# The Optimization of the Geometry of the Centrifugal Fan at Different Design Points

^{1}

^{2}

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## Abstract

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## 1. Introduction

^{3}/min, 40% full efficiency, and a noise level of 54.05 dB at the operating point. The optimization criteria of the researchers were the flow rate and the full efficiency of the impeller. For the calculation of the optimal values of the shape functions, a multi-stage calculation algorithm was created, which evaluates the influence of the variables on efficiency. In addition, a mathematical modeling algorithm was employed, which refines the step of the variable intervals, monitoring changes in the studied criteria. The researchers noted that the calculation time was greatly reduced at this stage, as the intervals that most satisfy the optimal values of the criteria were analyzed in the most detail. It was observed that the full efficiency increased by 3.1%, with a flow rate of 1.4 m

^{3}/min, when comparing the optimized profile impeller with the original one. The improvement in criteria was achieved by changing the leading and trailing angles of the profile string, and the greatest differences were observed at the trailing edge of the profile, which was highly convex.

- Differentiation, which is necessary for calculating the objective function, requires an initial program code that cannot be obtained from commercial packages;
- Numerical differentiation can be inaccurate and inefficient.

- The convergence of the problem depends only on the results of the objective function;
- Theoretical analysis shows that problems solved by global optimization methods can be solved in polynomial time, while deterministic methods always require exponentially increasing computation of the objective function (Dyer 1991). Despite the guarantee of finding a solution, deterministic algorithms are often rejected due to numerical differentiation and long execution time;
- Stochastic algorithms are more popular in engineering when it comes to solving optimization problems.

## 2. Materials and Methods

_{1}) and the quarter radii of the fan housing. The centers of curvature of the envelope helix are located more than 0.0625⋅${\mathrm{d}}_{1}$ from the origin of the coordinates. The radii of convexity of the quarters (moving away from the housing outlet) are 0.712⋅${\mathrm{d}}_{1}$, 0.837⋅${\mathrm{d}}_{1}$, and 0.962⋅${\mathrm{d}}_{1}$. The outer perimeter smoothly transitions. The height of the fan body is taken to be 86 mm, and the width of the outlet channel is 94 mm, paying attention to the dimensions of products common on the market (Figure 1). Figure 1 shows a comparison between a typical impeller body and the one used in this work. Frank P. Bleier’s Fan Handbook provides a schematic diagram describing the relationship between the impeller diameter and the quarter radii of the fan casing.

#### Optimization Problem Definition

^{3}/s), $P$ is flow pressure (Pa), ${K}_{P}$ is the compression ratio, and ${H}_{i}$ is the current power used by the fan motor (W).

^{3}/s), $P$ is flow pressure (Pa), and ${P}_{req}$ is the power needed to overcome air resistance (W).

## 3. Results

^{2}and, according to Equation (18), the flow velocity is ${\upsilon}_{p}$ = 13.15 m/s (at the first design point, the airflow rate blown by the Ziehl-Abegg fan is $Q$ = 500 m

^{3}/h).

#### 3.1. Fan Blade Leading- and Trailing-Angle Optimization

^{3}/h and a resistance of 75 Pa, with the fan operating at an angular speed of 2000 rpm. To maintain the integrity of the work, it is assumed that the device will have to overcome a system pressure increase of 70 Pa at the second design point. It is assumed that the fan will create an air flow rate of 180 m

^{3}/h when operating at a speed of 1930 rpm.

_{1}at the second design point is calculated as 11.48°. These calculations are also performed under the assumption that the front part of the blade is oriented towards the incoming air flow.

#### 3.2. Study of Fan Operating Curves

#### 3.2.1. Operating Curves at First Design Point

_{1}= 15° and β

_{2}= 89° works most efficiently in this mode. Performance and efficiency curves are determined for a fan with these geometry parameters.

^{3}/h) created by the fan, and the vertical Y axis shows the static pressure increase of the system (Pa). These characteristic curves are determined at different angular speeds, namely 1500, 2000, and 2500 rpm. These speeds are chosen based on the operating speeds of real fans with 140 mm diameter impellers.

^{3}/h when operating at angular speeds of 1500, 2000, and 2500 rpm, respectively. These points describe the extreme operating modes, since the device works only in the absence of system resistance. The maximum pressures generated by the fan reach 51.5, 99, and 145.5 Pa, respectively.

^{3}/h), and the vertical Y axis shows the static efficiency (%), which is calculated according to the equations discussed previously. The obtained data show that the maximum efficiencies of the fan optimized at the first DP reach 43.2, 45.6, and 46.2% when the device works at angular speeds of 1500, 2000, and 2500 rpm, respectively. It can also be observed that as the angular speed of the fan increases, the maximum static efficiency increases as well.

^{3}/h at a system resistance of 50.25 Pa. Operating at 2000 rpm, the maximum theoretical efficiency of the fan is achieved at a pressure of 96.5 Pa, with an air flow of 155 m

^{3}/h. Operating at the highest tested angular speed (2500 rpm), the fan achieves maximum efficiency at a system resistance of 143.15 Pa, creating a flow rate of 198 m

^{3}/h.

#### 3.2.2. Operating Curves at Second Design Point

_{1}= 12° and β

_{2}= 88° works most efficiently. Performance and efficiency curves are determined for a fan with these blade geometry parameters.

^{3}/h) produced by the fan on the horizontal X axis and the static resistance (Pa) of the system on the vertical Y axis. From the obtained operating curves, it can be seen that the maximum flows generated by the fan at the second DP reach 200, 271, and 343 m

^{3}/h when the device operates at 1500, 2000, and 2500 rpm, respectively. The maximum static pressure developed by this fan is 50 Pa at an angular speed of 1500 min

^{−1}and 94.5 and 143.5 Pa at angular speeds of 2000 and 2500 min

^{−1}, respectively.

^{3}/h) blown by the fan, and the vertical Y axis shows the static efficiency (%). It can be seen that at an angular speed of 1500 rpm, the maximum static efficiencies of the fan reach 41.3% and 44.1 and 44.5% at angular speeds of 2000 and 2500 rpm, respectively.

^{3}/h. At an angular speed of 2000 rpm, the fan optimized at the second DP is most efficient when blowing 156.5 m

^{3}/h at 90 Pa static resistance. Operating at the highest tested angular velocity, the fan reaches its theoretical efficiency peak at a pressure of 139 Pa, when it produces an airflow rate of 208 m

^{3}/h.

^{3}/min when comparing the optimized profile blade with the initial profile. The improvement in criteria was achieved by changing the angles of the starts and ends of the profile strings, with the greatest differences observed at the trailing edge of the profile, which was highly curved.

## 4. Summary and Discussion

- It is determined that at the point of maximum power (1st DP), the highest achievable value of the static efficiency of the optimized fan, which is in the medium flow-rate zone (56.7–61.4% of the maximum amount of blown air at the tested speeds), is 3.2–4.4% higher compared to the fan at the second DP when the test objects run at the same speed.
- The results collected during the virtual tests show that the test object, the geometry parameters of which are selected for the second DP, exhibits up to 12.5% higher static efficiency than the fan at the first DP operating with a low amount of blown air (11.1–35% of the maximum flow) and in the zone of high static system pressure gain (95.2–99.4% of the maximum sustained system resistance gain).
- Comparing the performance curves of the fans results in a 0.56–2.45% higher airflow rate for the fan optimized at the first DP compared to the maximum flow rate of the fan at the second DP in the absence of system static resistance.
- Reviewing the established operating characteristics at the same fan speeds, it is observed that the fan optimized at the first DP supports 1.4–4.5% higher static system pressure increases than the test object designed at the second DP.
- Based on the results of this research, we recommend selecting the operating modes of the fan in the stable zone.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Typical performance curves given in the ANSI/AMCA 210-16 standard: I—dependence of power consumption on flow rate; II—dependence of total pressure on flow rate; III—static pressure change from discharge; IV—dependence of full efficiency on debit; V—dependence of static efficiency on debit. Here reference points are numbered from 1 to 15.

**Figure 4.**“RG14R-4IO.Z8.4R” performance curves of a centrifugal fan (Ziehl-Abegg SE [22]). Here reference curves are numbered from 1 to 5.

**Figure 5.**Leading- and trailing-angle influence on full efficiency at 1st design point (DP): (

**a**) influence of angle ${\beta}_{1}$; (

**b**) influence of angle ${\beta}_{2}$.

**Figure 6.**Leading- and trailing-angle influence on full efficiency at 2nd design point (DP): (

**a**) influence of angle ${\beta}_{1}$; (

**b**) influence of angle ${\beta}_{2}$.

**Figure 7.**Operating parameters of optimized impeller at 1st design point (DP:) (

**a**) performance; (

**b**) static efficiency.

**Figure 8.**Operating parameters of optimized impeller at 2nd design point (DP): (

**a**) performance; (

**b**) static efficiency.

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**MDPI and ACS Style**

Ragauskas, P.; Tetsmann, I.; Jasevičius, R.
The Optimization of the Geometry of the Centrifugal Fan at Different Design Points. *Appl. Sci.* **2024**, *14*, 3530.
https://doi.org/10.3390/app14083530

**AMA Style**

Ragauskas P, Tetsmann I, Jasevičius R.
The Optimization of the Geometry of the Centrifugal Fan at Different Design Points. *Applied Sciences*. 2024; 14(8):3530.
https://doi.org/10.3390/app14083530

**Chicago/Turabian Style**

Ragauskas, Paulius, Ina Tetsmann, and Raimondas Jasevičius.
2024. "The Optimization of the Geometry of the Centrifugal Fan at Different Design Points" *Applied Sciences* 14, no. 8: 3530.
https://doi.org/10.3390/app14083530