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Optimum techno-eco performance requisites for vacuum annulus tube collector–assisted double-slope solar desaltification unit integrated modified parabolic concentrator

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Abstract

This work presents a novel approach for a double-slope solar desaltification system having parallel array of evacuated annular tube collectors with compound parabolic modified concentrators (DS-SDS-EATC-MCPC) that are observed for eco-design requisites for the optimum performance with environ-economic viabilities. The proposed scheme has been configured to obtain the utmost probable basin’s medium hotness as 99.6 °C of having greater depth of water (0.16 m) for the East–West-faced direction of basin peak cover (30°) along with South-oriented evacuated annular tube (30°). The highest circulation pace (thermo syphon) is obtained ~ 55 kg/h. The generalized efficiencies (energy-exergy) of the system are 46.53% and 3.62%, correspondingly. The everyday distillate (16.94 kg) and its production cost (energy $0.007/kWh; exergy $0.013/kWh) at a titular selling cost ($0.07/l) maintains its goodness. The CO2 mitigates (energy-exergy) and green earned credits are 139.74 and 77.30 tons, and $1396 and $772.24, in that order. The framework outlay of the scheme is quite stumpy at $200.79, and productivity of the model is set up > 100% that shows the scheme as appreciably realistic. The evident distillate at little operating cost, ecological returns, elevated alleviation, and short payoff period makes the arrangement sustainable, viable for reasonable collector areas, and optimum EATC with MCPC as eco-design requisites for the projected scheme.

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Data availability

The datasets used and analyzed during the current study are available from the corresponding author on reasonable request.

Abbreviations

\({A}_{a}\) :

Accumulative opening area for MCPC

\({A}_{g}\) :

Top glaze area (m2)

\({A}_{b}\) :

Basin liner area (m2)

\({A}_{rc}\) :

Annular tube receiver area

\({C}_{w}, {C}_{f}\) :

Water mass specific heat capacity (J/kg K)

\(d\) :

Interior dia of inner annular tube (m)

\({E}_{e}\) :

Energetic growth (kWh)

\({E}_{x}\) :

Exergetic growth (kWh)

\({F}^{^{\prime}}\) :

Annular tube efficiency aspect

\({G}_{r}\) :

Grashof number

\({h}_{ba}\) :

Net heat transmission factor from liner to ambiance (W/m2 K)

\({h}_{bw}\) :

Heat transmission factor (convective) from liner to water (W/m2 K)

\({h}_{t-g}, {h}_{o}\) :

Heat loss factor (convention) from top glass to ambiance (W/m2 K)

\({h}_{t-wg}\) :

Net heat transmission factor from water surface to top glaze cover (W/m2 K)

\({h}_{c-wg}\) :

Heat transmission coefficient (convective) of brackish water to top glass cover (W/m2 K)

\({h}_{e-wg}\) :

Heat transmission factor (evaporative) of brackish water to top glass cover (W/m2 K)

\({h}_{r-wg}\) :

Heat transmission factor (radiative) from brackish water to top glass cover (W/m2 K)

\({h}_{r-ev}\) :

Thermal loss factor (radiative) of annular tube along vacuum region (W/m2 K)

\({h}_{saf}\) :

Overall heat transmission factor from absorber to annular tube water (W/m2 K)

\({I}_{d}(t)\) :

Solar irradiance (diffused and reflected) (W/m2)

\({I}_{s}(a)\) :

Solar energy engrossed at annular tube receiver (W/m2)

\({I}_{s}(t)\) :

Radiative astral energy (instantaneous) at SDS unit (W/m2)

\({I}_{b}(t)\) :

Irradiated solar beam radiation over EATC collectors (W/m2)

\({K}_{g}\) :

Glass thermal conductivity (W/m K)

\({K}_{b}\) :

Basin liner thermal conductivity (W/m K)

\({K}_{w}\) :

Water thermal conductivity (W/m K)

L:

Latent heat (water) for vaporization (J/kg)

\({L}_{EATC}\) :

Annular tube length (m)

\({\dot{m}}_{ewg}\) :

Yield hourly distillation (kg/h)

\({\dot{m}}_{f}\) :

Thermo syphon flow rate in annular tube (kg/s)

\({m}_{w}\) :

Quantity of brackish medium in still (kg)

\({m}_{f}\) :

Quantity of water in EATC (kg)

\({n}_{o}\) :

Air refractive index

\({n}_{g}\) :

Glaze refractive index

\({n}_{w}\) :

Water refractive index

\({N}_{u}\) :

Nusselt no.

\({N}_{sh}\) :

Sunshine hour numbers

\({P}_{r}\) :

Prandtl number

\({p}_{w}\) :

Vapor pressure (partial) at the surface of still’s water (Pa, N/m2)

\({p}_{gi}\) :

Vapor pressure (partial) at of top glaze interior face (Pa, N/m2)

\({\dot{Q}}_{N-EATC}\) :

Rate of heat grow in SDS through paralleled N-EATC-MCPC arrangement (kJ/s)

\({\dot{q}}_{ewg}\) :

Heat transmission rate of evaporation from brackish water to glass cover up (kJ/s)

\({R}_{a}\) :

Rayleigh no.

\({R}_{e}\) :

Reynold no.

\({R}_{g}\) :

Glaze reflectivity

\({R}_{i1}\) :

Internal tube interior radius (m)

\({R}_{i2}\) :

External tube interior radius (m)

\({R}_{o2}\) :

External tube exterior radius (m)

\({R}_{sc}\) :

Selective absorber reflectivity

\({T}_{a}\) :

Atmosphere temperature (°C)

\({T}_{b}\) :

Temperature of basin liner (°C)

\({t}_{b}\) :

Liner depth (m)

\(t\) :

Time (s)

\({t}_{g}\) :

Glaze thickness (m)

\({T}_{sa}\) :

Selective absorber temperature (°C)

\({T}_{f}\) :

Annular tube fluid (water medium) temperature (°C)

\({T}_{fo1}\) :

Exit water temperature from independent EATC (°C)

\({T}_{N-fo}\) :

Exit temperature of associative water medium impending through N-EATC (°C)

\({T}_{w}\) :

SDS basin water mass temperature (°C)

\({T}_{go}\) :

Top glaze temperature of external face (°C)

\({T}_{gi}\) :

Top glaze temperature of interior face (°C)

\({U}_{saa}\) :

Net heat transmission (loss) factor from external annular tube

V :

Air velocity (average) (m/s

ALN:

Aluminum nitride

CCPC:

Combined parabolic collector

CPC:

Parabolic collector

DS:

Slope

EATC:

(Vacuum) annular tube collector

FP:

Plate

MCPC:

Combined parabolic collector (modified)

OCPC:

Combined parabolic collector (oriented)

SDS:

Solar desaltification system

\(\nu\) :

Kinematic viscosity water (m2/s)

\({\beta }^{^{\prime}}\) :

Water volumetric thermal expansion coefficient (K−1)

\(\alpha\) :

Absorber absorptivity

\(\mu\) :

Dynamic viscosity of water (N·s/m2)

\({\alpha }_{g}\) :

Glass absorptivity

\({\alpha }_{w}\) :

Water absorptivity

\({\alpha }_{b}\) :

Liner absorptivity

\({\eta }_{i}\) :

Instantaneous efficiency (%)

\({\eta }_{e}\) :

Energy efficiency (%)

\({\eta }_{x}\) :

Exergy efficiency (%)

\(\tau\) :

Transmissivity

\(\sigma\) :

Constant of Stefan-Boltzmann (W/m2 K4)

\(\rho\) :

Density (kg/m3)

\({\varepsilon }_{eff}\) :

Emissivity (effective)

\({\varepsilon }_{g}\) :

Glaze emissivity

\({\varepsilon }_{w}\) :

Water emissivity

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Authors and Affiliations

  1. Department of Mechanical Engineering, Delhi Technological University, Delhi, 110042, India

    Ashok Kumar Singh & Samsher Gautam

  2. Mechanical Engineering Department, Galgotias College of Engineering and Technology, 201306, Greater Noida, UP, India

    Ashok Kumar Singh

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  1. Ashok Kumar Singh
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  2. Samsher Gautam
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Contributions

Ashok Kumar Singh: conceptualization, data curation, formal analysis, validation, investigation, methodology, software, writing—original draft.

Samsher Gautam: supervision, resources, visualization, project administration.

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Correspondence to Ashok Kumar Singh.

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Appendix

Appendix

Relations were utilized to solve Eq. (1) following Singh and Samsher (2020), Duffie and Beckman (2006), and Dunkle (1961) as stated,

$${U}_{saa}={\left(\frac{{R}_{o2}\mathrm{ln}\left(\frac{{R}_{i2}}{{R}_{i1}}\right)}{{K}_{g}}+\frac{1}{{h}_{r-v}}+\frac{{R}_{o2}\mathrm{ln}\left(\frac{{R}_{o2}}{{R}_{o1}}\right)}{{K}_{g}}+\frac{1}{{h}_{o}}\right)}^{-1}$$
$${I}_{s}\left(a\right)={I}_{b}\left(t\right).{(\propto \tau )}_{eff}$$
$${(\propto \tau )}_{eff}={R}_{sc}\alpha {\tau }^{2}\left({A}_{a}/{A}_{rc}\right)$$
$${h}_{o}={h}_{c-wg}+{h}_{r-wg}=5.7+3.8V$$
$${h}_{r-v}={\varepsilon }_{eff}.\sigma \left[{\left({T}_{f}+273.15\right)}^{2}+{\left({T}_{sa}+273.15\right)}^{2}\right]\times \left[{T}_{f}+{T}_{sa}+546.30\right]$$
$${\varepsilon }_{eff}={\left(1/{\varepsilon }_{g}+1/{\varepsilon }_{w}-1\right)}^{-1}$$

Expressions were utilized to solve Eqs. (7), (10), (17), and (19) as mentioned,

$${F}_{1}=\frac{{F}^{\mathrm{^{\prime}}}.{h}_{saf}}{({F}^{\mathrm{^{\prime}}}{h}_{saf}+{U}_{saa})};{F}_{2}=1-\frac{\left({A}_{rc}.{F}_{r}\right){U}_{L}}{{\dot{m}}_{f}{C}_{f}};{U}_{L}=\frac{{F}^{\mathrm{^{\prime}}}.{h}_{saf}.{U}_{saa}}{({F}^{\mathrm{^{\prime}}}{h}_{saf}+{U}_{saa})}$$
$${F}_{r}=\frac{{\dot{m}}_{f}{C}_{f}}{{A}_{rc}.{U}_{L}}\left\{1-exp\left(-\frac{2\pi {R}_{i1}{L}_{EATC}.{U}_{L}}{{\dot{m}}_{f}{C}_{f}}\right)\right\}$$
$${h}_{t-gE}={h}_{t-gW}=5.7+3.8V$$
$${U}_{cE}={h}_{t-gE}/\left(1+\frac{{h}_{t-gE}}{{K}_{g}/{t}_{g}}\right);{U}_{cW}={h}_{t-gW}/\left(1+\frac{{h}_{t-gW}}{{K}_{g}/{t}_{g}}\right)$$

Relations were utilized to solve Eqs. (20)-(21) as mentioned (Cooper 1973; Dunkle 1961; Singh and Samsher 2021a, b, c; Singh and Samsher 2022),

$${\alpha }_{g}^{A}=\left(1-{R}_{g}\right){\alpha }_{g};{R}_{g}=1-\left[4{n}_{o}{n}_{g}/\left\{\left({n}_{o}+{n}_{g}^{2}\right)\times (1+{n}_{o})\right\}\right]$$
$${h}_{t-wgE}={h}_{e-wgE}+{h}_{r-wgE}+{h}_{c-wgE}$$
$${h}_{t-wgW}={h}_{c-wgW}+{h}_{e-wgW}+{h}_{r-wgW}$$
$${h}_{r-wgE}={\varepsilon }_{eff}.\sigma \left\{{\left({T}_{w}+273.15\right)}^{2}+{\left({T}_{giE}+273.15\right)}^{2}\right\}\left\{{T}_{w}+{T}_{giE}+546.30\right\}$$
$${h}_{r-wgW}={\varepsilon }_{eff}.\sigma \left\{{\left({T}_{w}+273.15\right)}^{2}+{\left({T}_{giW}+273.15\right)}^{2}\right\}\left\{{T}_{w}+{T}_{giW}+546.30\right\}$$
$${h}_{c-wgW}=0.88\times {\left\{\left({T}_{w}-{T}_{giW}\right)+\frac{\left({T}_{w}+273.15\right)\times \left({P}_{w}-{P}_{giW}\right)}{(268.9\times {10}^{3}-{P}_{w})}\right\}}^{(1/3)}$$
$${h}_{c-wgE}=0.884{\left\{\left({T}_{w}-{T}_{giE}\right)+\frac{\left({P}_{w}-{P}_{giE}\right)\left({T}_{w}+273.15\right)}{268.9\times {10}^{3}-{P}_{w}}\right\}}^{1/3}$$
$${h}_{e-wgE}=16.273 \times {10}^{-3}{h}_{c-wgE}\left\{\frac{{P}_{w}-{P}_{giE}}{{T}_{w}-{T}_{giE}}\right\}$$
$${h}_{e-wgW}=16.273 \times {10}^{-3}{h}_{c-wgW}\left\{\frac{{P}_{w}-{P}_{giW}}{{T}_{w}-{T}_{giW}}\right\}$$
$${h}_{r-EW}={h}_{r-WE}=0.034\times \sigma \left\{{\left({T}_{giE}+273.15\right)}^{2}+{\left({T}_{giW}+273.15\right)}^{2}\right\}\left\{{T}_{giE}+{T}_{giW}+546.3\right\}$$
$${P}_{w}=\mathrm{exp}[25.317-\frac{5144}{({T}_{w}+273.15)}]$$
$${P}_{giE}=exp[25.317-\frac{5144}{{T}_{giE}+273.15}]$$
$${P}_{giW}=exp\left(25.317-\frac{5144}{{T}_{giW}+273.15}\right)$$

Equations were utilized to solve Eq. (22) as mentioned (Tiwari 2014; Singh and Samsher 2021a, b, c),

$${h}_{bw}=\left({K}_{w}/{t}_{b}\right)\left\{C{\left({R}_{a}\right)}^{1/n}\right\}$$
$${\alpha }_{w}^{A}=\left\{\left(1-{R}_{g}\right)\left(1-{\alpha }_{g}\right)(1-{R}_{w}){\alpha }_{w}\right\}$$
$${R}_{w}=\left[1-\left(4{n}_{o}{n}_{w}\right)/\left\{\left({n}_{o}+{n}_{w}^{2}\right)(1+{n}_{o})\right\}\right]$$
$${R}_{a}=\frac{g{\beta }^{\mathrm{^{\prime}}}{\rho }^{2}{X}^{3}{C}_{w}\Delta T}{\mu {K}_{w}};{G}_{r}=\frac{g{\beta }^{\mathrm{^{\prime}}}{\rho }^{2}{X}^{3}\Delta T}{{\mu }^{2}};{P}_{r}=\frac{\mu {C}_{w}}{{K}_{w}}$$
$$X=\left({L}_{o}-{B}_{o}\right)/2(\mathrm{For rectangular horizontal surface})$$
$$X=\frac{\mathrm{Area} (A)}{\mathrm{Perimeter} (P)} (\mathrm{For other surfaces})$$

Expressions were utilized to solve Eq. (25) as mentioned (Tiwari 2014),

$${h}_{ba}={\left\{\left({t}_{b}/{K}_{b}\right)+0.357\right\}}^{-1}$$
$${\alpha }_{beff}=\left({\alpha }_{b}^{A}.{h}_{bw}\right)/\left({h}_{ba}+{h}_{bw}\right)$$
$${U}_{bwa}=\left({h}_{bw}\times {h}_{ba}\right)/\left({h}_{ba}+{h}_{bw}\right)$$

Relations utilized to solve Eqs. (26)-(29), (31) as mentioned,

$${U}_{taE}=\left({U}_{cE}\times {A}_{gE}\times {h}_{t-wgE}\right)/\left[\frac{{A}_{b}}{2}\times {h}_{t-wgE}+{A}_{gE}\times ({h}_{r-EW}+{U}_{cE})\right]$$
$${U}_{taW}=\left({U}_{cW}\times {h}_{t-wgW}\times {A}_{gW}\right)/\left[{h}_{t-wgW}.\frac{{A}_{b}}{2}+{A}_{gW}.({h}_{r-WE}+{U}_{cW})\right]$$
$${h}_{1E}^{^{\prime}}=\left({A}_{gE}.{h}_{t-wgE}\right)/\left[\frac{{A}_{b}}{2}.{h}_{t-wgE}+{A}_{gE}.({h}_{r-EW}+{U}_{cE})\right]$$
$${h}_{1W}^{^{\prime}}=\left({h}_{t-wgW}.{A}_{gW}\right)/\left[\frac{{A}_{b}}{2}.{h}_{t-wgW}+{A}_{gW}.({h}_{r-WE}+{U}_{cW})\right]$$
$${h}_{2E}^{^{\prime}}=\left(\frac{{A}_{b}}{2}.{h}_{t-wgE}\right)/\left[{h}_{t-wgE}.\frac{{A}_{b}}{2}+{A}_{gE}\times ({h}_{r-EW}+{U}_{cE})\right]$$
$${h}_{2W}^{^{\prime}}=\left(\frac{{A}_{b}}{2}.{h}_{t-wgW}\right)/\left[{h}_{t-wgW}.\frac{{A}_{b}}{2}+{A}_{gW}\times ({h}_{r-WE}+{U}_{cW})\right]$$
$$a=\frac{1}{{m}_{w}{C}_{w}}\times \left[{U}_{eff}^{DS}+{h}_{r-EW}.\frac{{A}_{b}}{2}.\left({h}_{1E}^{^{\prime}}+{h}_{1W}^{^{\prime}}\right)+{\dot{m}}_{f}{C}_{f}.\left(N-1\right)\right]$$
$${U}_{eff}^{DS}=\left(\frac{{U}_{taE}}{2}+\frac{{U}_{taW}}{2}+{U}_{bwa}\right)\times {A}_{b}+{U}_{L}\times \left({A}_{rc}\times {F}_{r}\right)$$
$$f\left(t\right)=\left[{{U}_{eff}^{DS}\times T}_{a}+\left\{{I}_{sE}\left(t\right)+{I}_{sW}\left(t\right)\right\}\times \left({{\alpha }_{beff}\times \frac{{A}_{b}}{2}+\alpha }_{w}^{A}\times \frac{{A}_{g}}{2}\right)+\left({A}_{rc}.{F}_{r}\right).{F}_{1}.{\left(\propto \tau \right)}_{eff}.{I}_{b}\left(t\right)+\frac{{A}_{b}}{2}\left\{{T}_{giW}.{h}_{r-EW}({h}_{1E}^{^{\prime}}+{h}_{1W}^{^{\prime}})+{\alpha }_{g}^{A}\left({h}_{1E}^{^{\prime}}.{I}_{sE}\left(t\right)+{h}_{1W}^{^{\prime}}.{I}_{sW}\left(t\right)\right)\right\}\right]/\left({m}_{w}{C}_{w}\right)$$
$$\left(Nu.Gr\right)/Pr=\left(g.{\beta }^{^{\prime}}.{d}^{4}.\dot{q}\right)/\left({\nu }^{2}.\mu .{C}_{f}\right)$$
$$Nu=\frac{h.X}{{K}_{w}};\nu =\mu /\rho$$

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Singh, A.K., Gautam, S. Optimum techno-eco performance requisites for vacuum annulus tube collector–assisted double-slope solar desaltification unit integrated modified parabolic concentrator. Environ Sci Pollut Res 29, 34379–34405 (2022). https://doi.org/10.1007/s11356-021-18426-x

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