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3 – Theoretical Background and System Analysis DHW tank VS TS VCW TCW V'S TS VM Tm V'CW TCW No mixing Mixing Figure 3.25 Principle of the mixing of hot and cold water in a DHW tank during the tapping and charging modes. Since the water flow rate during the tapping period is in the order of 10 to 50 times higher than that of the charging period, the mixing is mainly a problem during tapping. In an idealized mixing process, the cold city water volume will be reduced by 1⁄2 VM, and the total water volume that has to be heated by the CO2 heat pump, will increase by 1⁄2 VM. The exergy loss in J due to the mixing can be estimated as follows, when using average values for the density ρ and the specific heat capacity cp: V ⎡T−TT−T ⎛T−T⎞⎤ ∆E= M ⋅ρ⋅cp ⋅(Tm −TCW )⋅⎢ S 0 + CW 0 −2⋅⎜ m 0 ⎟⎥ (3.23) Mixing zone where Tm = TS + TCW (3.24) 2 2 ⎢ TS TCW ⎝ Tm ⎠⎥ ⎣⎦ According to the first law of thermodynamics, the mixing process will not affect the total heating demand during the charging period, i.e.: VCW ⋅ρ⋅cp⋅(TS −TCW )= V'CW ⋅ρ⋅cp⋅(TS −TCW )+ VM⋅ρ⋅cp⋅(TS −Tm ) (3.25) However, the mixing of hot and cold water will increase the energy con- sumption for the CO2 heat pump unit, since the COP is heavily affected by the inlet water temperature to the DHW preheating gas cooler unit. Hence: VCW ⋅ρ⋅cp ⋅(TS −TCW ) ≤ V'CW ⋅ρ⋅cp ⋅(TS −TCW ) + VM ⋅ρ⋅cp ⋅(TS −Tm ) COPT−CW COPT−CW COPT−m (3.26) 58PDF Image | Residential CO2 Heat Pump System for Combined
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