The thermal compression process on the p–c–T plane for bottoming adsorption case is a–b–c–d (ideal) and a′ –b–c′ – d (with void volume effect). Similarly, e–f–g–h and e′ –f–g′ –h, represent the analogues for high stage thermal compression. In the two-stage thermal compression system, enhancement of density (a requisite for compression) is achieved in two stages. In the low stage the refrigerant is compressed up to an intermediate pressure pi. By passing through the intercooler, the adsorbate is cooled from desorption temperature (Tdes) back to the adsorption temperature (Tad) and then it enters the high stage compressor. The objective is to obtain as large an uptake difference as possible across each stage of compression (Cb − Ca and Cf − Ce).

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Although, Cb − Ca and Cf − Ce are the uptake differences across which thermal compressors are ideally expected to operate, in the actual operation they diminish by a–a′ and e–e′ (Fig. 1) due to the void volume created by interparticle gap, the macropores and to some extent, the mesopores.

In the first instance the refrigerant already present in the void volume of the thermal compressor gets adsorbed. This reduces the ability of filling of micropores by the adsorbate coming from the evaporator for the low stage and from the low stage compressor for the upper stage. In a similar way, during desorption, the adsorbate released from the micropores, in the first instance, increases the pressure in the void volume. Certain amount of the adsorbate does not contribute to the throughput of the compressor but undergoes cyclic changes within the compressor. Thus, the void volume in an adsorption compressor behaves identically like the clearance volume in a mechanical compressor.

There is an additional advantage of securing even a larger concentration difference across the thermal compressor in the high stage thermal case. Another parameter that has been investigated is the inter-stage pressure [Pi = (Pev * Pcond)0. 5] which is varied for 0. 8 ≤ Pi ≤ 1. 2. A major disadvantage of the above hybrid compression process is that the mechanical and adsorption segments have largely varying time constants. While a mechanical compressor has a cycle time of a few milliseconds, the adsorption segment requires several minutes to complete one cycle of compression process. Hence, a string of sufficiently large adsorber (typically four) will be required to ensure that the mass flow rate through each of the compressor segments is the same.

Performance indicators: The conventional COP will be retained as the first indicator and is defined as follows: COP =(Refrigeration effect)/((Wc + Qad)) 1The denominator therein combines the work (mechanical stage, Wc) and heat (adsorption stage, Qad) quantities, which does not provide a true measure. Hence, the heat quantity is converted into its exergy component using 298. 15 K as the reference temperature (Tref). At the same time the refrigeration effect is also replaced with the change in exergy of the refrigerant in the evaporator. The intrinsic COP is defined as: COP intrinsic =ΔEev/(Wc + Qad (1-Tref/Tdes)) 2where ΔEev is the change in exergy of the refrigerant in the evaporator which given by: ΔEev= m [(h1-h4)-Tref (s1-s4)] 3 An overall picture of efficacy of the hybrid cycle can be measured in terms of saving in power per kg of adsorbent used. ΔWcomp = (Wc1-Wc)/mch 4where Wc1 is the mechanical compressor work, if the entire compression was carried out in a single stage.

Evidently, Wc1–Wc would be the saving in energy due to compression supplemented by the thermal stage. For the sake of calculations, the isentropic efficiency is assumed to be 85%. The other indicators are the volumetric and uptake efficiencies, reduction in quantity of activated carbon used compared to single- and two-stage thermal compression. The volumetric efficiency of the mechanical compressor is calculated as follows: ɳvcomp =(1+C) (Psuction/Pi)^(1/m)-C*(Pdischarge/Pcon)^1/m -0. 015*(Pdischarge/Psuction) 5 here C is the clearance ratio (assumed to be 6%).

The pressure required for suction is set at 95% of inlet pressure (which is pe for low stage mechanical compression and pi for the high stage) and that at discharge to be 102% of discharge pressure (which is Pi for the low stage mechanical and Pcon for the high stage compression) to account for the pressure drops at suction and discharge ports and acceleration of refrigerant. The last term on the RHS of Eq. (5) accounts for leakages across the piston rings. The index m is taken as 1. 18 for HFC 134a. Uptake efficiency of an adsorption compressor is analogous to the volumetric efficiency of a mechanical compressor and is defined as follows (Fig. 5): ɳul= (Cb-Ca0) / (Cb-Ca) (6)and ɳuh=(Cf-Ce0)/ (Cf-Ce) (7) when adsorption compressor is in the lower (suffix l) or the upper (suffix h) stages, respectively. The above equations can be reduced to the following form: ɳu = 1+(Δρ/ΔC) (1/Peff - 1/Ps) (8) with Δρ= ρb -ρd or ρf-ρh and ΔC=Cb -Cd or Cf-Ch depending on whether the thermal compressor forms the low or high stage of the compression process. The value of ɳu < 1 since the process of compression requires that Δρ < 0. The suffixes eff and s refer to effective packing density and solid carbon density, respectively.

The data required for the analysis are the equation of state for HFC 134a (Tillner-Roth and Baehr, 1994) and the adsorption characteristics of activated carbon +HFC 134a system (Akkimaradi et al. , 2001). The entire calculation scheme was programmed on a Matlab platform. The sizing of each of the thermal compressors is done as follows. The mass flow rate of refrigerant (mr) to meet the cooling demands is arrived at from the cooling load and the enthalpy change of the refrigerant in the evaporator for a given set of condensing and evaporating temperatures. The minimum amount of refrigerant that needs to be adsorbed per adsorption bed is the product of this flow rate and the time of adsorption (τad)mad=(mr) τad (4)The minimum amount of activated carbon required per compressor to adsorb this quantity of refrigerant ismch=mad/(ΔC*ηu) (5)Eq. (5) assumes equilibrium conditions that are again not possible in practice because the cycle time has to be finite. A large cycle time will demand a large number of compressors and a short cycle time would cause a loss of throughput.

In a practical compressor, equilibrium is attained only after 3–5time constants. The time constant depends on the thermal diffusivity of the adsorption bed and is typically of the order of several minutes. Banker observes that the discharge from a HFC 134a adsorption cell drastically reduces after about one time constant which is also corroborated by Saha et al. During measurement of throughput during desorption of methane and azeotrope R-507a from activated carbon beds. In general, if the desorption is allowed for ‘n’ time constants, the loss due to non-equilibrium conditions would be (1 − e−n). Thus, a sacrifice of ∼33% of the throughput seems to be inevitable which forces the desorption to be stopped after about onetime constant which itself could extend to about a few 100’s of seconds. This is equivalent to a further loss of volumetric efficiency. Hence, the mass of charcoal required needs to be augmented as follows: mch=mr*τad(ΔC)1ηu-(1-e-n) (6)We define a multiplication factor for the amount of charcoal to account for the effect of void volume and the loss of throughput due to lack of equilibrium uptake conditions to limit cycle time, as follows: MF=1/(ηu-(1-e-n)) (7)This factor is similar to the ‘α’ factor proposed by Burger et al. for activated carbon–nitrogen systems. The volume of the compressor is calculated as follows: (8)V=mch/ρeffThe compressor is assumed to be a long slender cylinder of L/d ratio of ∼20 such that longitudinal heating and cooling will allow fast thermal equilibration. The material of construction of the cylinder is assumed to be stainless steel of 2 mm wall thickness.

The calculation scheme requires adsorption equilibrium data for the activated carbon + HFC 134 system which were obtained from and replicated in the Appendix. Thermodynamic properties of HFC 134a were evaluated from the equation of state proposed by Tillner-Roth and Baehr. The parameters that were varied are the evaporating temperature, −20 ⩽ Te ⩽ 10 °C (which determines pe in Fig. 1), the condensing temperature, 20 ⩽ Tcon ⩽ 40 °C (which determines the pressure Pcon in Fig. 1), the heat source temperature 80 ⩽ Tdes ⩽ 100 °C and the inter-stage pressure pi = x (PePcon)1/2 for 0. 8 ⩽ × ⩽ 1. 2. Heat inventories comprise of the need to heat the compressor body and activated carbon from adsorption to desorption temperatures, the enthalpy change of the adsorbed refrigerant and the heat of desorption. The last parameter is calculated using Eq. (A6) in the Appendix. A detailed evaluation procedure of each of these components is given by Banker et al..

The performance indicators are the individual stage uptake efficiencies, the coefficient of performance (COP) defined in the conventional way asCOP=Cooling produced/Heat supplied (9)and the exergetic efficiency defined asηex= COPCarnot /COP (10)where, Carnot COP=(Tdes-Tad)/Tdes*Te/(Tad-Te) (11)All the calculations were performed on Matlab platform.

## Results and discussion:

### Results of uptake efficiencies

For most comparative calculations, the inter-stage pressure is set at √(pcon. pe). shows an overview of uptake efficiencies for the low and high stages of two stage compression and that for the single stage for Maxsorb II, Fluka and Chemviron specimens of activated carbons at their respective achievable packing densities namely 280, 390 and 750 kg/m3. A line at ηu = 0. 77 is the minimum desirable uptake efficiency. It is seen that despite the low achievable packing density of powder form of Maxsorb II specimen, its uptake efficiencies are larger than those of the others because of good adsorption characteristics. Yet, a common feature is a rapid drop in uptake efficiencies of single stage compression with decreasing evaporating temperatures.

Indeed, it is this feature that set the agenda for adopting two stage compression which rightly shows a comparatively better uptake efficiency. Fluka and Chemviron specimens which did not permit good throughput te < ∼0 °C in single stage operation, are amenable to two stage compression for the operating conditions considered here. Thus, relatively weaker adsorption in specimens that prevent their usage in single stage compression, can be partially alleviated by a higher achievable packing density and/or two stage compression.