Comparative study between turbulence models in curved channels

Almeida, José Rodolfo Machado de; Ota, José Junji

doi:10.1590/2318-0331.252020190050

José Rodolfo Machado de Almeida

Universidade Federal do Paraná, Curitiba, PR, Brasil

http://orcid.org/0000-0002-9144-0823

José Junji Ota

Universidade Federal do Paraná, Curitiba, PR, Brasil

http://orcid.org/0000-0001-9653-1495

E-mails: ze.rodolfo@gmail.com (JRMA), ota.dhs@ufpr.br (JJO)

José Rodolfo Machado de Almeida: Literature review, development and application of the methodology, analysis of the results and discussion of the results.

José Junji Ota: Development of the methodology, analysis of the results and discussion of the results.

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Figure 1
Secondary Currents downstream of the curve. Source: Adapted from Gholami et al. (2014)Gholami, A., Akbar Akhtari, A., Minatour, Y., Bonakdari, H., & Javadi, A. A. (2014). Experimental and numerical study on velocity fields and water surface profile in a strongly-curved 90º Open Channel Bend. Engineering Applications of Computational Fluid Mechanics, 8(3), 447-461. http://dx.doi.org/10.1080/19942060.2014.11015528.
http://dx.doi.org/10.1080/19942060.2014.... .

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Figure 2
General layout of the experimental channel. Source: Adapted from Yamakawa (2015)Yamakawa, F. H. S. (2015). Estrutura do escoamento em canais trapezoidais em curva (Dissertação de mestrado). Programa de Pós-graduação em Engenharia de Recursos Hídricos e Ambientais, Universidade Federal do Paraná, Curitiba..

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Figure 3
General view of the flow at the curves 1 e 2. Source: Adapted from Yamakawa (2015)Yamakawa, F. H. S. (2015). Estrutura do escoamento em canais trapezoidais em curva (Dissertação de mestrado). Programa de Pós-graduação em Engenharia de Recursos Hídricos e Ambientais, Universidade Federal do Paraná, Curitiba..

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Figure 4
Superficial circulations observed. Source: Adapted from Yamakawa (2015)Yamakawa, F. H. S. (2015). Estrutura do escoamento em canais trapezoidais em curva (Dissertação de mestrado). Programa de Pós-graduação em Engenharia de Recursos Hídricos e Ambientais, Universidade Federal do Paraná, Curitiba..

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Figure 5
Flow velocity observed at the experimental channel. Source: Adapted from Yamakawa (2015)Yamakawa, F. H. S. (2015). Estrutura do escoamento em canais trapezoidais em curva (Dissertação de mestrado). Programa de Pós-graduação em Engenharia de Recursos Hídricos e Ambientais, Universidade Federal do Paraná, Curitiba..

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Figure 6
Depth Average Velocities in the experimental channel.

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Figure 7
Mesh size sensibility analysis.

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Figure 8
Computational domain of the numerical model.

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Figure 9
Boundary conditions at the numerical simulations.

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Figure 10
Test 1 – Streamlines.

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Figure 11
Test 1-D –Depth average velocity.

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Figure 12
Test 2 – Streamlines.

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Figure 13
Test 2 – Depth average velocity.

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Figure 14
Test 3 – Streamlines.

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Figure 15
Test 2 – Depth average velocity.

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Figure 16
Water depth – Experimental x Simulations.

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Table 1
Performed simulations.

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Table 2
Classification of the model through ht NSE coefficient.

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Table 3
Test 1 – Simulations performed.

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Table 4
Test 1 – Statistical characterization.

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Table 5
Test 2 – Simulations performed.

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Table 6
Test 2 – Statistical characterization.

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Table 7
Test 3 – Statistical characterization.

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Table 8
Computational time.

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Table 9
Computer characteristics.

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Test	Turbulence Model
1	Constant $ν_{t}$ model
2	Elder Model
3	$k - ε$ Model

Classification	Value of the coefficient NSE
Very good	0.75 < NSE < 1.00
Good	0.65 < NSE < 0.75
Acceptable	0.50 < NSE < 0.65
Not acceptable	NSE < 0.5

Simulation	Turbulent viscosity (m²/s)
1 – A	ν_t = 10^-1
1 – B	ν_t = 10^-2
1 – C	ν_t = 5 x 10^-3
1 – D	ν_t = 10^-3

Statistical evaluation	Test 1	Test 2	Test 3	Test 4
Statistical evaluation	( $ν_{t}$ = 0.1)	( $ν_{t}$ = 0.01)	( $ν_{t}$ = 0.005)	( $ν_{t}$ = 0.001)
MPE	0.87	5.88	5.55	0.96
MAE	0.041	0.034	0.028	0.036
AAPE	19.35	14.05	12.19	18.80
NSE	0.28	0.52	0.84	0.80

Simulation	Dimensionless parameters used
2 – A	$α_{l} =$ 6.0 ; $α_{t} =$ 0.2
2 – B	$α_{l} =$ 6.0 ; $α_{t} =$ 0.6
2 – C	$α_{l} =$ 6.0 ; $α_{t} =$ 1.0
2 – D	$α_{l} =$ 6.0 ; $α_{t} =$ 2.0

Statistical evaluation	Test 2-A	Test 2-B	Test 2-C	Test 2-D
Statistical evaluation	$α_{t}$ = 0.2	$α_{t}$ = 0.6	$α_{t}$ = 1.0	$α_{t}$ = 2.0
MPE	-5.96	1.96	8.04	18.43
MAE	0.044	0.034	0.032	0.029
AAPE	26.35	20.26	19.13	20.12
NSE	0.78	0.80	0.78	0.64

Position	Statistical evaluation
Position	MPE (%)	AAPE (%)	MAE (m/s)	NSE
Section A	12.80	12.80	0.033	0.20
Section B	7.03	10.68	0.027	0.64
Section C	-5.26	21.53	0.029	0.92
Section D	-4.67	19.65	0.032	0.94
Section E	1.69	14.97	0.030	0.92
Section F	11.49	15.79	0.030	0.91
Section G	8.23	13.44	0.035	0.87
Maximum	12.80	21.53	0.035	0.94
Average	4.47	15.55	0.031	0.77
Minimum	-5.26	10.68	0.027	0.20

Turbulence model:	Simulation speed
Constant viscosity model:	8,000 steps / hour
Elder Model:	11,600 steps / hour
$k - ε$ Model	8,100 steps / hour

Item	Characteristics
CPU	Intel® Core i7-4790K – 4.00GHz
RAM:	16.0GB
Operational Sistem	Windows® 10 Pro – 64 Bits
Number of cores used:	8 cores

[1] E-mails: ze.rodolfo@gmail.com (JRMA), ota.dhs@ufpr.br (JJO)

Brasil

Brasil

Comparative study between turbulence models in curved channels

Estudo comparativo entre modelos de turbulência em canais curvos

ABSTRACT