1 Copyright © 2009 by ASME

Proceedings of IMECE 2009

2009 ASME International Mechanical Engineering Congress and Exposition November 13-November 19, 2009, Lake Buena Vista, Florida, USA

IMECE2009-12852

HIGH PRESSURE FAN DESIGN FOR BIOGAS PLANTS

Philipp Epple, Mihai Miclea, Harald Schmidt and Antonio Delgado

Institute of Fluid Mechanics, LSTM Friedrich-Alexander University, Erlangen-

Nuremberg, Cauerstrasse 4, 91058 Erlangen, Germany

Tel: 004991318529496 Fax: 004991318529503

Corresponding author: philipp.epple@lstm.uni-erlangen.de

Hans Russwurm Russwurm Ventilatoren GmbH

Email: hans.russwurm@ruwu.de

ABSTRACT High pressure fans for thermal power generation stations, especially biogas plants, usually operate in a spiral casing at high pressures of about p=12.000 - 15.000 Pa and low flow rates of around Q=100 – 600 m³/s. The motor drive has a constant speed of 3.000 1/min. This corresponds to specific speeds of nq=3 – 6 min-1, which is already beyond the conventional range of single stage radial machines. Nowadays these fans for biogas plants usually operate at higher flow rates than specified or are multiple stage radial fans. Therefore a new class of radial impellers has been developed. These single stage impellers have a unique high pressure at a low flow rate operating point. In this work several impellers of this new class have been designed and validated with a commercial Navier-Stokes solver (ANSYS CFX). The design process is described in detail. It is based on a new extended analytical and numerical design method. It is shown that the prescribed unusual operating point can be achieved with single stage radial impellers. An in detail flow analysis is given showing the fundamental flow physics of these impellers. INTRODUCTION High pressure fans for biogas plants are already available on the market. Usually the impeller runs in a sealed casing, Figure 1. They exist as one stage as well as many stage fans. These high pressure fans operate at a flow rate of up to 12.000 m³/h. The corresponding pressure increase is up to 1500 daPa.

The main disadvantages of these conventional fans are: a) High pressure is always connected to high flow rates b) In many cases these radial fans have more than one stage, leading to high production costs. c) The impellers are riveted and not welded, Figure 2

Figure 1: Conventional fan for biogas plants

AIM OF THE PROJECT The aim of this project was to develop a one stage high pressure fan for biogas plants with the following characteristics:

1. nominal diameter from 630 mm – 1400 mm

Proceedings of the ASME 2009 International Mechanical Engineering Congress & Exposition IMECE2009

November 13-19, Lake Buena Vista, Florida, USA

IMECE2009-12852

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2. Pressure rise from 8.000 Pa to 15.000 Pa 3. Flow rates from 100 m³/h to 600 m³/h (28 l/s - 167

l/s). 4. The impeller shall be manufactured from welded

metal, according to the demand from steel, Cr-Ni-Steel or light metal materials.

Design goals 2) and 3) are summarized in Figure 3.

Figure 2: Conventional riveted high pressure fan

0

2000

4000

6000

8000

10000

12000

14000

16000

10 100 1000 10000

Pre

ssu

re [

Pa

]

Flow rate [l/s]

New Conventional

Figure 3: Conventional and new high pressure fan

operating window

In Table 1 the specific speed nq, the speed number σ as well as the diameter number δ for the conventional and the new fans are shown. It is clear that the new operating window in Figure 3 lies outside the Cordier diagram (Cordier, [1]) and hence of the optimum operating range of radial impellers. In fact the optimum machine for the new operating range would be a side channel machine, as can be seen in the extended Cordier diagram according to Grabow [2], partially represented in Figure 4.

Q Q DP nq σσσσ δδδδ

[m³/h] [ls] [Pa] [1/min] [-] [-]

Conventional 12000 3333 15000 45,82 0,29 3,69

New 100 28 8000 6,36 0,04 34,50

New 600 167 8000 15,58 0,10 14,08

New 600 167 15000 10,25 0,06 16,48New 100 28 15000 4,18 0,03 40,37

Table 1: Specific speed and specific diameter

However, there are two reasons why the choice is still a radial machine:

1. In order to achieve better efficiencies and to operate the impeller, it will be placed inside a spiral casing. The operating point of the impeller in the spiral casing will always lie at lower flow rates as the operating point of the impeller only due to the inevitable losses in total pressure in the spiral casing. For details see Miclea et all Fehler! Verweisquelle

konnte nicht gefunden werden.. 2. Besides of the main operating range as shown in

Figure 3, the impeller should be able to reach also high pressures at somewhat higher flow rates, having a broad operating range.

THE DESIGN PROCEDURE The general design procedure for radial impellers is described in detail in Epple ([6], [7] and [8]). Therefore only the main design equations will be presented here in order to understand the design process of the impellers. In order to analyse the design problem, one starts with the expression for the total and total-to-static pressures

22 2 2 2

2tanm

t u

cp u c u u

ßρ ρ

∆ = = −

(1.1)

( )2

2 2 2 2t-s 2 2 2 2

2

1 1p

2 2 sinm

cu w u

ßρ ρ

∆ = − = −

(1.2)

where the velocity components are explained in Figure 5. Since

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2 2u d nπ= (1.3)

where d2 is the exit diameter of the impeller and n is the rotating speed and

2

2 2

m

Qc

d bπ= (1.4)

22

2 2 2 2sin sin

w Qw

ß d b ßπ= = (1.5)

where Q ist he flow rate, d2 is the exit diameter of the

0,0

0,1

1,0

10,0

0,1 1,0 10,0 100,0

Sp

eed

nu

mb

er

σσ σσ

Diamater number δδδδ

Conventional

New

Axial

Diagonal

Radial

Side channel

New_18_CAB

Figure 4: Extended Cordier diagram

impeller, b2 the exit height of the impeller and ß2 the exit angle of the impeller, as shown in Figure 5, one can see that the maximum pressure is reached at zero flow rate and can be written as

( )22

,max 2 2

1 1

2 2t sp u d nρ ρ π−∆ = = (1.6)

and the maximum flow rate at zero pressure is 2 2

max 2 2 2sinQ d b n ßπ= (1.7)

From equations (1.2) to (1.7) one can easily show that 2

,max

,max

1t s t s

t s

Qp p

Q− −

−

∆ = ∆ −

(1.8)

which is the equation of a parabola. With the two equations (1.6), (1.7) and (1.8) it is possible to adjust the slope and shape of the head flow rate characteristic as shown in Figure 6.

Figure 5: Velocity triangles

where u1, u2: inlet/outlet peripheral velocity c1, c2: inlet/outlet absolute velocity cm2, cm2: inlet/outlet meridian absolute velocity cu2, cu2: inlet/outlet peripheral absolute velocity w1, w2: inlet/outlet relative velocity wm2, wm2: inlet/outlet meridian relative velocity wu2, wu2: inlet/outlet peripheral relative velocity α1, α2: inlet/outlet absolute flow angle ß2, ß2: inlet/outlet blade angle r1, r2: inlet/outlet radius d1, d2: inlet/outlet diameter

Figure 6: Head flow rate characteristic adjustment

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In the present development the motor drive was given and so was the constant speed of n = 3.000 1/min. Therefore, according to equation (1.6), in this preliminary 1D mean line design analysis, the maximum pressure is a function of the outer impeller diameter d2 only. Looking now at equation (1.7) one can see that, once the rotating speed n and the impeller’s outer diameter d2 are fixed, only the exit height b2 and the exit blade angle ß2 are still available to adjust the maximum flow rate Qmax and hence the slope of the head flow rate characteristic. In order to design high efficiency impellers, however, it is also necessary to look also at the ideal total-to-static efficiency, as described in Epple, [6], [7] and [8], which, considering equations (1.1) and (1.2), can be written as

( )( )

222 2 2

2 2 2 2

/ sin1

2 / tanmt s

t s

t m

u c ßp

p u u c ßη −

−

−∆= =

∆ − (1.9)

which can also be written in non dimensional form as

( )2

2

2

1 / sin1

2 1 / tant s

ß

ß

ϕη

ϕ−

−=

− (1.10)

where 2 2/mc uϕ = is the flow coefficient of the impeller. For

details please see Epple [6], [7] and [8].

Figure 7: Total-to-static efficiency as a function of the flow

coefficient

One can see that the total-to-static efficiency is a function of the impeller’s exit angle ß2 and the flow coefficient ϕ only. The

smaller the exit angle ß2, the higher the maximum total-to-static efficiency but the smaller also the maximum flow coefficient. The difference of the total and the total-to-static pressure is equal to the dynamic pressure at the exit of the impeller

22

1

2t t sp p cρ−∆ − ∆ = (1.11)

which means that the higher the total-to-static efficiency, as defined by equation (1.10), the less are the dynamic pressure losses at the exit of the impeller. This is a good efficiency definition to improve the efficiency of an impeller only. In the case of the impeller-spiral-casing-unit, however, it might happen that a high efficiency impeller, when running in a spiral casing, is worse as a not so good impeller running in another spiral casing. Hence, it is important to optimize the impeller-spiral-casing-unit. This is shown in detail in the continuation of this work, Miclea and Epple [13]. In the present part of the work, however, the focus is on the impeller only. As to the blade shapes, two kinds of blade shapes where used: circular arc blade shapes, as described e.g. in Eckert & Schnell [4] and Eck [3] and blades computed point by point inversely, as described in Epple [6], [7] and [8] and Pantell [11]. The design of the impellers was performed with an Excel based design software developed by the corresponding author. From here the geometry files where exported to a CAD program, PTC ProEngineer Wildfire 3.0, e.g. Köhler [9] and Lamit [10] the 3D models where built. From here grids where generated using the commercial grid generator ANSYS Icem and finally CFD computations where performed with ANSYS CFX. As a turbulence model the Shear Stress Transport Model from Menter [12] was chosen.

Figure 8: Flow domain of the inlet, impeller and outlet

In Figure 8 the CAD model of the flow model is shown. It includes an inlet domain, the full impeller and an outlet domain. Details of the impeller’s inlet nozzle are shown in Figure 9.

INLET

OUTLET

IMPELLER

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Figure 9: Flow domain detail of the inlet nozzle

Figure 10: Example of impeller grid

In Figure 10 a typical tetrahedral impeller grid is shown and in Table 2 a corresponding grid statistics is presented.

DOMAIN NR. ELEMENTS

INLET 293.540

IMPELLER 1.236.032

OUTLET 827.666

Total 2.357.238

Table 2: Grid statistics

REFERENCE GEOMETRY In order to start the optimization procedure, a starting geometry was supplied by the manufacturer. This geometry will be referenced as the “reference” impeller. The corresponding prototype is shown in Figure 11. The main dimensions of the reference impeller are shown in Table 3. Already the starting geometry was designed for high pressures and low flow rates, as can be seen by the very low ratio b2/d2=0.025, what can also be seen in Figure 11. The rotating speed of the reference impeller and all subsequent designs is

constant and equal to n=3.000 1/min. The blade shape was taken to be straight, except from the shaft to the inlet diameter, where they are circular inlet vane blades. The shroud is parallel to the hub, except at the entry cone. The resulting pressure and efficiency characteristics are shown in Figure 12 and Figure 13. One can see that the total-to-static efficiency is rather moderate, which was also expected since the exit angle ß2 is rather large, see equation (1.10) and Figure 7. This design will be improved in the next steps.

Figure 11: Prototype of the welded starting reference

impeller

ß1

[°]

ß2

[°]

d0

[mm]

d1

[mm]

d2

[mm]

b1

[mm]

b2

[mm] θθθθ [°] z

Reference 31 78,60 180 1000 40,0 25 59 8+8

Table 3: Main dimensions of the reference impeller

Figure 12: Head characteristic of the reference impeller

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Figure 13: Total-to-static efficiency of the reference

impeller

INFLUENCE OF THE INLET ANGLE FOR ß2=20° AND 25°

A first improved design proposal is summarized in Table 4

ß1 [°]

ß2 [°]

d0 [mm]

d1 [mm]

d2 [mm]

b1 [mm]

b2 [mm]

θθθθ [°]

z PR QR

Ref. 30,51 78,60 180 1000 40,0 25 59 8+8 1,00 1,00

New_1 10 25,00 340 360 1140 50,0 25 180 8 1,30 0,56

New_2 15 25,00 340 360 1140 50,0 25 180 8 1,30 0,56

New_3 20 25,00 340 360 1140 50,0 25 180 8 1,30 0,56

Table 4: Main dimensions of the new designs 1-3

In the last two columns of the table the pressure ratio PR, defined as the ration between the maximum total-to-static pressure of the new impeller divided by the maximum total-to-static pressure of the reference impeller, according to equation (1.6),

,max,

,max,

t s NEW

t s REF

pPR

p

−

−

∆=

∆ (1.12)

and the flow rate ratio QR, defined as the ration between the maximum flow rate of the new impeller divided by the maximum flow rate the reference impeller, according to equation (1.7),

max,

max,

NEW

REF

QQR

Q= (1.13)

are given.

One can see from Table 4 that these new designs have a larger outlet diameter d2 as the one from the reference impeller and hence a PR of 1,3 which is approximately confirmed by the results shown in Figure 14. However, the flow rate ration QR computed from the main dimensions in Table 4 is exceeded by far by the CFD simulations shown in Figure 13 and Figure 14. That means that the flow quality in the new designs 1-3 is much better than the one in the reference impeller, as can also be seen in the plot of the total-to-static efficiency in Figure 15. The difference between designs 1-3 is in the inlet angle only, which means different shock losses at the impellers entrance. It can be seen, that it is very important to find the best inlet angle, since it has a sensible influence on the whole impeller’s performance characteristics.

Figure 14: Total-to-static pressure of the new designs 1-3

Figure 15: Total-to-static efficiency of the new designs 1-3

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INFLUENCE OF THE WRAP ANGLE

As a next parameter study the wrap angle, as shown in Figure 16, was changed. The main dimension of the new impellers are shown in Table 5.

Figure 16: Wrap angle θθθθ

ß1 [°]

ß2 [°]

d0 [mm]

d1 [mm]

d2 [mm]

b1 [mm]

b2 [mm]

θθθθ [°]

z PR QR

Ref. 30,51 78,60 180 1000 40,0 25 59 8+8 1,00 1,00

New_5 15 20,00 340 360 1140 50,0 18 180 8 1,30 0,33

New_7 15 20,00 340 360 1140 50,0 18 150 8 1,30 0,33

New_8 15 20,00 340 360 1140 50,0 18 120 8 1,30 0,33

Table 5: Main dimensions for the wrap angle study

Figure 17: Total-to-static pressure for wrap angle study

The main results, i.e. the characteristics for the total-to-static pressure and the total-to-static efficiency are shown in Figure 17 and Figure 18 resp. One can see, that the smaller the wrap angle, i.e. the shorter the blades, the better the results. Also here, although the QR is very small, i.e. 0,33, the new designs achieve a flow rate above the reference impeller, showing that they are performing better, as is also confirmed by the total-to-static efficiency, Figure 18.

Figure 18: Total-to-static efficiency for wrap angle study

INFLUENCE OF THE EXIT ANGLE As known from the literature, e.g. Sigloch [14] and Enßlinger [5], the exit angle has a sensible influence on the performance of a radial impeller. As has been shown in the theory part, as for instance can be seen on equations (1.1), (1.2), (1.6), (1.7) and (1.10), the exit angle is proven also theoretically to be a sensible design parameter, having in fact influence on all relevant performance quantities of an impeller: flow rate, pressure and efficiency. Therefore the parameter study as summarized in Table 6 was performed.

ß1 [°]

ß2 [°]

d0 [mm]

d1 [mm]

d2 [mm]

b1 [mm]

b2 [mm]

θθθθ [°]

z PR QR

Ref. 30,51 78,60 180 1000 40,0 25 59 8+8 1,00 1,00

New_15 15 25,00 220 240 1000 40,0 25 180 8 1,00 0,43

New_16 15 35,00 220 240 1000 40,0 25 170 8 1,00 0,59

New_17 15 50,00 220 240 1000 40,0 25 160 8 1,00 0,78

New_18 15 80,00 220 240 1000 40,0 25 150 8 1,00 1,00

Table 6: Main dimensions for the exit angle study

The results presented in Figure 19 and Figure 20 show, that all these new designs have the same PR, which is pretty well confirmed by the CFD simulations. However, in the CFD results all these designs have a lower maximum flow rate, although New_18 has a QR equal to the reference impeller. Furthermore, all these designs have almost the same maximum flow rate, although they have quite different values of QR, as can be seen in Table 6. The reason here fore is, that these impellers have all a small inlet angle ß1=15° as compared with the reference impeller, ß1=30,51° and as a consequence they choke at higher flow rates, leading to the observed reduction of maximum flow rate as compared with the reference impeller.

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Figure 19: Total-to-static pressure for exit angle study

Figure 20: Total-to-static efficiency for exit angle study

As to the total-to-static efficiencies, as shown in Figure 20, one can see very nicely how the total-to-static efficiency increases as the exit angle ß2 decreases, which is consistent with the 1D meanline theory, as given by equation (1.10) and shown also in Figure 7. One can see that the maxima of the total-too-static efficiencies are shifted to the left of the one of the reference impeller, which is in agreement with the design goals. INFLUENCE OF THE OUTER DIAMETER

A very strong design parameter is the outer diameter d2, since it goes squared in the maximum pressure, equation (1.6) and also squared in the maximum flow rate, equation (1.7). The main dimensions for this parameter study are presented in Table 7.

ß1 [°]

ß2 [°]

d0 [mm]

d1 [mm]

d2 [mm]

b1 [mm]

b2 [mm]

θθθθ [°]

z PR QR

Ref. 30,51 78,60 180 1000 40,0 25 59 8+8 1,00 1,00

New_19 15 25,00 220 240 950 40,0 25 180 8 0,90 0,39

New_15 15 25,00 220 240 1000 40,0 25 180 8 1,00 0,43

New_2 15 25,00 340 360 1140 50,0 25 180 8 1,30 0,56

New_9 15 12,00 380 400 1200 60,0 30 120 12 1,44 0,37

Table 7: Main dimensions for outer diameter study

One can see that the maximum pressure, at zero flow rate, has to increase with the PR as shown in Table 7, which is quite well confirmed by the CFD computations as can be seen in Figure 21. However, the maximum flow rate, as predicted by the QR shown in Table 7, and which is expected to be roughly of the same order of magnitude for all four impellers New_12, New_15, New_2 and New_9, comes out to vary substantially between these four designs. In fact the outer diameter dominates, since the maximum flow rate drops according to the outer diameter of the impeller, as can be easily verified comparing the results of Figure 21 and Figure 22 with the outer diameters shown in Table 7. It is worth to mention, that for the impellers Ref. and New_15, which have the same outer diameter, the maximum flow rate is controlled by the exit angle ß2, which is much bigger for the Ref. impeller, and so is also the maximum flow rate. The impellers New_19 and New 15 are very similar, and so are also the total-to-static pressure and total-to-static efficiency characteristics, and hence the maximum flow rate. The reason why the impeller New_9 has by far the highest flow rate is not only because of its large outer diameter d2 and exit height b2 but also because it has the largest inlet diameter d1, see Figure 23. The small inlet diameter d1 of the impeller New_9 causes very high flow velocities at the impellers inlet and hence high losses so that the maximum flow rate is much smaller than the one of the impeller New_19. Impeller New_2 has the second largest inlet and outlet diameters and hence also the second largest maximum flow rate, confirming this dependency. The impellers New_15 and New_19 have the smallest outer and inner diameters and hence also the smallest maximum flow rates. It is worth to mention also, that the maximum efficiency of all these impellers, except for Ref., is around 40%. This is expected since all these impellers have the same exit angle ß2=25°, except New_9, which has an exit angle of ß2=12°, which is already very small, leading to very high relative velocities, equation (1.5), which restricts the further increase of efficiency keeping all these impellers at the same maximum efficiency level.

9 Copyright © 2009 by ASME

Figure 21: Total-to-static pressure for outer diameter study

Figure 22: Total-to-static efficiency for outer diameter

study

Figure 23: Influence of the inner diameter - New_19 (left)

and New_9 (rigth) both at Q=1000 l/s

POINT WISE COMBUTED BLADES AND CIRCULAR ARC BLADES

As a last study a comparison between point wise computed blades (PWCB) and circular arc blades (CAB, see Eck [3] and Eckert [4]) will be presented. Point wise computed blades are usually more efficient, when they are designed in such a way that a proper pressure gradient result in the blade channel, see e.g. Epple [6], [7] and [8] and Pantell [11]. Even so, since a parameterization for the blade angle is needed, there are some cases where a circular arc blade is to be preferred, especially when, because of the type of application of the impeller, the circular arc blades offer a batter blade channel enlargement at the inlet and the initial portion of the blades. This is the case for the present case of impeller.

ß1 [°]

ß2 [°]

d0 [mm]

d1 [mm]

d2 [mm]

b1 [mm]

b2 [mm]

θθθθ [°]

z PR QR

Ref. 30,51 78,60 180 1000 40,0 25 59 8+8 1,00 1,00

New_15 15 25,00 220 240 1000 40,0 25 180 8 1,00 0,43

New_17 15 50,00 220 240 1000 40,0 25 160 8 1,00 0,78

New_18 15 80,00 220 240 1000 40,0 25 150 8 1,00 1,00

Table 8: Main dimensions for the point wise computed

impellers blades (PWCB)

Six impellers were designed. The main dimensions are shown in Table 8. For each set of main dimensions two impellers were designed: one with inversely designed and computed point by point and one with circular arc blades, resulting in a total of six impellers. Furthermore, these impellers differ in the exit and the wrap angles only. In Table 9 the wrap angles of the point wise computed blades are compared with the wrap angles of the circular arc blades. One can see that the circular arc blades are all shorter, i.e. they have a smaller wrap angle.

θθθθ [°]

θθθθ [°]

PWCB CAB

New_15 180 118,6

New_17 160 87,8

New_18 150 58,6

Table 9: Wrap angles for point wise computed (PWCB) and

circular arc blades (CAB)

It is clear from Figure 24 and Figure 25 that the circular arc blades are performing much better for this application. In Figure 26 the stream lines for New_17 (CAB on top and PWCB on bottom) impellers are shown. Here one can see that the PWCB impeller is much more closed for small radii than the CAB impeller, leading to higher velocities and hence higher losses and worse performance. But no matter the type of

10 Copyright © 2009 by ASME

impeller, on e can see for all impellers that the smaller the exit angle ß2, the higher the total-to-static efficiencies.

Figure 24: Total-to-static pressure for PWCB and CAB

Figure 25: Total-to-static efficiency for PWCB and CAB

In Figure 26 one can see also, that the flow in these large impellers is accompanied by huge vortices, due to the low flow rates at which these impellers operate. This is inherent to this impeller type with small inlet and steep static-to-total pressure flow rate characteristic and cannot be avoided. Finally the impeller New_18CAB is shown in the Cordier diagram, Figure 4 (dotted line). One can see that the impeller covers the full range from radial to side channel impeller.

Figure 26: Circular arc blades (left) and point wise

computed blades (rigth)

CONCLUSIONS AND OUTLOOK The fundamental relations for impeller design and performance optimization were presented. They were then applied to design a new class of radial impellers for high pressure and low flow rate to be used in biogas plants. These impellers cover the range from radial to side channel impellers. It was shown with a sequence of designs how the performance characteristics can be adjusted changing the geometry of the impeller in order to achieve the design goal. In a next step, as shown in Miclea and Epple [13], these impellers where combined with spiral casings in order to design impeller - spiral - casing units. Although the method presented might at a first glance seem simple it was shown that the combined analytical and numerical method in fact is very powerful in order design radial impellers for special applications as well as to combine the method with spiral casing design methods in order to design full fans.

NOMENCLATURE PR [-] Pressure ratio QR [-] Flow rate ratio Re [-] Reynolds number b [m] blade height c [m s-1] absolute velocity d [m] diameter n [min-1] speed

nq [min-1] specific speed p [Pa] pressure r [m] radius s [m] blade thickness u [m s-1] peripheral velocity w [m s-1] relative velocity z [-] number of blades ∆ [-] variation of a quantity α [rad] diffuser blade angle,

Absolute impeller velocity angle ß [rad] impeller blade angle δ [-] diameter coefficient

ϕ [-] flow coefficient 2 2/mc uϕ =

11 Copyright © 2009 by ASME

η [−] efficiency

ν [m² s-1] kinematic viscosity of air ρ [kg m-3] density σ [-] speed coefficient Subscripts and Superscripts

1 at the impeller inlet 2 at the impeller exit t total s static

REFERENCES [1] Cordier, O.: Ähnlichkeitsbedingungen für

Strömungsmaschinen, BWK Bd. 6, Nr. 10 Oktober 1953.

[2] Grabow, Gerd: Das erweiterte „Cordier“-Diagram für Strömungs- und Verdrängermaschinen, Energietechnik, 42 Jg., Heft 1, Januar 1972.

[3] Eck, B., 1991, „Ventilatoren – Entwurf und Betrieb der Radial-, Axial- und Querstromventilatoren“, 5. Auflage, Springer – Verlag, Berlin

[4] Eckert, B. und Schnell, E.: „Axialkompressoren und Radialkompressoren, Anwendung – Theorie – Berechnung“, Springer – Verlag, Berlin, 1953

[5] Enßlinger, J., 1952, „Wirkungsgradsteigerung von Ventilatoren radialer Bauart durch strömungstechnisch richtige Formgebung der Flügelräder”, M.A.N. Forschungsheft, S. 59-67

[6] Epple, Ph., Ilic, C., and Durst, F., 2006, Conference on Modeling Fluid Flow (CMFF ’06), “Combined Analytical and Numerical Radial Fan Performance Optimization”, Budapest, pp. 1110- 1117

[7] Epple, Ph., Miclea, M., Ilic, C. Delgado, A: An Extended Analytical And Numerical Design Method With Applications Of Radial Fans

[8] Epple, Ph., Karic, B., Ilíc, �C, Becker, S., Durst, F and Delgado. A: Design of radial impellers: a combined extended analytical and numerical method, Proc. IMechE, Part C: J. Mechanical Engineering Science, 2009, 223(C4), 901 917. DOI: 10.1243/09544062JMES1196

[9] Köhler, P., 2003, Pro/ENGINEER Praktikum, VIEWEG Studium Technik, Wiesbaden.

[10] Lamit, L.G., 2004, Pro/ENGINEER Wildfire, Thomson Brooks/Cole, Belmont, UK.

[11] Pantell, K., 1949, „Über die Schaufel-ausbildung von Turbo-Arbeitsmaschinen”, Konstruktion, Heft 3, S. 77-82

[12] Menter, F.R., 1993, “Zonal two-equation k-ω turbulence models for aerodynamic flows”, AIAA Paper 96-2906

[13] Miclea, M., Epple, Ph., Schmidt, H. and Delgado, A:

“High Efficiency Design Of High Pressure Radial Fan Spiral

Casings Used For Biogas Transport”, Proceedings of

IMECE2009 2009 ASME International Mechanical

Engineering Congress and Exposition, Orlando.

[14] Sigloch, H., 1993, „Strömungsmaschinen, Grundlagen und Anwendungen“, 2. Auflage, Carl Hanser Verlag München