Solar Water Heating Theory R T Dobson

Transcription

1 Solar Water Heating Theory R T Dobson Senior Lecturer rtd@sun.ac.za 1

2 The Objective of this talk is to present the basic theory on which solar water heaters work. We will consider flat plate solar water heaters (both thermosyphon and pumped) as well as evacuated tube solar water heaters 2

3 Contents How do we?: Collect the heat Transport the heat Store the transferred heat 3

4 A little about myself Nuclear Energy Solar Energy Missile Manufacture Management Heat Transfer Lecturer My research philosophy is: Adaptive engineering were we try and engineer our heat transfer systems to make exclusive use of natural forces such as gravity, surface tension density gradients and buoyancy to do the job for us without the use of any mechanically moving parts such as pumps and mechanical activators and active electronic and mechanical controls and switches 4

5 We used the roof and the car park as our solar water heater test laboratory at Kwikot LTD, Edinburg Road, Benoni Solar panels Integral Solar water heaters 5

6 Thelma (Kwikot Factory Personal manager) cooking pap along side Benoni Lake in

7 Front and back-page of our Frost Resistance Panel 7

8 Solar water heater configurations Integral Thermosyphon Pumped Close-coupled Swimming pool 8

9 Integral solar water heater Solar collector and Water Storage all in one unit Collector Water storage 9

10 Thermosyphon solar water heater Collector Water storage Solar collector below water Storage and water flows by thermosyphonic action 10

11 Pumped solar water heater Solar collector below water storage. Water is pumped Collector Water storage Water Pump 11

12 Close-coupled Thermosypon solar water heater Solar collector and water storage separated but on a common integrated support platform to look like a single unit Collector Water storage Roof 12

13 Close-coupled Indirect Tank-in in-tank Thermosyphon solar water heater Thermosyphon (or natural circulation indirect solar water heating system Tank-in-tank heat exchanger Water storage tank Solar collector Circulation loop containing anti-freeze and water solution 13

14 Swimming pool solar water heater Water pumped from pool up to solar collectors on roof Solar collector High-pressure pump Open water tank 14

15 Swimming pool solar water heating system 15

16 F hot = ρ hot gh Thermosyphon solar water heating system How does it work? H F cold = ρ cold gh The density of the hot fluid is less than the density of the cold fluid. The force of attraction to the earth of the hot fluid is less than for the cold fluid. As a result of this force imbalance cold fluid sinks and the hot fluid rises and the fluid circulates around the loop. The denser or heavier fluid package will sinks and pushes the less-dense or lighter fluid up 16

17 Thermosyphon solar water heating system Glass cover Hot water rises Hot Cold Insulation Cold Cold water water sinks sinks 17

18 Basic theory: Divide the system into control volumes and apply the conservation of mass, momentum and energy x m& out m& v out P out m& h out m& in Conservation of mass: τ x m& v m in = m& in m& out t P in m& h in Conservation of momentum: mv = mv & in mv & out mg τ x Pout P t U Conservation of energy and heat transfer: t mg ( in) T A in Q& = heat transfer T hot out R = mh & mh & + Q& cold heat transfer 18

19 Basic heat transfer theory: Heat transfer equation: Q& = T hot T R cold [W] Hot Q & x Cold Conduction: Convection: R R = ka x 1 R = ha = [ C/W] [ C/W] Radiation: ( 2 2)( ) [ 1 Hot Q & Cold Fluid εaσ ( T ) + ( T ) ( T ) + ( T ) Q & Hot vacuum Cold 19

20 Basic theory: Effect of glazing (glass) Q & shortwave solar incident Q & reflected longwave Q & radiation Q & convection Q & shortwave solar incident Q & reflected Q & longwave Q & radiation Q & convection Glass conduction longwave Q & radiation Absorber Insulation Q & conduction 0 (a) No glass cover Absorber Insulation Q & conduction 0 (b) With glass cover plate 20

21 Evacuated-tube tube solar water heaters Hot water Hot water Vapour Cold water glass Condensate Evacuated double walled glass tube Vacuum Black paint Evacuated double walled glass tube + heat pipe 21

22 Typical domestic evacuated-tube tube solar water heater installation 22

23 Typical pumped indirect solar water heating system Heat exchanger Water storage tank Pump Expansion tank 23

24 Basic theory: Heat collection Q & solar Q & reflected Q & lost = U T collector T surroundin Q & Q & ( ) gair into water ( τα ) Q& solar = 1 = τα & in Q solar Q& water out = mct & Q & water out τ αq& Q& into collector= solar water int o tank = mct & Heat storage water in ( T T ) U collector Q& water in surroundingair Water storage tank = m& ct water in ταq& solar ( T ) = mc & ( T T ) collector & Q in Q& lost surroundingair = Q& absorbedby water - U T water out water in Q& water in = m& ct water in 24

25 Typical solar water heater collector characteristics Collector efficiency, η (%) Black paint Black paint + Glass Evacuated glass tube Selective coating + Glass Solar collector thermal perfofmance characteristic is : η = a + b Q& where solar colloector efficiencyη = Q& heat input factor heat loss factor Q& a = Q& solar input solar ( T T ) c collected input τα Q& = Q& solar a solar heat collected τα - U T b = Q& = solar heat into water mc & = Q& = ( T ) collector ( T T ) water out = τα, and Q& Q& solar solar surrounding air water in Temperature difference, T c T a ( C) T T where water in + water out Tc 2 25

26 My Up to 40% electricity savings 50 % efficient 500 W/m 2 over an 8 hour period Overheating?? Air bubbles?? Pressure?? Thanks Expansion relief?? Automatic air relief?? Corrosion?? Gas loaded heat pipe temperature control?? Freezing?? Reverse thermosyphoning?? 26

27 Typical pumped indirect solar water heating system Heat exchanger Water storage tank Pump Expansion tank 27

28 Consider a hollow pipe with a variable diameter and fashioned into a closed loop and also containing a working fluid z z Theoretical modeling g Expansion tank Divide the loop up into a number of smaller control volumes, apply the equations of change to each control volume, and integrate around the loop! 28

29 Theoretical modeling (cont.) Conservation of Mass m Single phase flow = 0 = m& in m& out t m Two-phase flow 0 = m& in m& out but mass enters the t expansion tank instantaneously Assumptions: * One-dimensional flow m& = ρva * Both liquid and vapour phases are incompressible * Density (pressure) waves occur instantaneously, ie speed of sound >> m& 29

30 Theoretical modeling (cont.) Conservation of Energy Single phase flow for the i th control volume with the temperature T expressed explicitly: Heat transfer rate T t+ t i = T t i + t m t i c ( Q& + mi & mi & ) t in,out in out m = ρ A z c = specific heat i = enthalpy 30

31 Theoretical modeling (cont.) Conservation of Energy Two-phase flow for the i th control volume with the temperature T expressed explicitly: u t + t i = u t i + If u t+ t < u f then If u t+ t > u f then x t+ t t t i m c T ( Q& + mi & m& i ) in,out in t+ t t+ t t+ t hp = u cv and x = 0 t+ t hp sat and T =T u = u + xu, t+ t t+ t t+ t = u uf ufg, where hp f fg i = i f + xi fg, u f = cvthp and i f = cpthp. out 31

32 Conservation of Momentum applied to heat pipe control volumes to determine the mass flow rate Buoyancy driving term Theoretical modeling (cont.) Frictional-resistance term N N k C + k f, lo,kφlo,k Lk Lf,equiv,k 2 ρ L m m k kg sin φ & 2 d & k k = 1 ρ r A k = 1 k i,hp x,k = N k N k dt Lk Lk k = 1Ax, k k = 1Ax, k Assumptions: * Quasi-eqilibrium * Both liquid and vapour phases are incompressible * Homogeneous two-phase flow model * Hydrostatic pressure at a point (Archimedes and Boussinesq s approximation) 32