Application of Semi-Empirical Ventilation Models in A Mediterranean Greenhouse with Opposing Thermal and Wind Effects. Use of Non-Constant Cd (Pressure Drop Coefficient Through the Vents) and Cw (Wind Effect Coefficient)

López-Martínez, Alejandro; Molina-Aiz, Francisco D.; Valera-Martínez, Diego L.; López-Martínez, Javier; Peña-Fernández, Araceli; Espinoza-Ramos, Karlos E.

doi:10.3390/agronomy9110736

Open AccessArticle

Application of Semi-Empirical Ventilation Models in A Mediterranean Greenhouse with Opposing Thermal and Wind Effects. Use of Non-Constant C_d (Pressure Drop Coefficient Through the Vents) and C_w (Wind Effect Coefficient)

by

Alejandro López-Martínez

^1,*

,

Francisco D. Molina-Aiz

¹

,

Diego L. Valera-Martínez

¹

,

Javier López-Martínez

¹,

Araceli Peña-Fernández

¹

and

Karlos E. Espinoza-Ramos

²

¹

CIAIMBITAL Research Centre, University of Almería, Ctra. de Sacramento s/n, 04120 Almería, Spain

²

Department of Engineerings, University Center of the South Coast, University of Guadalajara. Av. Independencia Nacional 151, Autlán de Navarro, 48900 Jalisco, Mexico

^*

Author to whom correspondence should be addressed.

Agronomy 2019, 9(11), 736; https://doi.org/10.3390/agronomy9110736

Submission received: 14 October 2019 / Revised: 5 November 2019 / Accepted: 7 November 2019 / Published: 10 November 2019

(This article belongs to the Special Issue Greenhouse Technology)

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Abstract

The present work analyses the natural ventilation of a multi-span greenhouse with one roof vent and two side vents by means of sonic anemometry. Opening the roof vent to windward, one side vent to leeward, and the other side vents to windward (this last vent obstructed by another greenhouse), causes opposing thermal G_T (m³ s⁻¹) and wind effects G_w (m³ s⁻¹), as outside air entering the greenhouse through the roof vent circulates downward, contrary to natural convection due to the thermal effect. In our case, the ventilation rate R_M (h⁻¹) in a naturally ventilated greenhouse fits a second order polynomial with wind velocity u_o (R_M = 0.37 u_o² + 0.03 u_o + 0.75; R² = 0.99). The opposing wind and thermal effects mean that ventilation models based on Bernoulli’s equation must be modified in order to add or subtract their effects accordingly—Model 1, in which the flow is driven by the sum of two independent pressure fields

G_{M 1} = \sqrt{| G_{T}^{2} \pm G_{w}^{2} |}

, or Model 2, in which the flow is driven by the sum of two independent fluxes

G_{M 2} = | G_{T} \pm G_{w} |

. A linear relationship has been obtained, which allows us to estimate the discharge coefficient of the side vents (C_dVS) and roof vent (C_dWR) as a function of u_o [C_dVS = 0.028 u_o + 0.028 (R² = 0.92); C_dWR = 0.036 u_o + 0.040 (R² = 0.96)]. The wind effect coefficient C_w was determined by applying models M1 and M2 proved not to remain constant for the different experiments, but varied according to the ratio u_o/∆T_io^0.5 or δ [C_wM1 = exp(−2.693 + 1.160/δ) (R² = 0.94); C_wM2 = exp(−2.128 + 1.264/δ) (R² = 0.98)].

Keywords: greenhouse; natural ventilation; sonic anemometry; ventilation model

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MDPI and ACS Style

López-Martínez, A.; Molina-Aiz, F.D.; Valera-Martínez, D.L.; López-Martínez, J.; Peña-Fernández, A.; Espinoza-Ramos, K.E. Application of Semi-Empirical Ventilation Models in A Mediterranean Greenhouse with Opposing Thermal and Wind Effects. Use of Non-Constant C_d (Pressure Drop Coefficient Through the Vents) and C_w (Wind Effect Coefficient). Agronomy 2019, 9, 736. https://doi.org/10.3390/agronomy9110736

AMA Style

López-Martínez A, Molina-Aiz FD, Valera-Martínez DL, López-Martínez J, Peña-Fernández A, Espinoza-Ramos KE. Application of Semi-Empirical Ventilation Models in A Mediterranean Greenhouse with Opposing Thermal and Wind Effects. Use of Non-Constant C_d (Pressure Drop Coefficient Through the Vents) and C_w (Wind Effect Coefficient). Agronomy. 2019; 9(11):736. https://doi.org/10.3390/agronomy9110736

Chicago/Turabian Style

López-Martínez, Alejandro, Francisco D. Molina-Aiz, Diego L. Valera-Martínez, Javier López-Martínez, Araceli Peña-Fernández, and Karlos E. Espinoza-Ramos. 2019. "Application of Semi-Empirical Ventilation Models in A Mediterranean Greenhouse with Opposing Thermal and Wind Effects. Use of Non-Constant C_d (Pressure Drop Coefficient Through the Vents) and C_w (Wind Effect Coefficient)" Agronomy 9, no. 11: 736. https://doi.org/10.3390/agronomy9110736

APA Style

López-Martínez, A., Molina-Aiz, F. D., Valera-Martínez, D. L., López-Martínez, J., Peña-Fernández, A., & Espinoza-Ramos, K. E. (2019). Application of Semi-Empirical Ventilation Models in A Mediterranean Greenhouse with Opposing Thermal and Wind Effects. Use of Non-Constant C_d (Pressure Drop Coefficient Through the Vents) and C_w (Wind Effect Coefficient). Agronomy, 9(11), 736. https://doi.org/10.3390/agronomy9110736

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Application of Semi-Empirical Ventilation Models in A Mediterranean Greenhouse with Opposing Thermal and Wind Effects. Use of Non-Constant C_d (Pressure Drop Coefficient Through the Vents) and C_w (Wind Effect Coefficient)

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