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JEMMME (Journal of Energy, Mechanical, Material, and Manufacturing Engineering) 
Vol. 6, No. 1, 2021 
 
ISSN  2541-6332  |  e-ISSN  2548-4281 
Journal homepage: http://ejournal.umm.ac.id/index.php/JEMMME 

 

Adanta | History of Utilization of the Computational Fluid Dynamics Method for … 1 

 

 

Application of Computational Fluid Dynamics 
Method for Cross-flow Turbine in Pico Scale 

 
Imam Syofiia, Dendy Adantab, Aji Putro Prakosoc, Dewi Puspita Saria 

aStudy Program of Mechanical Engineering Education, Universitas Sriwijaya  
Jalan Palembang-Prabumulih km. 32 Indralaya, 30662, South Sumatera, Indonesia 

 
bDepartment of Mechanical Engineering, Faculty of Engineering, Universitas Sriwijaya  
Jalan Palembang-Prabumulih km. 32 Indralaya, 30662, South Sumatera, Indonesia 

 

cDepartment of Mechanical Engineering, Faculty of Manufacturing Technology, Universitas Jendral Achmad 
Yani  

Cimahi, 40531, West Java, Indonesia 
e-mail: dendyadanta@ymail.com 

 

 
Abstract 

 
 Crisis electricity was a crucial issue in the rural area. Crossflow turbine (CFT) 

in pico in pico scale is the best option for electricity provider for rural areas. 
Due to its usefulness and development of computer technology, 
computational fluid dynamics method application for CFT study becomes 
increasingly frequent. This paper compiles the implementation of the 
computational fluid dynamic (CFD) approach for CFT on a pico scale. Based 
on the literature, the Renormalization Group (RNG) 𝑘 − ɛ turbulence model is 
recommended to predict the flow field that occurs in CFT because its error is 

lower than others turbulence models, the RNG 𝑘 − ɛ error of 3.08%, standard 
𝑘 − ɛ of 3.19%, and transitional SST of 3.10%. Furthermore, six-degrees of 
freedom (6-DoF) is recommended because it has an error of 3.1% than a 
moving mesh of 9.5% for the unsteady approach. Thus, based on the review, 

the RNG 𝑘 − ɛ turbulence model and 6-DoF are recommended for the CFT on 
the pico scale. 

  

 Keywords: Pico hydro; cross-flow turbine; CFD; RANS; RNG 𝑘 − ɛ; 6-DoF  
 approach 

 

  
 

1. INTRODUCTION  
 The CFD has categorized an impulse turbine because the blade dominantly absorbs 
the water kinetic energy to generate power [1][2]. The CFT absorbs energy in two stages 
[3]. The two-stage energy transfer makes flow field (turbulence phenomena) that occurs 
is rotating flow [4][5]. The rotating flow in CFT is interesting to be studied because by 
understanding the flow field, the losses can be minimized (efficiency increases) [6][3] 
[7][8][9][10][11]. 
 Improving the CFT can be used analytically, numerically, experimentally, or a 
combination of those methods. The development of computer technology makes the CFD 
method increasingly frequent [12][5]. In 1985, the CFD successfully characterized the 
fluid flow characteristic inside the CFT's nozzle, and the optimum design of CFT's nozzle 
was recommended [8]. Furthermore, by CFD results, the optimum angle of attack was 
proposed [7][13]. Investigation of the best pressure distribution for promising nozzle 
designs using CFD analysis. [14].  
 In the early twenty-first century, CFD software was allowed to investigate more 
complex fluid dynamics [15] with two or three dimensional (2 or 3D), steady or transient 
analysis about CFT at a more affordable price [9][10][11][16][17]. In 2008, A quasi 2D 
steady-state approach was carried out to find the optimal guide vane angle and 

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characterize its internal flow [16]. In 2011, a thorough investigation of the internal flow of 
CFT was undertaken, and the influence of shaft inside CFT was discovered [17]. Some 
losses were found in CFT's hydrodynamic flow using 2D transient CFD simulations [17]. 
Several research on CFT was undertaken in 2013, beginning with an exhaustive literature 
review and some quasi 2D and 3D transient simulations to determine the optimal design 
of CFT [9]; then, the results are validated and explored in subsequent studies [18][19]. 
The CFT performance was successfully improved by altering the nozzle curvature by a 
3D steady-state numerical analysis. [10]. Furthermore, another study of CFT nozzle 
enhancement has discovered a 90% efficiency utilizing numerical simulations validated 
by experimental results [11][20]. Their research was currently focused on increasing CFT 
efficiency by doubling the nozzle size [21]. 
 The CFT numerical simulations are becoming more complicated to obtain more 
detailed findings. The turbine motion can be a numerical calculation result employing rigid 
body alternatives inside a 6-DoF approach. [22]. This option has been used in some 
recent studies to acquire a deeper investigation or to produce some breakthrough 
enhancements to CFT design [1][6][23]. By analyzing three cases of CFT in 2018, the 6-
DoF technique was utilized to find the effect of airfoil profile on the internal flow 
characteristic and the turbine's performance. [6]. The findings revealed that the airfoil 
profile might positively impact the flow field; it does not affect its performance because the 
impulse effect is more powerful than the reaction [6]. Furthermore, the effect of blade 
curvature depth on its performance was conducted in 2018 [1]. Then, the calculation 
formula for the outer diameter ratio with blade curvature depth was proposed [23]. 
 The current study attempted to summarize CFT progress, particularly utilizing a 
numerical approach. This paper summarizes some investigations on the quality of CFD 
results for simulating pico hydro CFT. Its goal is to offer the best unsteady technique and 
turbulence model for CFD numerical simulation on a pico scale. 
 

2. STUDY OF THE CFT IN 20TH CENTURY  
 A. Michell menemukan CFT pada tahun 1903, dan D. Banki menemukan 
pendekatan teoretisnya yang kemudian disempurnakan oleh Sonnek pada tahun 1923 
[24]. The CFT's optimum specific speed, according to Mockmore and Merryfield (1994) 
[3], was 14, which was higher than other impulse turbines. The results also revealed that 
the CFT performs consistently under varying water discharge [3]. The pressure at the tip 
of the CFT's nozzle was not zero, according to Haimerl (1960) [25], so this turbine isn't 
strictly an impulse turbine.  
 The influence of CFT's nozzle shape and size on its performance was examined by 
Nakase (1982) [26]. Nakase (1982) [26] recommended a height-to-width ratio for CFT 
nozzles based on Equation 1. 
 

𝑆𝑜

𝑅𝜆
≅ 0.26 (1) 

 
where S0 is the nozzle's initial height, R is the CFT outer radius, and λ is the nozzle's 
discharge angle. The suggestion was put to the test, and it improved CFT performance to 
the point where it could attain 82% efficiency [26]. Then, according to Durgin and Fay 
(1984) [28], the first stage energy transfer contributed roughly 83% of overall energy 
transfer to CFT performance; this discovery is still relevant [16]. According to Fukutomi et 
al. (1985) [8], the numerical approach is an appropriate alternative for improving the 
CFT's nozzle. Then in 1991, Fukutomi et al. [27] examined the CFT flow field and 
concluded the effect of a diameter ratio on the CFT performance. 
 Khosrowpanah et al. (1988) [24] discovered that the 90o λ is optimum for CFT. Then, 
Khosrowpanah et al. (1993) [7] and (1994) [13] defined that the 22o angle of attack (α) for 
CFT is optimum; this result is verified [28]. Finally, Aziz and Totapally (1994) [13] proved 
the Mockmore and Merryfield [3] results and concluded that propose of the 0.68 diameter 
ratio (d/D) is optimum conditions. 
 Before the 21st century, the finding of CFT studies is it's the primary design 
parameter of CFT. Table 1 summarizes investigations conducted before the twenty-first 
century. 



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Table 1. The CFT studies before 21st century 

  

 

The angle 
of attack 

(α) 

Nozzle 
design 

Nozzle 
discharge 
angle (λ) 

Diameter 
ratio (d/D) 

Blade 
number 

(Nb) 

Aziz (1994) [13]      

Fukutomi et al. 
(1992) [27] 

     

Khosrowpanah et 
al. (1988) [24] 

     

Fukutomi et al. 
(1985) [8] 

     

Durgin and Fay 
(1984) [29] 

     

Nakase (1982) 
[26] 

     

Haimerl (1960) 
[25] 

     

Mockmore and 
Merryfield (1949) 

[3] 
     

 

3. THE CFT STUDY IN 21ST CENTURY 
 The CFD simulation was employed in practically all CFT investigations in the twenty-

first century. The CFD is frequently utilized because it is inexpensive, quick, and allows 

for detailed visualization of the flow field [30]. Kaniecki (2002) [25] attempted to increase 

CFT performance by added a draft tube into the outflow and evaluating the flow 

characteristics through the draft tube using the CFD simulation. The CFD simulations 

were used by Kaniecki and Steller (2003) [4] to study the flow pattern of CFT and 

categorize it as a reaction turbine. Choi et al. (2006) [31] characterized the effect of blade 

angle on the internal flow and found that the best outlet angle of the blade (β2) is 90o by 

CFD simulation. Then, Choi et al. (2007) [32] studied internal flow with nozzle shape 

change by CFD simulation and discovered that the CFT possesses both impulse and 

reaction turbine characteristics. Next, according to Choi et al. (2008) [16], the internal flow 

feature significantly impacts the CFT performance. Andrade et al. (2011) [17] 

characterized internal flow as a function of turbine angular velocity. They concluded that 

the recirculation flow that happens as a shock should be minimized so that the turbine 

can function effectively [17]. 

 Sammartano et al. investigated CFT optimization using the CFD simulation. In 2014, 

Sammartano et al. [33] developed CFT nozzles that can be modified for changing 

discharge circumstances. In 2015, Sammartano et al. [34] attempted to use CFT to create 

energy and flow controls for the water conveyance system outright. In 2016, Sammartano 

et al. [19] verified the optimization done in 2013 [9], which also used the velocity 

corrected inlet velocity formula. In addition, Sammartano et al. (2016) [19] examined 

different turbulence models to find the best turbulent model for the CFT. 

 The CFD approach has been used in some research to increase CFT performance. 

The CFT nozzle was revised by Acharya (2015) [10] to improve its performance. The CFT 

nozzle has been redesigned, increasing its efficiency from 63.7 to 76.6% [10]. 

 Adhikari and Wood (2017) [11] did several tests to develop high-efficiency CFT and 

improved the nozzle tip. Furthermore, Adhikari and Wood (2018) [20] studied flow 

patterns and turbine performance when CFTs were operated at part-load, resulting in 

more efficient water discharge regulation of CFTs. Then, to increase efficiency, Adhikari 



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and Wood (2018) [21] examined CFT with a twin nozzle. Finally, a review paper related to 

the effort of various investigations to achieve the high efficiency of CFT was published at 

the end of 2018 as a summary of earlier [28]. Table 2 summarizes much research 

conducted in the twenty-first century. 

 
Table 2. The CFT studies in 21st century 

Authors 
Experiment 
efficiency 

Numerical 
efficiency 

Adhikari, et.al. (2017-2018) [11][20][21] 84% 91% 

Chichkhede, et.al. (2016) [2] - 88% 

Acharya, et.al. (2015) [10] - 76,6% 

Sammartano, et.al. (2013-2016) [9][33][34][19] 80,6% 79,4% 

De Andrade, et.al. (2011) [17] 72% 76% 

Choi, et.al. (2006-2008) [31][32][16] 76,2% 65,7% 

Kaniecky, et.al. (2002-2003) [25][4] 78,6% 74,3% 

 
 The 3D domain was used for all of the CFD simulation studies in Table 2. In 2018 
[6], 2D CFD analysis was done to increase CFT performance by altering the turbine blade 
with an airfoil profile. It was discovered that there are some turbulence features in the 
internal flow of the CFT that affect its performance. In addition, a 2D CFD study [1] was 
conducted to explore the effect of the curve of the blade on its performance. 
 

4. TURBULENCE MODEL STUDY FOR THE CFT IN PICO SCALE 
 Three turbulent models (k-ε model, RNG k-ε model, and Transitional SST) were 

compared to establish the effects on CFD simulation (prediction) [19]. Table 3 
summarizes the outcomes of the comparison. The k-ε and RNG k-ε model have higher 
average relative error (ḡ) than Transitional SST [19], as seen in Table 3. Equation 2 
defines the relative error [19]. 
 

ḡ =
𝜂𝑠𝑖𝑚−𝜂𝑒𝑥𝑝

𝜂𝑒𝑥𝑝
  (2) 

 
and Equation 3 is used to define the absolute relative error (gRE). 
 

𝑔𝑅𝐸 =
|𝜂𝑠𝑖𝑚−𝜂𝑒𝑥𝑝|

𝜂𝑒𝑥𝑝
  (3) 

 
where ɳexp is turbine efficiency by experimental and ɳsim is efficiency by CFD simulation. 
This research was carried out in a 3D domain, which means there are more walls than in 
a 2D simulation, and the turbulence model of k-ε with the near-wall treatment has a minor 
weakness compared to the k-ε standard.  
 

Table 3. In various turbulence models, relative error, according to Sammartano et al. [19] 

Vt/U Transitional SST k-ε RNG k-ε 

2,2 0,58% -2,07% 0,07% 

2,0 -1,55% -5,93% -3,37% 

1,8 -0,96% -5,45% -3,20% 

1,6 -1,16% -3,95% -2,83% 

1,4 -1,15% -3,56% -3,07% 

ḡ -0,70% -3,91% -2,39% 

gRE 0,91% 3,91% 2,41% 



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 Siswantara et al. [5] verified Sammartano et al. [19] study. Siswantara et al. [5] utilize 

a 2D model, whereas Sammartano et al. [19] employ a 3D model. Furthermore, 

Siswantara et al. [5] proposed a 2D representation of the performance and flow field for 

CFT in pico scale. Therefore, the 2D analysis able is used to determine the effect of 

turbulence model utilization. Table 4 summarizes the findings of Siswantara et al. [5]. 

 
Table 4. Relative error CFD simulation by Siswantara et.al. [5] 

Turbulence model ḡ 𝒈𝑹𝑬̅̅ ̅̅ ̅ 

Transitional SST -3,10% 3,10% 

k-ε -2.65% 3,19% 

RNG k-ε -2,50% 3,08% 

  

 From Table 4, all turbulence model has 𝑔𝑅𝐸̅̅ ̅̅̅ of 3%. The deviation error of each model 

of below 0.11%. In CFT in pico scale CFD simulation, the turbulence model effect 

appears to be ignorable. Moreover, the transitional SST has a greater 𝑔𝑅𝐸̅̅ ̅̅̅ than RNG k-ε, 

this is contradicting to previous findings [5][19]. These investigations found that the 

maximum 𝑔𝑅𝐸̅̅ ̅̅̅ of CFT CFD simulation using difference turbulence model is less than 4%. 

Indicated that thrid turbulence model are close enough to predict the CFT performance in 

pico scale. 

 Table 3 and 4, for CFT simulation in pico scale, the k-ε standard is recommended 

since it requires less computational power (simpler equation) than Transitional SST and 

RNG k-ε. However, to confirm the validity of findings (feasibility k-ε standard turbulence 

model) the 𝑦+ in near-wall should be of 30 ≤y+≤300 range [35]. 

 

5. UNSTEADY APPROACH FOR THE CFT CFD SIMULATION IN PICO 

SCALE 
 The CFT CFD simulation was carried out with ANSYS Fluent software utilizing two 

unsteady approaches: moving mesh and 6-DoF [36]. Figure 1 shows a comparison of the 

two approaches.  

 

1.2 1.4 1.6 1.8 2.0 2.2
55

60

65

70

75

80

(%)

V
t
/U

 Experiment

 6-DOF

 moving mesh

 
Graphic 1. Comparison 6-DoF with moving mesh, and experimental [36] 

 
 



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 Graphic 1 shows that the 6-DoF has closer to experimental than the moving mesh. 

The 𝑔𝑅𝐸̅̅ ̅̅̅ with the 6-DoF to experimental data of 3.1%, while the 𝛿𝑅𝐴̅̅̅̅̅ of the moving mesh 

of 9.5% [36]. As a result, it can be stated that the 6-DoF approach is appropriate for CFT 

CFD simulations on the pico scale. 

 

6. CONCLUSION 
  A review of CFT studies was undertaken, focusing on the unsteady numerical 
approach for CFD simulation. Based on results, 𝑔𝑅𝐸̅̅ ̅̅̅ of 3.08% for RNG k-ε, 3.19% for 

standard k-ε, and 3.10% for transitional SST. As a result, it is recommended RNG 𝑘 − ɛ 

turbulence model for CFT 2D numerical simulation. The 6-DoF is recommended for the 

unsteady approach because it has 𝑔𝑅𝐸̅̅ ̅̅̅ of 3.1% lower than the moving mesh of 9.5%. 

 

ACKNOWLEDGEMENT 
Thans to Universitas Sriwijaya to facilitates this research. 
 

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	Adanta1
	Chichkhede
	Mockmore
	Kaniecki
	Siswantara
	Adanta6
	Aziz7
	Fukutomi8
	Sammartano9
	Acharya
	Adhikari11
	Adanta12
	Aziz13
	Pereira
	Ansys15
	Choi16
	DeAndrade
	Sammartano18
	Sammartano19
	Adhikari20
	Adhikari21
	Ansys22
	Adanta23
	Khosrowpanah
	Maciej
	Nakase
	Fukutomi27
	Adhikari28
	Durgin
	Versteeg
	Choi31
	Choi32
	Sinagra
	Sammartano34
	Fluent
	Prakoso