Nonequilibrium unsteady thermodynamic and spatio-temporal properties of ground source heat pumps

Size: px

Start display at page:

Download "Nonequilibrium unsteady thermodynamic and spatio-temporal properties of ground source heat pumps"

Osborn Woods
5 years ago
Views:

1 Nonequilibrium unsteady thermodynamic and spatio-temporal properties of ground source heat pumps Olga Kordas Senior Researcher, KTH Royal Institute of Technology (Stockholm, Sweden), Eugene Nikiforovich Professor, Institute of Hydromechanics of NASU (Kyiv, Ukraine),

2 Presentation to cover Motivation Problem statement Dimensionless parameters Similarity problems for VGS Energy analysis of VGS systems Conclusions

3 Motivation Sizing of BHE a vital issue in the design of VGS Conventional engineering theories of BHE are based on the assumptions of constancy of temperature or heat fluxes along a borehole. The assumptions are grounded on Kelvin s theory of heat sources: unsteady, one dimensional, self similar solution The assumptions mean that the amount of extracted heat is directly proportional to the length of the BHE There is no justification for these assumptions for actual operating conditions of VGS The conventional theories do not deliver on optimization of the BHE length

4 Goals To elaborate an unsteady phenomenological thermodynamic theory of VGS as an integrated system combining soil, BHE, and GSHP in a nonequilibrium thermodynamic system. To study fundamental laws of energy exchange in VGS in order to develop new approaches to construction of energy-efficient schemes for VGS using similarity methods and laboratory modeling.

5 Thermodynamic scheme for a VGS ENERGY QUANTITY E = c $% ρ ' T % t, r, x -, k /%, α /% T % t, r, x - = 0, k /%, α /% V r ds 6 ENERGY QUALITY CARNOT HP T?@AB COP = T?@AB T G Soil source of low temperature energy T -, α /, k / T - BHE T CADEF Evaporator T G Compressor L, R, k %, α %, V h ;, k ;, α ;, T G h <=, k <=, α <= T T?@AB CONDUCTIVITY + CONVECTION PHASE CHANGE COMPRESSION

6 Correlation between Energy and Hydrodynamic parameter of VGS E - = h CAD V = c $ ρδtv = c $ ρδtv MNE S V MNE = E - c $ ρδts

7 Dimensionless governing equations, initial and boundary conditions ENERGY EQUATIONS Z[ α ] /% = Z r Z[ ], for r 1 ZF Z= Z= INITIAL CONDITIONS θ / = θ % = 1 at t = 0 and all r and x Z[ \ + 1 ZF r_ Z[ \ = G Z r Z[ \, for r 1 Z` = Z= Z= BOUNDARY CONDITIONS θ / = θ %, for r = 1, for all x Z[ \ Z= = k /% Z[ ], for r = 1, for all x Z= θ / 1 as r, for all x θ % = 0, for x = 0 and r 1

8 Similarity problems for VGS All dimensionless characteristics of the problem are: two parametric depend on two similarity parameters α sb = α s αb and k sb = k sg kb In particular, L - = φ α /%, k /% _i jk \

9 Example BRINE 30% propylene glycol and 70% water k % = 0.44 W/mK, α % = 1.1 r 10 st m _ /s SOIL 1. Sand with 20% water content k / = 1.33 W/mK, α / = 9.26 r 10 st m _ /s k sb = 3. 02, α sb = Granite k / = 3.5 W/mK, α / = 1.19 r 10 s m _ /s k sb = 7. 95, α sb =

10 Analysis of results ENERGY QUANTITY E(t, α /%, k /%, x - ) = c $ ρ ' [T % t, r, x -, α /%, k /% E t, x -, α /%, k /% = 6 E c $ ρ TV G = 4 ' θ % (t, r, x -, α /%, k /% )(1 r _ )rdr - T % t, r, x - = 0, α /%, k /% ]V r ds Capacity of the well Dimensionless debit of the energy well ENERGY QUALITY COP M=A@F = T?@AB T?@AB T G = 1 1 T - T?@AB + G θœ t, x -, β, γ = 2 ' Θ % t, x -, r, α /%, k /% rdr - T θœ t, x -, α /%, k /% T?@AB Ω t, x 0, α sb, k sb = E t, x 0, α sb, k sb, θ (t, x 0, α sb, k sb ) Average dimensionless temperature The fundamental energy characteristic

11 Capacity E of a borehole heat exchanger (BHE) as a function of its dimensionless length, time and similarity parameters α sb, and k sb granite sand with 20% water content

12 Calculated average dimensionless temperature θ t, x -, β, γ as a function of dimensionless length x -, dimensionless time t, and similarity parameters α sb, k sb granite sand with 20% water content

13 CONCLUSIONS Developed an unsteady phenomenological hydrothermodynamic theory of VGS - an integrated system combining soil, BHE, and GSHP in a nonequilibrium thermodynamic system The introduced fundamental energy characteristic Ω t, x 0, α sb, k sb = E t, x 0, α sb, k sb, θ t, x 0, α sb, k sb of an energy well for a given VGS completely defines the quantitative and qualitative energy characteristics of a given VGS The results allow for new scientific-technological approaches to creating optimum strategies for the design, control and operation of VGS

14 Acknowledgements The authors gratefully acknowledge the financial support from the Swedish Institute.

Pumped Heat Electricity Storage: Potential Analysis and ORC Requirements

Pumped Heat Electricity Storage: Potential Analysis and ORC Requirements Institute of Combustion and Gas Dynamics Chair of Thermodynamics Dennis Roskosch, Burak Atakan ASME ORC 2017 Milano September 15,