Integrated modelling of single port, steady-state thermal discharges in unstratified coastal waters

Abstract

An integrated model is presented for the calculation of the discharge of thermal effluents from power plants into coastal waters; the model consists of the near field model CorJet and the far field model FLOW-3DL that are interconnected via an active coupling algorithm. Firstly, the model is validated using experimental data; moreover, calculations are compared with passive coupling simulations to identify the dominant differences among these methods. Then, the model is applied to simulate the single-port thermal discharge originating from a thermal power plant to the non-stratified coastal waters in the region of Mantoudi in Evia, Greece. Model predictions are compared with CORMIX far field estimations and calculations employing passive coupling. Calculations verify the need for the application of an integrated active model. The detailed information for the coupling algorithm that is contained in this paper, including its difficulties and their resolution, permits its implementation to any active coupling between practically any near field with any far field model.

Appendix

The starting point of the mentioned NF model calculation procedure is the end of the ZOFE, where the values of the eight variables are given by Eqs. (29)–(36)

$$\begin{aligned} \text{ Q}_\mathrm{e}&= \sqrt{2}\text{ Q}_\mathrm{o} \end{aligned}$$

(29)

$$\begin{aligned} \text{ M}_{\mathrm{Xe}}&= \text{ M}_\mathrm{o} \cos {\uptheta }_\mathrm{e} \cdot \cos {\upsigma }_\mathrm{e}\end{aligned}$$

(30)

$$\begin{aligned} \text{ M}_{\mathrm{Ye}}&= \text{ M}_\mathrm{o} \cos {\uptheta }_\mathrm{e} \cdot \sin {\upsigma }_\mathrm{e} \end{aligned}$$

(31)

$$\begin{aligned} \text{ M}_{\mathrm{Ze}}&= \text{ M}_\mathrm{o} \sin {\uptheta }_\mathrm{e} \end{aligned}$$

(32)

$$\begin{aligned} \text{ Q}_\mathrm{e} \cdot \Delta \text{ T}_{\mathrm{jete}}&= \text{ Q}_\mathrm{o} \cdot \Delta \text{ T}_{\mathrm{jeto}} \end{aligned}$$

(33)

$$\begin{aligned} \text{ X}_{\mathrm{jete}}&= \text{ L}_\mathrm{e} \cos \left( {\frac{\uptheta _\mathrm{o} +{\uptheta }_\mathrm{e} }{2}}\right)\cos \left( {\frac{\upsigma _\mathrm{o} +\upsigma _\mathrm{e} }{2}} \right) \end{aligned}$$

(34)

$$\begin{aligned} \text{ Y}_{\mathrm{jete}}&= \text{ L}_\mathrm{e} \cos \left( {\frac{\uptheta _\mathrm{o} +{\uptheta } _\mathrm{e} }{2}}\right)\sin \left( {\frac{\upsigma _\mathrm{o} +\upsigma _\mathrm{e} }{2}} \right) \end{aligned}$$

(35)

$$\begin{aligned} \text{ Z}_{\mathrm{jete}}&= \text{ Z}_\mathrm{o} +\text{ L}_\mathrm{e} \sin \left( {\frac{{\uptheta }_\mathrm{o} +{\uptheta } _\mathrm{e} }{2}} \right) \end{aligned}$$

(36)

and for the additional three variables ${\uptheta }_{\mathrm{e}}, \upsigma _{\mathrm{e}}$ and $\text{ M}_{\mathrm{e}}$ at the end of ZOFE by Eqs. (37)–(39)

$$\begin{aligned} {\uptheta }_\mathrm{e}&= \sin ^{-1}\left( {\sin {\upgamma }_\mathrm{e} \sin \delta _\mathrm{o} }\right)\end{aligned}$$

(37)

$$\begin{aligned} {\upsigma }_\mathrm{e}&= \tan ^{-1}({\sin {\upgamma } _\mathrm{e} \cos \delta _\mathrm{o} }/{\cos {\upgamma } _\mathrm{e} )}\end{aligned}$$

(38)

$$\begin{aligned} \text{ M}_\mathrm{e}&= \text{ M}_\mathrm{o} \end{aligned}$$

(39)

In the above equations the subscript “o” refers to the values of the variables at the discharge location and the subscript “e” refers to their values at the end of ZOFE. $\text{ L}_{\mathrm{e}}$ is the modified ZOFE length, ${\upgamma }_{\mathrm{o}}$ is the transverse discharge angle relative to the ambient current direction, $\delta _{\mathrm{o}}$ is the projection of ${\upgamma }_{\mathrm{o}}$ onto the x–y plane and ${\upgamma }_{\mathrm{e}}$ is the final transverse angle of the $\text{ L}_{\mathrm{e}}$, calculated by Eqs. (40)–(44). $\text{ U}_{\mathrm{o}}$ in Eq. (44) and $\text{ Fr}_{\mathrm{o}}$ in Eq. (40) are the discharge velocity and the densimetric Froude number, respectively, at the location of discharge.

$$\begin{aligned}&\displaystyle \text{ L}_\mathrm{e} =5\cdot \text{ D}\cdot (1-3.22\sin {\upgamma }_\mathrm{o} /\text{ R})\cdot (1-\text{ e}^{{-2\text{ Fr}_\mathrm{o}}/{4.67}})\end{aligned}$$

(40)

$$\begin{aligned}&\displaystyle {\upgamma }_\mathrm{o} =\sin ^{-1}\left( {\sqrt{1-\cos ^{2} _\mathrm{o} \cdot \cos ^{2}{\upsigma } _\mathrm{o} }} \right)\end{aligned}$$

(41)

$$\begin{aligned}&\displaystyle \delta _\mathrm{o} =\tan ^{-1}\left( {\frac{\tan {\uptheta }_\mathrm{o} }{\sin \upsigma _\mathrm{o} }} \right) \end{aligned}$$

(42)

$$\begin{aligned}&\displaystyle {\upgamma } _\mathrm{e} =\tan ^{-1}\left( {\frac{\sin {\upgamma } _\mathrm{o} }{\cos {\upgamma }_\mathrm{o} +(\sqrt{2}-1)/\text{ R}}} \right) \end{aligned}$$

(43)

$$\begin{aligned}&\displaystyle \text{ R}=\frac{\text{ U}_\mathrm{o} }{\text{ u}_\mathrm{a} } \end{aligned}$$

(44)