferentially spaced from each other and a scroll type casing accommodating the impeller, wherein specifications of the impeller and the scroll type casing are determined so as to satisfy the correlation expressed by the formula -A τ + B< 10.0 (where τ = b / δ 3 , b = (δ 3 - c)(C 4 / X) + c, c = Cδ 1 , δ 1 = {(2 π r) / n} - t, δ 3 = 2 π (r + X) / n, C d : tongue clearance, n : number of the blades, t : thickness of the blades, r : outside radius of the impeller, A, B, C, X : constants determined through tests). It is possible to make the air discharged from the interblade channels collide with the tongue of the scroll type casing after the circumferential velocity distribution of the air has become fairly uniform by determining the specifications of the impeller and the scroll type casing so as to satisfy the correlation expressed by the formula - A τ + B < 10.0 (where τ = b / δ 3 , b=( δ 3 - c)(C d / X) + c, c = Cδ 1, δ 1 = {(2 π r)/n} - t, δ 3 = 2 π (r + X)/n, C d : tongue clearance, n : number of the blades, t : thickness of the blades, r : outside radius of the impeller, A, B, C, X : constants determined through tests). Thus, tongue interference sound of the multiblade centrifugal fan decreases. According to the present invention, there is provided a method for designing a multiblade centrifugal fan comprising an impeller having numerous blades circumferentially spaced from each other and a scroll type casing accommodating the impeller, wherein specifications of the impeller and the scroll type casing are determined so as to satisfy the correlation expressed by the formula -47.09 τ + 50.77 < 10.0 (where τ = b/δ 3 , b=( δ 3 - c)(C 4 / X) + c, X = 0.8 δ 2 , c = 0.3 δ 1 , δ 1 = {(2 π r)/n} - t, δ 2 = (2 π r)/n, δ 3 = 2 π (r + X)/n, C d : tongue clearance, n : number of the blades, t: thickness of the blades, r : outside radius of the impeller). It is possible to make the air discharged from the interblade channels collide with the tongue of the scroll type casing after the circumferential velocity distribution of the air has become fairly uniform by determining the specifications of the impeller and the scroll type casing so as to satisfy the correlation expressed by the formula -47.09 τ + 50.77 < 10.0 (where τ = b/δ 3 , b=( δ 3 - c)(C d / X) + c, X = 0.8 δ 2 , c = 0.3δ 1 , δ 1 = {(2 π r)/n} - t, δ 2 = (2 π r)/n, δ 3 = 2 π (r + X)/n, C 4 : tongue clearance, n : number of the blades, t : thickness of the blades, r : outside radius of the impeller). Thus, the tongue interference sound of the multiblade centrifugal fan decreases. In the drawings: Figure 1 is a diagram showing the layout of a measuring apparatus for measuring air volume flow rate and static pressure of an impeller used for measuring the efficiency of the impeller alone. Figure 2(a) is a plan view of a tested impeller and Figure 2(b) is a sectional view taken along line b-b in Figure 2(a). Figure 3 shows experimentally obtained correlation diagrams between the total pressure coefficient of the impeller alone and the flow coefficient  . Figure 4 shows experimentally obtained correlation diagrams between the total pressure coefficient of the impeller alone and the flow coefficient  X based on the outlet sectional area of the interblade channel. Figure 5 shows correlation between the diameter ratio ξ of the impeller and the flow coefficient  Xmax based on the outlet sectional area of the interblade channel which gives the maximum total pressure efficiency of the impeller alone plotted on a log-log graph. Figure 6 is an explanatory diagram showing the relation between the flow coefficient  and the outlet angle  of the air discharged from the impeller. Figure 7 shows the configuration of the stream line of the air flow discharged from the impeller. Figure 8 is an explanatory diagram showing the relation between the radial velocity of the air u at the outlet of the impeller and radial velocity of the air U in the portion of the scroll type casing adjacent to the out'let of the impeller. Figure 9 is a diagram showing the layout of a measuring apparatus for measuring air volume flow rate and static pressure of a multiblade radial fan. Figure 10 is a diagram showing the layout of a measuring apparatus for measuring the sound pressure level of a multiblade radial fan. Figure 11 is a plan view of a tested casing used for measuring the sound pressure level of a multiblade radial fan. BL defines the Base Line. Figure 12 is a plan view of a tested casing used for measuring the sound pressure level of a multiblade radial fan. Figure 13 is a plan view of a tested casing used for measuring the sound pressure level of a multiblade radial fan. Figure 14 is a plan view of a tested casing used for measuring the sound pressure level of a multiblade radial fan. Figure 15 is a plan view of a tested casing used for measuring the sound pressure level of a multiblade radial fan. Figure 16 is a plan view of a tested casing used for measuring the sound pressure level of a multiblade radial fan. Figure 17 is a plan view of a tested casing used for measuring the sound pressure level of a multiblade radial fan. Figure 18 shows correlation diagrams between minimum specific sound level K Smin and the divergence angle of the scroll type casing  z . Figure 19 shows correlation diagrams between κ = (1 - η (  x ) / η (  Xmax) ) and  X /  Xmax . Figure 20 shows the air flow in the impeller. Figure 21 shows the circumferential velocity distribution of the air discharged from the interblade channels of the multiblade radial fan. DR defines the direction of rotation. Figure 22 shows the manner in which the circumferential velocity distribution of the air discharged from the interblade channels of the multiblade radial fan becomes uniform. Figure 23 shows the velocity distribution of the two-dimensional jet flow discharged from a nozzle. Figure 24 is an explanatory diagram showing the half band width of the air flow discharged from the interblade channel of the multiblade radial fan. Figure 25(a) is a plan view of a tested impeller used for measuring the sound pressure level and Figure 25(b) is a sectional view taken along line b-b in Figure 25(a). IBC defines the inlet breadth of the channel. OBC defines the outlet breadth of the channel. Figure 26 is a plan view of a tested casing used for measuring the sound pressure level of a multiblade radial fan. (No. 1 casing - outside diameter of the impeller 70.0mm) Figure 27 is a plan view of a tested casing used for measuring the sound pressure level of a multiblade radial fan. (No. 2 casing - outside diameter of the impeller 100.0mm, 99.0mm) Figure 28 is a plan view of a tested casing used for measuring the sound pressure level of a multiblade radial fan. (No. 3 casing - outside diameter of the impeller 100.0mm, 99.0mm) Figure 29 is a plan view of a tested casing used for measuring the sound pressure level of a multiblade radial fan. (No. 4 casing - outside diameter of the impeller 100.0mm) Figure 30 is a plan view of a tested casing used for measuring the sound pressure level of a multiblade radial fan.(No. 5 casing - outside diameter of the impeller 99.0mm) Figure 31 is a plan view of a tested casing used for measuring the sound pressure level of a multiblade radial fan. (No. 6 casing - outside diameter of the impeller 100.0mm, 99.0mm) Figure 32 is a plan view of a tested casing used for measuring the sound pressure level of a multiblade radial fan. (No. 7 casing - outside diameter of the impeller 100.0mm, 99.0mm) Figure 33 is a plan view of a tested casing used for measuring the sound pressure level of a multiblade radial fan. (No. 8 casing - outside diameter of the impeller 150.0mm) Figure 34 shows an example of the sound level spectrum obtained by the sound pressure level measurement. Figure 35 shows the correlation between the nondimensional number r and the dominant level of the tongue interference sound. Figure 36 shows the correlation between (a) the dominant level of the tongue interference sound and (b) the difference between the A-weighted 1/3 octave band overall sound pressure level with tongue interference sound and the A-weighted 1/3 octave band overall sound pressure level without tongue interference sound. [THE BEST MODE FOR CARRYING OUT THE INVENTION] [I] Invention relating to the design criteria for achieving compatibility between the impeller (4) and the scroll type casing (STC) accommodating the impeller of the multiblade radial fan Preferred embodiments of the present invention will be described. [A] Performance test of the impeller alone Measurement tests of the total pressure efficiency of the impeller alone were carried out on multiblade radial fans with different diameter ratios. (1) Test conditions <1> Measuring apparatus The measuring apparatus is shown in Figure 1. 9 defines a base. An impeller was put in a double chamber type air volume flow rate measuring apparatus (1) (product of Rika Seiki Co. Ltd., Type F-401). A motor (6) for driving the impeller was disposed outside of the the air volume flow rate measuring apparatus. The air volume flow rate measuring apparatus was provided with a bellmouth (5) opposite the impeller. The air volume flow rate measuring apparatus was provided with an air volume flow rate control damper and an auxiliary fan (2) for controlling the static pressure near the impeller. The air flow discharged (DAF) from the impeller was straightened by a straightening grid (8). The air volume flow rate of the impeller was measured using orifices (7) located in accordance with the AMCA standard. The static pressure near the impeller was measured through a static pressure measuring hole (3) disposed near the impeller. <2> Tested impellers The outside diameter (D) and the height (HI) of all tested impellers were 100mm and 24mm respectively. The thickness of the circular base plate (12) and the annular top plate (10) of all tested impellers was 2mm. Impellers with four different inside diameters (D) were made. Different impellers had a different number of radially directed flat plate blades (11) disposed at equal circumferential distances from each other and different blade thickness (t). A total of 8 kinds of impellers were made and tested. The particulars of the tested impellers are shown in Table 1, and Figures 2(a) and 2(b). (2) Measurement, Data processing <1> Measurement The air volume flow rate of the air discharged from the impeller and the static pressure at the outlet of the impeller were measured for each of the 8 kinds of impellers shown in Table 1 when rotated at the revolution speed shown in Table 1, while the air volume flow rate of the air discharged from the impeller was varied using the air volume flow rate control damper (18). <2> Data processing From the measured value of the air volume flow rate of the air discharged from the impeller and the static pressure at the outlet of the impeller, a total pressure efficiency defined by the following formula was obtained. η = ( P s + P v )Q/W In the above formula, η : total pressure efficiency P s : static pressure P v = ( ρ /2 )(u 2 + v 2 ) : dynamic pressure ρ : density of the air u = Q/S : radial velocity of the air at the outlet of the impeller v = rω : circumferential velocity of the outer periphery of the impeller S = 2πrh : outlet sectional area of the impeller Q : air volume flow rate of the air discharged from the impeller W : power r : outside radius of the impeller h : height of the blade of the impeller ω : angular velocity of revolution (3) Test results Based on the results of the measurements, a correlation between the total pressure efficiency η of the impeller alone and the flow coefficient of the impeller  expressed by the following formula was obtained for each tested impeller. The correlations are shown in Figure 3.  = u/v Based on the results of the measurements, a correlation between the total pressure efficiency η of the impeller alone and the flow coefficient of the impeller  X based on the outlet sectional area of the interblade channel (20) expressed by the following formula was obtained for each tested impeller. The correlations are shown in Figure 4.  X = u X / v In the above formula, u X = Q/S X : radial air velocity at the outlet of the impeller based on the outlet sectional area of the interblade channel S X = ( 2 π r - nt )h : outlet sectional area of the impeller based on the outlet sectional area of the interblade channel n : number of the radially directed blades t : thickness of the radially directed blades As is clear from Figure 4, the flow coefficient of the impeller  X based on the outlet sectional area of the interblade channel which gives the maximum value of the total pressure efficiency η depends on the diameter ratio of the impeller only and not on the number of the blades or the breadth of the interblade channel. Correlation between the diameter ratio of the impeller ξ and the flow coefficient  Xmax based on the outlet sectional area of the interblade channel which gives the maximum value of the total pressure efficiency η was obtained from Figure 4. Figure 5 shows the correlation plotted on a log-log graph. As is clear from Figure 5, the correlation between  Xmax and ξ defines a straight line with the inclination of 1.641 on a log-log graph. As described above, the correlation between  Xmax and ξ is expressed by the following formula 1.  Xmax = 0.295ξ 1.641 In the above formula,  Xmax : flow coefficient based on the outlet sectional area of the interblade channel which gives the maximum value of the total pressure efficiency η ξ = D 1 /D : diameter ratio of the impeller D 1 : inside diameter of the impeller D : outside diameter of the impeller  max corresponding to  Xmax can be derived from formula 1, the definition of , i.e.  = u/v, and the definition or  X , i.e.  X = u X / v (where u X = Q/S X : radial air velocity at the outlet of the impeller based on the outlet sectional area of the interblade channel, S X = (2 π r - nt )h : outlet sectional area of the impeller based on the outlet sectional area of the interblade channel, n : number of the radially directed blades, t : thickness of the radially directed blades).  max is expressed by the following formula 2.  max = (1-nt/(2πr))  Xmax = 0.295(1-nt/(2πr)) ξ 1.641 [B] Compatibility between the impeller and the scroll type casing (1) Hypothesis As shown in Figure 6, flow coefficient  ( = u/v) is the tangent of the outlet  of the air discharged from the impeller. It is thought that the air discharged from the impeller forms a free vortex. Thus, as shown in Figure 7, the crossing angle of concentric circle whose center coincides with the rotation center of the impeller and the stream line (SL) of the air discharged from the impeller is kept at the outlet angle  of the air discharged from the impeller, i.e. tan -1 , irrespective of the distance from the rotation center of the impeller. Thus, it is thought that compatibility between the scroll type casing and the impeller is achieved and the quietness of the multiblade radial fan is optimized when the divergence angle  2 (logarithmic spiral angle) of the scroll type casing coincides with tan -1 . Based on the aforementioned results of the measurement test of the total pressure efficiency of the impeller alone and the aforementioned discussion about compatibility between the scroll type casing and the impeller, it is thought that a multiblade radial fan with optimized quietness, wherein compatibility between the scroll type casing and the impeller is achieved and the sound level is minimized when the impeller is driven under the condition of the maximum total pressure efficiency, can be designed by setting the divergence angle  Z of the scroll type casing at the arctangent of  max , i.e. tan -1  max , obtained by the aforementioned formula 2. As shown in Figure 8, the height H of the radially directed blades of the impeller is different from the height H t of the scroll type casing accommodating the impeller. Thus, when the radial air velocity at the outlet of the impeller is u, the radial air velocity U in the portion of the scroll type casing for accommodating the impeller adjacent the outlet of the impeller is U = u(H/H t ). Thus, the flow coefficient  S of the impeller against the scroll type casing is  S = (H/H t )  (where  : flow coefficient of impeller alone) and the  Smax is  Smax = (H/H t )  max . From the above, it is thought that a multiblade radial fan with optimized quietness wherein compatibility between the scroll type casing and the impeller is achieved and the sound level is minimized when the impeller is driven under the condition of the maximum total pressure efficiency can be designed by determining the divergence angle  Z of the scroll type casing based on the following formula 3.  Z = tan -1  Smax = tan -1 [ ( H/H t )  max ] = tan -1 [ 0.295 (1-nt/(2 π r))(H/H t ) ξ 1641 ] (2) Confirmation test of compatibility between the scroll type casing and the impeller It was confirmed by measurements that the quietness of the multiblade radial fan is optimized when the divergence angle  Z of the scroll type casing satisfies the formula 3. <1> Measuring apparatuses 1 ○ Measuring apparatus for measuring air volume flow rate and static pressure The measuring apparatus used for measuring air volume flow rate and static pressure is shown in Figure 9. The fan body of the multiblade radial fan had an impeller, a scroll type casing for accommodating the impeller and a motor. An inlet nozzle (14) was disposed on the suction side of the fan body (15). A double chamber type air volume flow rate measuring apparatus (product of Rika Seiki Co. Ltd., Type F-401) was disposed on the discharge side of the fan body. The air volume flow rate measuring apparatus was provided with an air volume flow rate control damper and an auxiliary fan for controlling the static pressure at the outlet of the fan body (DF). The air flow discharged from the fan body was straightened by a straightening grid. The air volume flow rate of the fan body was measured using orifices located in accordance with the AMCA standard. The static pressure at the outlet of the fan body was measured through a static pressure measuring hole disposed near the outlet of the fan body. 2 ○ Measuring apparatus for measuring sound pressure level The measuring apparatus for measuring sound pressure level is shown in Figure 10. An inlet nozzle was disposed on the suction side of the fan body. A static pressure control chamber (17) of a size and shape similar to those of the air volume flow rate measuring apparatus was disposed on the discharge side of the fan body. The inside surface of the static pressure control chamber was covered with sound absorption material (16). The static pressure control chamber was provided with an air volume flow rate control damper for controlling the static pressure at the outlet of the fan body. The static pressure at the outlet of the fan body was measured through a static pressure measuring hole located near the outlet of the fan body. The sound pressure level corresponding to a certain level of the static pressure at the outlet of the fan body was measured. The motor was installed in a soundproof box (19) lined with sound absorption material. Thus, the noise generated by the motor was confined. The measurement of the sound pressure level was carried out in an anechoic room. The A-weighted sound pressure level was measured at a point on the centerline of the impeller and Im above the upper surface of the casing. <2> Tested impellers, Tested casings 1 ○ Tested impellers No.1 impeller (ξ = 0.4), No.4 impeller (ξ = 0.58) and No.5 impeller (ξ = 0.75) in Table 1 were used as tested impellers. 2 ○ Tested casings The height of the scroll type casing was 27mm. The divergence configuration of the scroll type casing was a logarithmic spiral defined by the following formula. The divergence angle  Z was 2.5° , 3.0 ° , 4.5 ° , 5.5 ° and 8.0 ° for No.1 impeller, 3.5 ° , 4.1 ° , 4.5 ° , 5.5 ° and 8.0 ° for No.4 impeller and 3.0 ° , 4.5 ° , 5.5 ° , 6.0 ° and 8.0 ° for No.5 impeller. r Z = r[exp ( Θ tan  Z )] In the above formula, r Z : radius of the side wall of the casing measured from the center of the impeller r : outside radius of the impeller Θ : angle measured from a base line, 0 ≦ Θ ≦ 2 π  Z : divergence angle of the scroll type casing The tested casings are shown in Figure 11 to Figure 17. 3 ○ Revolution speed of the impeller The revolution speeds of the impeller during the measurement are shown in Table 1. <3> Measurement The air volume flow rate of the air discharged from the fan body, the static pressure at the outlet of the fan body, and the sound pressure level were measured for each of the combinations of No.1 impeller (ξ = 0.4 ), No.4 impeller (ξ = 0.58), No.5 impeller (ξ = 0.75) in Table 1 and the scroll type casings of Figure 11 to Figure 17 when rotated at the revolution speed shown in Table 1, while the air volume flow rate of the air discharged from the fan body was varied using the air volume flow rate control damper. <4> Data processing From the measured value of the air volume flow rate of the air discharged from the fan body, the static pressure at the outlet of the fan body, and the sound pressure level, a specific sound level K S defined by the following formula was obtained. K S = SPL(A)-10log 10 Q( P t ) 2 In the above formula, SPL(A) : A-weighted sound pressure level, dB Q : air volume flow rate of the air discharged from the fan body, m 3 /s P t : total pressure at the outlet of the fan body, mmAq <5> Test results Based on the results of the measurements, a correlation between the specific sound level K S and the air volume flow rate was obtained for each combination of No.1 impeller, No.4 impeller and No.5 impeller in Table 1 and the scroll type casings of Figure 11 to Figure 17. The correlation between the specific sound level K S and the air volume flow rate Q was obtained on the assumption that a correlation wherein the specific sound level K S is K S1 when the air volume flow rate Q is Q 1 exists between the specific sound level K S and the air volume flow rate Q when the air volume flow rate Q and the static pressure p at the outlet of the fan body obtained by the air volume flow rate and static pressure measurement are Q 1 and p 1 respectively, while the specific sound level K S and the static pressure p at the outlet of the fan body obtained by the sound pressure level measurement are K S1 and p 1 respectively. The above assumption is thought to be reasonable as the size and the shape of the air volume flow rate measuring apparatus used in the air volume flow rate and static pressure measurement are substantially the same as those of the static pressure controlling box used in the sound pressure level measurement. The measurements showed that the specific sound level K S of each tested combination of No.1 impeller, No.4 impeller and No.5 impeller in Table 1 and the scroll type casings of Figure 11 to Figure 17 varied with the air volume flow rate or the flow coefficient. The variation of the specific sound level K S is generated by the effect of the casing. Thus, it can be assumed that the minimum value of the specific sound level K S , i.e. the minimum specific sound level K Smin in each combination of No.1 impeller, No.4 impeller and No.5 impeller in Table 1 and the scroll type casings of Figure 11 to Figure 17, represents the specific sound level K S when the outlet angle  of the air discharged from the impeller against the casing coincides with the divergence angle  Z of the scroll type casing and the impeller becomes compatible with the scroll type casing. Correlations between the minimum specific sound level K Smin and the divergence angle  Z of the scroll type casing are shown in Figure 18 for No.1 impeller, No.4 impeller and No.5 impeller in Table 1. <6> Discussion As is clear from Figure 18, the minimum specific sound level K Smin is minimized when the divergence angle  z of the scroll type casing is 2.5° in No.1 impeller, the minimum specific sound level K Smin is minimized when the divergence angle  Z of the scroll type casing is 4.1° in No.4 impeller, and the minimum specific sound level K Smin is minimized when the divergence angle  Z of the scroll type casing is 6.0° in No.5 impeller. On the other hand, the optimum value of the divergence angle  Z of the scroll type casing for No.1 impeller, No.4 impeller and No.5 impeller obtained by formula 3 are 2.46° , 3.94° and 5.99°, respectively. Thus, the divergence angle of the scroll type casing which minimizes the minimum specific sound level K Smin is in good agreement with the optimum divergence angle of the scroll type casing obtained by formula 3. The following facts are clear from the above. 1 ○ Results of the measurements for No.5 impeller ( ξ =0.75) shown in Figure 18 should be observed. The minimum specific sound level K Smin in each measured combination is shown in Figure 18. As mentioned earlier, the outlet angle of the air discharged from the impeller against the scroll type casing coincides with the divergence angle  Z of the scroll type casing, and the flow coefficient  S of the impeller against the scroll type casing is tan Z when the specific sound level K S is K Smin . Thus, the flow coefficient  S of the impeller against the scroll type casing is tan3.0° in the measured combination I (the divergence angle  Z of the scroll type casing is  Z = 3.0 ° in the measured combination I ), the flow coefficient  S of the impeller against the scroll type casing is tan4.5° in the measured combination II (the divergence angle  Z of the scroll type casing is  Z = 4.5 ° in the measured combination II), the flow coefficient  S of the impeller against the scroll type casing is tan5.5° in the measured combination III (the divergence angle  Z of the scroll type casing is  Z = 5.5 ° in the measured combination III), the flow coefficient  S of the impeller against the scroll type casing is tan6.0° in the measured combination IV (the divergence angle  Z of the scroll type casing is  Z = 6.0 ° in the measured combination IV), and the flow coefficient  S of the impeller against the scroll type casing is tan8.0° in the measured combination V(the divergence angle  Z of the scroll type casing is  Z = 8.0 ° in the measured combination V). Supposing that a multiblade radial fan having No.5 impeller installed in the scroll type casing with divergence angle of 6.0° is driven under conditions wherein the flow coefficients  S of the impeller against the scroll type casing are tan3.0 ° , tan4.5° , tan5.5° , tan6.0° and tan8.0° , then the outlet angle  of the air discharged from the impeller against the scroll type casing does not coincide with the divergence angle  Z (  Z = 6.0 °) of the scroll type casing under the driving conditions wherein the flow coefficients  S of the impeller against the scroll type casing are tan3.0°, tan4.5° , tan5.5° and tan8.0° , and the specific sound levels K S under the driving conditions wherein the flow coefficients  S of the impeller against the scroll type casing are tan3.0 ° , tan4.5° , tan5.5° and tan8.0° are larger than the minimum specific sound levels in the measured combinations I, II, III and V respectively. On the other hand, the outlet angle  of the air discharged from the impeller against the scroll type casing coincides with the divergence angle  Z (  Z = 6.0 °) of the scroll type casing under the driving condition wherein the flow coefficients  S of the impeller against the scroll type casing is tan6.0° . Thus, the specific sound level K S under the driving condition wherein the flow coefficient  S of the impeller against the scroll type casing is tan6.0° is equal to the minimum specific sound level in the measured combination VI. Thus, the quietness of the multiblade radial fan having No.5 impeller installed in the scroll type casing with divergence angle of 6.0° is optimized under the driving condition wherein the flow coefficient  S of the impeller against the scroll type casing is tan6.0° . As mentioned earlier, the optimum value of the divergence angle  Z of the scroll type casing against No.5 impeller obtained by the formula 3 is 5.99 °. The divergence angle  Z obtained by formula 3 is equal to the arctangent of the flow coefficient  S of the impeller against the scroll type casing when the impeller is driven under the condition wherein the total pressure efficiency η is maximum. Thus, the total pressure efficiency η of No.5 impeller becomes maximum when the flow coefficient  S of the impeller against the scroll type casing is tan5.99 °. The above discussion proves for No.5 impeller that a multiblade radial fan wherein the quietness is optimized when the impeller is driven under a condition wherein the total pressure efficiency η is maximum can be designed by determining the divergence angle of the scroll type casing based on formula 3. In the same way, it is proved for No.1 and No.4 impellers that a multiblade radial fan wherein the quietness is optimized when the impeller is driven under a condition wherein the total pressure efficiency η is maximum can be designed by determining the divergence angle of the scroll type casing based on formula 3. 2 ○ Results of the measurements for No.5 impeller ( ξ =0.75) in Figure 18 should be observed. The minimum specific sound level K Smin in each measured combination is shown in Figure 18. As is clear from Figure 18, the minimum specific sound level K Smin is minimized in the measured combination IV, that is the minimum specific sound level K Smin is minimized when the divergence angle  Z of the scroll type casing is 6.0 °. Thus, the quietness of No.5 impeller is optimized when it is installed in a casing with divergence angle of 6.0 ° (it is reasonable to conclude that the minimum specific sound level K Smin is minimized in the measured combination IV because the total pressure efficiency of No.5 impeller becomes maximum, the energy loss of the No.5 impeller becomes minimum, and the sound of No.5 impeller alone which causes the energy loss of the No.5 impeller becomes minimum in the measured combination IV). On the other hand, the optimum value of the divergence angle  Z of the scroll type casing against No.5 impeller obtained by formula 3 is 5.99 °. The above discussion proves for No.5 impeller that the quietness of the multiblade radial fan can be optimized by determining the divergence angle of the scroll type casing based on formula 3. In the same way, it is proved for No.1 and No.4 impellers that the quietness of the multiblade radial fan can be optimized by determining the divergence angle of the scroll type casing based on formula 3. (3) Design criteria for achieving the compatibility between the impeller and the scroll type casing for accommodating the impeller of the multiblade radial fan. 1 ○ A multiblade radial fan wherein compatibility between the scroll type casing and the impeller is achieved, the sound level is minimized, and the quietness is optimized when the impeller is driven under the condition wherein the total pressure efficiency η is maximum can be designed by determining the divergence angle  Z of the scroll type casing based on formula 3. 2 ○ The quietness of the multiblade radial fan can be optimized by determining the divergence angle  Z of the scroll type casing based on formula 3. [ C ] Further development of the design criteria (1) Expansion of formula 3 Correlations between κ = (1- η (  X ) / η (  Xmax) )and  X /  Xmax derived from Figure 4 are shown in Figure 19. As is clear from Figure 19, the decrease of the total pressure efficiency η from its maximum value is 6% or so even if  X is varied ± 25% from  Xmax . As is clear from Figure 19, the increase of the minimum specific sound level K Smin from its minimum value is 3dB to 4dB even if  X is varied ±25% from  Xmax . Thus, it is thought that the efficiency and the quietness of the multiblade radial fan do not decrease so much even if the right side of formula 3 is varied about ±25% when the divergence angle  Z of the scroll type casing is determined based on formula 3. Thus, it is thought that the following formula U can be used as the design criteria for achieving compatibility between the impeller and the scroll type casing.  Z = tan -1 [ 0.295 ε (1-nt/(2 π r))( H/H t ) ξ 1.641 ] In the above formula, 0.75 ≦ ε ≦ 1.25 (2) Range of the diameter ratio of the impeller As is clear from Figure 5, the correlation diagram between the diameter ratio ξ of the impeller and the flow coefficient  Xmax based on the outlet sectional area of the interblade channel which gives the maximum value of the total pressure efficiency η is substantially linear over the range 0.4 ≦ ξ ≦ 0.9. Judging from this fact, it is thought that formula 4 can be expandedly used for an impeller whose diameter ratio ξ is in the range of 0.3 ≦ ξ ≦ 0.9. However, it is rather hard to achieve satisfactory quietness in an impeller whose diameter ratio ξ is as large as 0.9 or so, while it is rather hard to dispose numerous radially directed blades in an impeller whose diameter ratio ξ is as small as 0.3 or so. Thus, formula 4 is preferably used for an impeller whose diameter ratio ξ is in the range of 0.4 ≦ ξ ≦ 0.8. (3) Range of the divergence angle  Z of the scroll type casing A scroll type casing whose divergence angle  Z is too small cannot provide a satisfactory air volume flow rate, while a scroll type casing whose divergence angle  Z is too large is troublesome to handle because its outside dimensions are too large. Thus, the divergence angle  Z of the scroll type casing is preferably in the range of 3.0 ° ≦  Z ≦ 8.0° . (4) Range of H/D 1 When the ratio H/D 1 of the height H of the radially directed blades to the inside diameter D 1 of the impeller is too large, vortices are generated in the interblade channels as shown in Figure 20, which degrades the aerodynamic performance and the quietness of the impeller. Generally speaking, the ratio H/D 1 is set at 0.8 to 0.9 in the sirocco fan and 0.6 or so in the radial fan. Thus, the the ratio H/D 1 is preferably in the range of H/D 1 ≦ 0.75. (5) Range of H/H t When the ratio H/H t of the height H of the radially directed blades to the height of the scroll type casing is to small, the air discharged from the impeller is discharged from the casing before it sufficiently diffuses in the casing. Thus, some portions of the space in the casing are not effectively utilized. Thus, the ratio H/H t is preferably in the range of 0.65 ≦ H/H t so as to sufficiently diffuse the air discharged from the impeller in the casing. [II] Invention to provide design criteria for decreasing sound caused by interference between the tongue of the scroll type casing and the blades of the impeller of the multiblade radial fan, and to provide design criteria for decreasing sound caused by interference between the tongue of the scroll type casing and the blades of the impeller of the multiblade centrifugal fan as generally defined to include the multiblade radial fan Preferred embodiments of the present invention are described. [ A ] Theoretical background L.Prandtl states that the half band width b of a two dimensional jet flow discharged from a nozzle (22) (supposing that the flow velocity of a two dimensional jet flow at its center line L is u m, so that half band width b is twice as long as the distance between a point where the flow velocity u is u = u m /2 and the center line L of the two dimensional jet flow ) is proportional to the distance x from the nozzle as shown in Figure 23 (Prandtl,L The mechanics of viscous fluids. In W.F.Dureand(ed.): Aerodynamic Theory, III, 16-208(1935)). The air flow discharged from the interblade channels (20) of the impeller of the multiblade radial fan can be regarded as two dimensional jet flows discharged from the same number of radially directed nozzles as the blades of the impeller disposed along the outer periphery of the impeller. Supposing that, as shown in Figure 24, the breadth of the interblade channel at the outer periphery of the impeller of the multiblade radial fan is δ 1 , the interblade pitch at the outer periphery of the impeller of the multiblade radial fan is δ 2 , the half band width of the air flow discharged from the interblade channel at the outer periphery of the impeller of the multiblade radial fan is c, the radial distance of the point where the half band width of the air flow discharged from the interblade channel is equal to the virtual interblade pitch (supposing that the blades extend radially beyond the outer periphery of the impeller, so that the virtual interblade pitch is the interblade pitch in the region where the blades extend radially beyond the outer periphery of the impeller) from the outer periphery of the impeller is X, the virtual interblade pitch at the point where the radial distance from the outer periphery of the impeller is X is δ 3 , and the distance from the outer periphery of the impeller is x, then the half band width b of the air flow discharged from the interblade channel of the impeller of the multiblade radial fan is obtained by the following formula based on the theory of Prandtl. b= (δ 3 - c)x/X + c δ 1 , δ 2 and δ 3 are obtained by the following formulas. δ 1 = {(2 π r)/n} - t δ 2 = (2 π r)/n δ 3 = 2 π (r + X)/n In the above formulas, n is number of the blades, t is thickness of the blades, and r is outside radius of the impeller. b is divided by δ 3 so as to make the formula 5 nondimensional. Then, τ = b/δ 3 = { (δ 3 - c)x/X + c } / δ 3 It can be conclude that the nondimensional number τ represents the degree of the diffusion of the air flow discharged from the interblade channel of the impeller of the multiblade radial fan, or the degree of the uniformization of the circumferential distribution of the air velocity . Thus, it is thought that the design criteria for decreasing the tongue interference sound of the multiblade radial fan can be obtained by using the nondimensional number τ . [ B ] Sound level measurement tests Sound level measurement tests were carried out on a plurality of impellers of the multiblade radial fan with different diameter ratio. (1) Test conditions <1> Tested impellers, Tested casings 1 ○ Tested impellers A total of 39 kinds of impellers with different outside diameter, diameter ratio, number of blades, blade thickness, etc. were made and tested. The particulars of the tested impellers are shown in Table 2, and Figures 25(a) and 25(b). 2 ○ Tested casings The height of the scroll type casings was 27mm. The divergence configuration of the scroll type casings was a logarithmic spiral defined by the following formula. The divergence angle  Z was 4.50°. r Z = r[exp (Θ tan Z ) ] In the above formula, r Z : radius of the side wall of the casing measured from the center of the impeller r : outside radius of the impeller Θ : angle measured from a base line, 0 ≦ Θ ≦ 2π  Z : divergence angle of the scroll type casing A plurality of casings with different tongue radius R and tongue clearance C d were made for each group of impellers with the same outside diameter so as to accommodate the impellers belonging to the group and were tested. The tested casings are shown in Figures 26 to 33. <2> Measuring apparatuses 1 ○ Measuring apparatus for measuring air volume flow rate and static pressure The measuring apparatus used for measuring air volume flow rate and static pressure is shown in Figure 9. The fan body had an impeller, a scroll type casing for accommodating the impeller and a motor. An inlet nozzle was disposed on the suction side of the fan body. A double chamber type air volume flow rate measuring apparatus (product of Rika Seiki Co. Ltd., Type F-401) was disposed on the discharge side of the fan body. The air volume flow rate measuring apparatus was provided with an air volume flow rate control damper and an auxiliary fan for controlling the static pressure at the outlet of the fan body. The air flow discharged from the fan body was straightened by a straightening grid. The air volume flow rate of of the air discharged from the fan body was measured using orifices located in accordance with the AMCA standard. The static pressure at the outlet of the fan body was measured through a static pressure measuring hole disposed near the outlet of the fan body. 2 ○ Measuring apparatus for measuring sound pressure level The measuring apparatus for measuring sound pressure level is shown in Figure 10. An inlet nozzle was disposed on the suction side of the fan body. A static pressure control chamber of a size and shape similar to those of the air volume flow rate measuring apparatus was disposed on the discharge side of the fan body. The inside surface of the static pressure control chamber was covered with sound absorption material. The static pressure control chamber was provided with an air volume flow rate control damper for controlling the static pressure at the outlet of the fan body. The static pressure at the outlet of the fan body was measured through a static pressure measuring hole located near the outlet of the fan body. The sound pressure level corresponding to a certain level of the static pressure at the outlet of the fan body was measured. The motor was installed in a soundproof box lined with sound absorption material. Thus, the noise generated by the motor was confined. The measurement of the sound pressure level was carried out in an anechoic room. The A-weighted sound pressure level was measured at a point on the centerline of the impeller and 1m above the upper surface of the casing. (2) Measurement Measurements were carried out as follows. 1 ○ One specific impeller belonging to one specific group of impellers with the same outside diameter, number of blades and blade thickness was set in one specific casing belonging to the corresponding group of casings with different tongue radius and tongue clearance. 2 ○ Sound level of the fan was measured for each of a plurality of combinations of the air volume flow rate of the discharged air from the fan and the revolution speed of the impeller with the same flow coefficient  of 0.106. The reason for setting the flow coefficient  at 0.106 will be explained.As shown in Figure 6, flow coefficient  ( = u/v, u = Q/S : radial air velocity at the outlet of the impeller, v = rω : circumferential velocity of the impeller at the outer periphery of the impeller, Q : air volume flow rate, S = 2πrh : outlet sectional area of the impeller, r : outside radius of the impeller, h : height of the impeller, ω : angular velocity of the impeller ) is the tangent of the outlet angle  of the air discharged from the impeller. It is thought that the air discharged from the impeller forms a free vortex. Thus, as shown in Figure 7, the crossing angle of a concentric circle whose center coincides with the rotation center of the impeller and the stream line of the air discharged from the impeller is kept at the outlet angle  of the air discharged from the impeller, i.e. tan -1 , irrespective of the distance from the rotation center of the impeller. Thus, compatibility between the scroll type casing and the impeller is achieved and the sound caused by incompatibility between the scroll type casing and the impeller is eliminated when the divergence angle  Z (logarithmic spiral angle) of the scroll type casing coincides with tan -1 . In the present measurement, tan -1  was made coincide with the divergence angle  Z of the scroll type casing, i.e. 4.5 ° , so as to eliminate sounds other than the tongue interference sound as far as possible. Thus, the flow coefficient  was set at 0.106.The correlation between the sound level of the fan and the air volume flow rate of the discharged air from the fan was obtained on the assumption that a correlation wherein the specific sound level is K, when the air volume flow rate is Q 1 exists between the specific sound level K and the air volume flow rate Q when the air volume flow rate and the static pressure at the outlet of the fan body obtained by the air volume flow rate and static pressure measurement are Q 1 and p 1 respectively, while the specific sound level and the static pressure at the outlet of the fan body obtained by the sound pressure level measurement are K, and p 1 respectively. The above assumption is thought to be reasonable as the size and the shape of the air volume flow rate measuring apparatus used in the air volume flow rate and static pressure measurement are substantially the same as those of the static pressure controlling box used in the sound pressure level measurement. 3 ○ Dominant level of the tongue interference sound was obtained by visually inspecting the spectrum of the measured sound for each of the plurality of combinations of air volume flow rate of the discharged air from the fan and the rotation velocity of the impeller with the same value, 0.106, of the flow coefficient . The dominant level of the tongue interference sound was obtained as the difference between the tongue interference sound level and the mean value of the sound level in the frequency range near the frequency of the tongue interference sound. The dominant level of the tongue interference sound of the specific one impeller set out in 1 ○ was obtained as the mean value of the plurality of dominant levels of the tongue interference sound obtained by the aforementioned procedure. One example of the spectra obtained by the sound level measurements is shown in Figure 34. One example of the results of the sound level measurements for one specific impeller is shown in Table 3. 4 ○ Another one specific impeller belonging to the one specific group of the impellers set out in 1 ○ was set in the one specific casing set out in 1 ○ so as to carry out 2 ○ and 3 ○ , thereby obtaining the dominant level of the tongue interference sound of the another one specific impeller. In the same way, the dominant levels of the tongue interference sound of all of the impellers belonging to the one specific group set out in 1 ○ were obtained. 5 ○ The dominant level of the tongue interference sound of the combination of the one specific group of the impellers set out in 1 ○ and the one specific casing set out in 1 ○ was obtained as the mean value of a plurality of dominant levels of the tongue interference sound obtained by 3 ○ and 4 ○ . One specific test was defined by a series of the procedures 1 ○ to 5 ○ . 6 ○ In the same way as 1 ○ to 5 ○ , the dominant level of the tongue interference sound of the combination of the one specific group of the impellers set out in 1 ○ and another one specific casing belonging to the group of the casings set out in 1 ○ was obtained. Another one specific test was defined by a series of the procedures of 6 ○ . 7 ○ In the same way as 6 ○ , a total of 47 kinds of tests were carried out for a total of 47 kinds of combinations of a plurality of groups of the impellers and a plurality of casings so as to obtain dominant levels of the tongue interference sound. Test results are shown in Table 4. In Table 4, impeller numbers belonging to the group of the impellers, casing number, specifications of the impellers, specifications of the casing and the dominant level of the tongue interference sound corresponding to each test are also shown. (3) Discussion <1> Correlation between the tongue interference sound and the nondimensional number τ It is thought that, if the half band width b of the air flow discharged from the interblade channel (20) is equal to or larger than δ 3 at the radial position of the tongue of the scroll type casing (TSTC) in Figure 24, then the tongue interference sound is hardly generated because the velocity distribution of the air flow discharged from the interblade channel is fairy uniform at the radial position of the tongue of the scroll type casing. That is, it is thought that, if τ obtained by formula 9 is equal to or larger than 1 when tongue clearance C d of the scroll type casing is substituted for x in formula 5, then the tongue interference sound is hardly generated. It is supposed that, also in Table 4, τ of each combination of the group of the impellers and the scroll type casing corresponding to the test number wherein the tongue interference sound did not appear, obtained by substituting the tongue clearance C d of the scroll type casing of the aforementioned combination for x in formula 5, calculating formulas 6 to 8 using the outside radius r, number of blades n, and blade thickness t of the group of the impellers of the aforementioned combination, and calculating τ based on formula 9, is equal to or greater than 1. Based on the aforementioned supposition, was obtained for each test number in Table 4 by substituting the tongue clearance C d of the corresponding scroll type casing for x in formula 5, calculating formulas 6 to 8 using the outside radius r, number of blades n, and blade thickness t of the corresponding group of the impellers, and calculating τ based on formula 9. Thereafter, X and c in formula 5 was determined so as to make the threshold value of τ (if τ is smaller than the "threshold value", then the tongue interference sound does not appear, i.e. the dominant level of the tongue interference sound becomes negative, while if τ is equal to or larger than the "threshold value", then the tongue interference sound appears, i.e. the dominant level of the tongue interference sound becomes positive) is substantially equal to 1. The determined value of X and c are as follows. X = 0.8 δ 2 , c = 0.3δ 1 τ was obtained for each test number in Table 4 by substituting the tongue clearance C d of the corresponding scroll type casing for x in formula 5, substituting 0.8δ 2 and 0.3δ 1 for X and c in formula 5 respectively, calculating formulas 6 to 8 using the outside radius r, number of blades n, and blade thickness t of the corresponding group of the impellers, and calculating τ based on formula 9. The calculated values of τ are shown in Table 4. Correlations between τ in Table 4 and the dominant level of the tongue interference sound are shown in Figure 35. As is clear from Figure 35, in spite of some degree of scattering, there is a definite correlation between τ in Table 4 and the dominant level of the tongue interference sound wherein the dominant level of the tongue interference sound is substantially zero in the region of τ equal to or larger than 1 and linearly increases as τ decreases in the region of τ smaller 1. As mentioned earlier, the dominant levels of the tongue interference sound shown in Table 4 are mean values of the results of numerous sound level measurements. So, it is thought that measurement errors are small. Thus, the correlation of Figure 35 is sufficiently trustworthy. The correlation between τ and the dominant level of the tongue interference sound in the region of τ smaller than 1 in Figure 35 can be approximated to the following line by the least square approximation method. Z = -47.09τ + 50.77 In the formula, Z is the dominant level of the tongue interference sound. <2> Allowable value of the dominant level of the tongue interference sound Generally, the A-weighted (0 to 20kH Z ), 1/3 octave band overall sound pressure level is used in sound pressure level measurement. Considering the characteristic of the A-weighted filter, sound pressure level measurements wherein tongue interference sound with a frequency range of about 2KH Z to 7KH Z appeared were observed for a plurality of impellers. In the observed measurements, the A-weighted, 1/3 octave band overall sound pressure level was compared with the A-weighted, 1/3 octave band overall sound pressure level without the 1/3 octave band sound pressure level of the frequency range wherein the tongue interference sound was present. The results of the comparison are shown in Table 5. Dominant levels of the tongue interference sound derived from the spectra of the sound are also shown in Table 5. Correlations between the dominant level of the tongue interference sound and the difference between the 1/3 octave band overall sound pressure level with the tongue interference sound and the 1/3 octave band overall sound pressure level without the tongue interference sound are shown in Figure 36. As is clear from Table 5 and Figure 36, when the dominant level of the tongue interference sound is equal to or less than 10dB, the difference between the 1/3 octave band overall sound pressure level with the tongue interference sound and the 1/3 octave band overall sound pressure level without the tongue interference sound is equal to or less than 0.5dB. Considering the fact that the allowable value of measurement error of a precision sound level meter is 0.5dB, the difference of 0.5dB is not significant for A-weighted, 1/3 octave band overall sound level. Thus, it is thought that, if the dominant level of the tongue interference sound is restricted equal to 10dB or less, the tongue interference sound does not sound noisy to a person. Actually, the tongue interference sound with a dominant level equal to or less than 10dB was not considered noisy by those making the measurement. Thus, it is thought that the tongue interference sound can be sufficiently decreased by setting the allowable value of the dominant level of the tongue interference sound at 10dB. [ C ] Design criteria The following design criteria for decreasing the tongue interference sound of the multiblade radial fan are derived from the aforementioned discussion. The specifications of the impeller and the scroll type casing should be determined to satisfy the following formula. -47.09 τ + 50.77 < 10.0 (where τ = b/δ 3 , b=( δ 3 - c)(C 4 / X) + c, X = 0.8δ 2 , c = 0.3δ 1 , δ 1 = {(2 π r)/n} - t, δ 2 = (2 π r)/n, δ 3 = 2 π (r + X)/n C d : tongue clearance, n: number of the blades, t : thickness of the blades, r : outside radius of the impeller). An embodiment of the present invention regarding the design criteria for decreasing the sound caused by the interference between the tongue of the scroll type casing and the impeller has been described above. However, the present invention is not restricted to the above described embodiment. The above described embodiment concerns the multiblade radial fan having an impeller with numerous radially directed blades disposed at an equal circumferential distance from each other and a scroll type casing for accommodating the impeller. However, it is thought that the same design criteria as for the multiblade radial fan can be obtained for the multiblade centrifugal fan wherein the leading edges of the blades of the multiblade radial fan are knuckled or bent in the direction of rotation (if the leading edges of the radially directed blades are bent in the direction of rotation, inlet angle of the air into the interblade channels decreases, and the sound level decreases), the multiblade sirocco fan having an impeller with numerous forward-curved blades disposed at an equal circumferential distance from each other and a scroll type casing for accommodating the impeller, the multiblade turbo fan having an impeller with numerous backward-curved blades disposed at an equal circumferential distance from each other and a scroll type casing for accommodating the impeller, etc., by carrying out the same sound level measurements as described above, determining X and c in formula 5, obtaining the same correlations between τ and the dominant level of the tongue interference sound as shown in Figure 35, and determing the same correlation line as shown in Figure 35. As is clear from Figure 35, the relation - 47.09τ + 50.77 < 10.0 is equivalent to the relation τ > 0.866. Thus, the aforementioned design criteria are equivalent to the design rule " the tongue of the scroll type casing should be located at or outside of the radial position where the ratio of the half band width of a jet flow discharged from an interblade channel to the virtual interblade pitch at a radial position where the half band width of adjacent two jet flows discharged from adjacent two interblade channels are equal to the virtual interblade pitch is 0.866. " It is thought that the aforementioned ratio varies with the type of the centrifugal fan and can be determined based on the sound level measurement. Thus, it is thought that the tongue interference sound of the multiblade centrifugal fan can be generally decreased by " locating the tongue of the scroll type casing at or outside of the radial position where the ratio the half band width of a jet flow discharged from an interblade channel to the virtual interblade pitch at a radial position where the half band width of adjacent two jet flows discharged from adjacent two interblade channels are equal to the virtual interblade pitch is a certain value near 1." It is thought that the half band width of a jet flow discharged from an interblade channel increases as the distance from the outer periphery of the impeller increases, and the ratio of the half band width of a jet flow at a certain radial position to the virtual interblade pitch at the radial position increases as the distance from the outer periphery of the impeller increases. Thus, it is thought that it is possible to make the air discharged from the interblade channels collide with the tongue of the scroll type casing after the circumferential velocity distribution of the air has become fairly uniform so as to decrease the tongue interference sound of the multiblade centrifugal fan by "locating the tongue of the scroll type casing at or outside of the radial position where the ratio of the half band width of a jet flow discharged from an interblade channel to the virtual interblade pitch is a certain value near 1." [III] Invention of a method for driving the impeller of the multiblade radial fan under a systematically derived condition of maximum efficiency As is clear from the aforementioned formula 2, the impeller of the multiblade radial fan can be driven under the condition of maximum efficiency by driving the impeller so as to make the flow coefficient  equal to 0.295(1 - nt/(2 π r )) ξ 1.641 (where n : number of the radially directed blades, t : thickness of the radially directed blades, r : outside radius of the impeller, ξ : diameter ratio of the impeller). As pointed out earlier, it is clear from Figure 19 that the decrease of the total pressure efficiency η from its maximum value is 6% or so even if  X is varied ± 25% from  Xmax . Thus, it is thought that, when the driving condition of the multiblade radial fan is determined based on formula 2, the efficiency of the multiblade radial fan does not decrease so much even if the right side of formula 2 is varied about ± 25%. Thus, it is thought that the following formula 10 can be used as the design criteria for systematically determining the driving condition of the maximum efficiency of the impeller of the multiblade radial fan.  = 0.295 ε (1-nt/(2 π r)) ξ 1.641 In the above formula, 0.75 ≦ ε ≦ 1.25 As is clear from Figure 5, the correlation diagram between the diameter ratio ξ of the impeller and the flow coefficient  Xmax based on the outlet sectional area of the interblade channel which gives the maximum value of the total pressure efficiency is substantially linear over the range 0.4 ≦ ξ ≦ 0.9. Judging from this fact, it is thought that formula 10 can be expandedly used for an impeller whose diameter ratio ξ is in the range of 0.3 ≦ ξ ≦ 0.9. However, it is rather hard to achieve the satisfactory quietness in an impeller whose diameter ratio ξ is as large as 0.9 or so, while it is rather hard to dispose numerous radially directed blades in an impeller whose diameter ratio ξ is as small as 0.3 or so. Thus, formula 10 is preferably used for an impeller whose diameter ratio ξ is in the range of 0.4 ≦ ξ ≦ 0.8. Load on the impeller of the multiblade radial fan varies and the driving condition of the impeller of the multiblade radial fan varies with the shape and the size of the casing for accommodating the impeller of the multiblade radial fan and the nozzle and duct connected to the casing. Thus, the shape and the size of the casing for accommodating the impeller of the multiblade radial fan and the nozzle and duct connected to the casing should be adequately studied so as to realize the driving condition determined by formula 10. [INDUSTRIAL APPLICABILITY OF THE INVENTION] A multiblade radial fan and a multiblade centrifugal fan with optimized quietness can be obtained by applying the design criteria in accordance with the present invention. The multiblade radial fan can be driven under the condition of maximum efficiency by applying the design criteria in accordance with the present invention. Impeller No. Outside diameter of the impeller (mm) Inside diameter of the impeller (mm) Diameter ratio Number of blades Blade thickness (mm) Rotation speed of the impeller at the measurement of the efficiency of the impeller alone (rpm) Rotation speed of the impeller at the measurement of the sound level (rpm) 1 100 40 0.40 120 0.3 5400 see note 1 2 100 40 0.40 40 0.5 5400 3 100 58 0.58 144 0.3 5400 4 100 58 0.58 144 0.5 5400 7000 5 100 75 0.75 144 0.5 5400 see note 2 6 100 75 0.75 100 0.5 5400 7 100 90 0.90 240 0.5 5400 8 100 90 0.90 120 0.5 5400 note 1 : 5000, but 7000 for  Z = 2.5° note 2 : 5000, but 7000 for  Z = 4.5°, 5.5°, 6.0° Table of reference signs Fig.1 1 Double chamber type air volume flow rate measuring apparatus 2 Auxiliary fan 3 Static pressure measuring hole 4 Impeller 5 Bellmouth 6 Motor 7 Orifice 8 Straightening grid 9 Base Fig. 2 (a) 10 Annular plate 11 Radially directed flat plate blade Fig. 2 (b) 10 Annular plate 11 Radially directed flat plate blade 12 Circular base plate HI Height of impeller Fig. 3 η Total pressure efficiency  flow coefficient Fig. 4 η Total pressure efficiency Φ x Flow coefficient based on outlet sectional area of the interblade channel Fig. 5 Φ x max ξ Fig. 6 4 Impeller 11 Radially directed blade 20 Interblade channel DAF Discharged air flow Fig. 7 4 Impeller SL Stream line Fig. 8 4 Impeller STC Scroll type casing Fig. 9 1 Double chamber type air volume flow rate measuring apparatus 2 Auxiliary fan 3 Static pressure measuring hole 4 Impeller 6 Motor 7 Orifice 8 Straightening grid 14 Inlet nozzle 15 Fan body OF Outlet of the fan STC Scroll type casing Fig. 10 3 Static pressure measuring hole 4 Impeller 6 Motor 14 Inlet nozzle 15 Fan body 16 Sound absorption material 17 Static pressure control chamber 18 Damper 19 Soundproof box OF Outlet of the fan STC Scroll type casing Fig. 11 BL Base line OF Outlet of the fan STC Scroll type casing Fig. 12 BL Base line OF Outlet of the fan STC Scroll type casing Fig. 13 BL Base line OF Outlet of the fan STC Scroll type casing Fig.14 BL Base line OF Outlet of the fan STC Scroll type casing Fig. 15 BL Base line OF Outlet of the fan STC Scroll type casing Fig. 16 BL Base line OF Outlet of the fan STC Scroll type casing Fig. 17 BL Base line OF Outlet of the fan STC Scroll type casing Fig. 18 Ksmin Minimum specific sound level  Z Divergence angle of the casing Fig. 20 4 Impeller 20 Interblade channel Fig. 21 4 Impeller 20 Interblade channel 21 Blade DR Direction of rotation TSTC Tongue of the scroll type casing Fig. 22 4 Impeller 20 Interblade channel DR Direction of rotation Fig. 23 22 Nozzle b Half hand width Fig. 24 4 Impeller 20 Interblade channel 21 Blade Cd Tongue clearance Cl Center of the impeller R Tongue radius TSTC Tongue of the scroll type casing Fig. 25 (a) 4 Impeller 10 Annular plate 20 Interblade channel 21 Blade IBC Inlet breadth of the channel OBC Outlet breadth of the channel Fig. 25 (b) 4 Impeller 10 Annular plate 12 Circular base plate 20 Interblade channel 21 Blade H Height Fig. 26 4 Impeller BL Base line OF Outlet of fan R Tongue radius STC Scroll type casing Fig. 27 4 Impeller BL Base line OF Outlet of fan R Tongue radius STC Scroll type casing Fig. 28 4 Impeller BL Base line OF Outlet of fan R Tongue radius STC Scroll type casing Fig. 29 4 Impeller BL Base line OF Outlet of fan R Tongue radius STC Scroll type casing Fig. 30 4 Impeller BL Base line OF Outlet of fan R Tongue radius STC Scroll type casing Fig. 31 4 Impeller BL Base line OF Outlet of fan R Tongue radius STC Scroll type casing Fig. 32 4 Impeller BL Base line OF Outlet of fan R Tongue radius STC Scroll type casing Fig. 33 4 Impeller BL Base line OF Outlet of fan R Tongue radius STC Scroll type casing

Claims: A method for designing a multiblade centrifugal fan comprising an impeller (4) having numerous blades (21) circumferentially spaced from each other and a scroll type casing (STC) accommodating the impeller, characterized in that the tongue of the scroll type casing (TSTC) is determined to be located at the radial position where the ratio of the half band width (b) of a jet flow discharged from an interblade channel (20) to the virtual interblade pitch is a value in the range of greater than 0.866 and smaller than, or equal to, 2.92. A method for designing a multiblade centrifugal fan according to claim 1, wherein the tongue of the scroll type casing (TSTC) is determined to be located at the radial position where the ratio of the half band width (b) of a jet flow discharged from an interblade channel (20) to the virtual interblade pitch at a radial position where the half band width (b) of two adjacent jet flows discharged from two adjacent interblade channels (20) are equal to the virtual interblade pitch is a value in the range of greater than 0.866 and smaller than, or equal to, 2.92. A method for designing a multiblade centrifugal fan according to claim 1, wherein specifications of the impeller (4) and the scroll type casing (STC) are determined so as to satisfy the correlation expressed by the formula -Aτ + B < 10.0 (where τ = b / δ 3 , b = (δ 3 - c)(C d /X) + c, c = Cδ 1 , δ 1 = {(2 π r) / n} - t, δ 3 = 2 (r + X) / n, C d : tongue clearance, n : number of the blades, t : thickness of the blades, r : outside radius of the impeller (4), A, B, C, X : constants determined through tests). A method for designing a multiblade centrifugal fan according to claim 1, wherein specifications of the impeller (4) and the scroll type casing (STC) are determined so as to satisfy the correlation expressed by the formula - 47.09 τ + 50.77 < 10.0 (where τ = b / δ 3 , b = (δ 3 - c)(C d / X) + c, X=0.8δ 2 , c=0.3δ 1 , δ 1 = {(2 π r)/n}-t, δ 2 =(2 π r)/n, δ 3 = 2π(r+X)/n, C d : tongue clearance, n : number of the blades, t : thickness of the blades, r: outside radius of the impeller). A multiblade centrifugal fan comprising an impeller having numerous blades circumferentially spaced from each other and a scroll type casing (STC) accommodating the impeller (4), characterized In that the tongue of the scroll type casing (TSTC) is located at the radial position where the ratio of the half band width (b) of a jet flow discharged from an ihterblade channel to the virtual interblade pitch is a value in the range of greater than 0.866 and smaller than, or equal to, 2.92. A multiblade centrifugal fan according to claim 5, wherein the tongue of the scroll type casing (TSTC) is located at the radial position where the ratio of the half band width (b) of a jet flow discharged from an interblade channel (20) to the virtual interblade pitch at a radial position where the half band width of two adjacent jet flows discharged from two adjacent interblade channels are equal to the virtual interblade pitch is a value in the range of greater than 0.866 and smaller than, or equal to, 2.92. A multiblade centrifugal fan according to claim 5, wherein specifications of the impeller (4) and the scroll type casing (STC) are determined so as to satisfy the correlation expressed by the formula - A τ + B < 10.0 (where τ = b/δ 3 , b = (δ 3 - c)(C d / X) + c, C = Cδ 1, δ 1 = {(2 π r) / n}-t, δ 3 = 2 π (r + X) / n, C d : tongue clearance, n : number of the blades, t : thickness of the blades, r : outside radius of the impeller, A, B, C, X : constants determined through tests). A multiblade centrifugal fan according to claim 5, wherein specifications of the impeller (4) and the scroll type casing (STC) are determined so as to satisfy the correlation expressed by the formula - 47.09 τ + 50.77 < 10.0 (where τ = b / δ 3 , b = (δ 3 - c)(C d / X) + c, X=0.8 δ 2, c = 0.3 δ 1 , δ 1 = {(2 π r) / n}- t, δ 2 = (2 π r) / n, δ 3 = 2 π (r + X) / n, C d : tongue clearance, n : number of the blades, t : thickness of the blades, r : outside radius of the impeller).

Inventors: HATAKEYAMA MAKOTO, KAWAGUCHI HIDEKI, NAKAMURA YOSHINORI, SHINBARA NOBORU, UEMURA TAKESHI, HATAKEYAMA, MAKOTO, KAWAGUCHI, HIDEKI, NAKAMURA, YOSHINORI, SHINBARA, NOBORU, UEMURA, TAKESHI, HATAKEYAMA, Makoto Toto Ltd. 1-1, Nakashima, KAWAGUCHI, Hideki Toto Ltd. 1-1, Nakashima, NAKAMURA, Yoshinori Toto Ltd. 1-1, Nakashima, SHINBARA, Noboru Toto Ltd. 1-1, Nakashima 2-chome, UEMURA, Takeshi Toto Ltd. 1-1, Nakashima 2-chome
Applicants: TOTO LTD, TOTO LTD.
Application year: 1996
Main classification: F04D29
IPC codes: F04D29