Coupling of the specified closed systems with refrigerants for a given VT

For a VT, the cooling or heating effect is strongly dependent of its inlet and outlet pressures which must be matched with the system operation requirement for a given refrigerant. Therefore, the coupling of a VT with a system essentially aims at identifying the suitable pressures at certain defined temperature ranges; the coupling process also involve re-dimensioning of VT, if needed, to deliver the specified cooling or heating effect. Optimization can be achieved by switching refrigerants if necessary. Out of the six scenarios and sub-scenarios for each of the two systems, only three for each them (Figure 3.15a1, a3 and d, and Figure 3.17a1, a3 and d) need to be considered, as the coupling procedures can be adapted and outcome applied to the other three. They are re-drawn respectively in Figure 3.18i, ii, and iii, and Figure 3.20i, ii and iii, showing the key state points of the two systems on the T-s diagram, particularly showing the application of the boundary line for the cooling system.

i

ii

iii

Figure 3.18 Key state points (●) and the boundary lines used in the coupling process for the defined cooling system

4′ {T4′, p4′} 1{T1, p1} 2 3{T3, p3} 4 {T4, p4} 5 {T5, p5} T s Cr P{Tp} 6 {T6, p6} T s Cr P{Tp} _{1{T1, p1}} 2 3{T3, p3} 4 {T4, p4} 5 {T5, p5} 6 {T6, p6} 4′ {T4′, p4′} 1{T1, p1} 2 3{T3, p3} 4{T4, p4} 5 {T5, p5} T s Cr _Boundary 6 {T6, p6} 4′{T4′, p4′}

The Cooling System

Preliminary observations based on the CFD results show that, for a given refrigerant and a VT inlet temperature, a higher chamber inlet velocity would lead to a larger cooling effect. Therefore, a key assumption is made prior to start of the procedures, i.e. the refrigerant velocity at the VT nozzle outlet is assumed to be at the sonic speed or choked, which is the maximum speed possible for a convergent nozzle. Also it should be noted that for the cooling system, the VT inlet and outlet pressures are initially unknown. The proposed coupling procedures are as follows:

1. Locate the VT inlet state (T3, p3) on the T-s diagram

As noticed from the preliminary CFD runs, at a constant pressure, a higher VT inlet temperature (within the range of 20 to 40 °C) would lead to only little changes in cooling effect. On the other hand, a higher VT inlet pressure would generate a bigger cooling effect when the inlet temperature is kept constant. Accordingly, for any chosen temperature T3 in the range of 20 to 40 °C, the corresponding pressure p3 can only be chosen at a point either on the boundary line or close to the critical pressure line10. For a Group 1 refrigerant, if T3 is smaller than the Tp, as represented in Figure 3.18i, p3 is taken as the saturated pressure at T3. On the other hand, if T3 is larger than the Tp, as seen in Figure 3.18ii, p3 is taken as the pressure of the point either on the boundary line or close to the critical pressure line. Figure 3.18iii presents the situation for a Group 2 refrigerant, and p3 is the pressure of the point either on the boundary line or again close to the critical pressure line.

2. Calculate the total temperature and total pressure of the refrigerant at the VT inlet The total temperature T3-total and pressure p3-total, as required in the CFD simulation, can be determined by employing basic gas dynamics calculations, using the static temperature (T3), pressure (p3) and a specified refrigerant velocity at the nozzle inlet. 3. Obtain the required VT cold end temperature Tc

The VT cold end temperature Tc (obtained by the CFD simulation) is to match with the required Hx2 exit temperature T6 (Note: the specified design Hx2 exit temperature T6 is previously set between -5 to 15 °C). If Tc is lower than T6, the coupling is

considered successful, otherwise the chosen VT must be changed and/or an alternative refrigerant should be considered. The details of changing the VT dimensions and switching the refrigerants are introduced in Chapter 6 based on the understanding of the influence of fluid properties and of the development of velocity fields in the VT. To show the method clearly, the full procedure is summarised in Figure 3.19.

Figure 3.19 Procedure of coupling the cooling system with the refrigerant for a given VT

T3-total, p3-total

Gas dynamics calculations

VT re-dimensioning Evaluate alternative Refrigerants Yes No No Coupling successful, T5 = Tc, p5 = pc Refrigerant Group 1 p3

Pressure of the point on the boundary line of Sub-area

IV or close to the critical pressure line

p3

Pressure of the point on the boundary line or

close to the critical pressure line T3, p3 Tc, pc CFD, established 2-D VT model p3 Pressure of the point with saturated

temperature T3 Group 2 T3 > Tp Tc < T6 Coupling unsuccessful Yes vin

The Heating System

In the liquid-pump VT heating system, (Figure 3.16), the VT cold end pressure is governed by the condensing temperature and the VT inlet conditions are controlled by the varying heat input to (or temperature of) the boiler.

Preliminary CFD results show that the heating effect would be the largest when the inlet pressure reaches certain values, above which further increases of pressure will lead to a larger temperature drop between the VT inlet and hot end, resulting in a smaller heating effect. In addition, at a constant VT inlet pressure, a larger degree of vapour superheat always leads to a bigger heating effect. Therefore, the key is to determine the combination of VT inlet pressure and its corresponding degree of vapour superheat which will deliver the largest heating effect and whether this meets the design heating requirement. The procedures to identify this combination are presented in Figure 3.20 and described as follows.

1. Identify the VT inlet pressure value (p4) and its corresponding degree of super heat (ΔTsh) for a specified VT inlet temperature within the range of T4 (= 60 °C ~ 80 °C). For a specified T4, the pressure p4 is known if the degree of the superheat,ΔTsh (= T4 – T3), is specified too, where T3 is the saturated temperature at p3 which has in fact the same value as p4. For either a Group 1 or Group 2 refrigerant, the degree of superheat (ΔTsh,i) can be systematically and decrementally adjusted, giving T3,i = T4 – ΔTsh,i (i = 1, 2⋯n), as shown in Figure 3.21 and ΔTsh,i should be no larger than T4 – T8.

2. Calculate the total temperature and pressure of the refrigerant at the VT inlet, procedures similar to Step 2 in the cooling system are implemented.

3. Obtain the required VT hot end temperature Th, i-1.

The Th,i-1 (obtained by the CFD simulation) is to match with the required Hx exit temperature (T7) (Note: the desired heating temperature range is 80 ~ 100 °C). If Th,i is smaller than Th,i-1, Th,i-1 is taken as the largest possible heating temperature. The Th,i- 1 is checked against the required Hx exit temperature (T7), and if Th,i-1 > T7, the coupling is considered successful, otherwise changes in the VT dimensions and alternative refrigerants should be considered. The full algorithm is summarised in Figure 3.21.

i

ii

iii

Figure 3.20 Key state points (●) used in the coupling process for the specified heating system s 1 2 3{T3, p3} 4{T4, p4} 5{T5, p5} 7{T7, p7} 6{T6, p6} 8{T8, p8} T Cr P ΔTsh 7′{T7′, p7′} s 1 2 3 {T3, p3} 4{T4, p4} 5{T5, p5} 7{T7, p7} 8{T8, p8} T 6{T6, p6} Cr P ΔTsh 7′{T7′, p7′} 1 2 3{T3, p4} 4{T4, p4} 5{T5, p5} 7′{T7′, p7′} 8{T8, p8} 6{T6, p6} s T Cr ΔTsh 7{T7, p7}

Figure 3.21 Procedure of coupling the heating system with the refrigerant for a given

VT No

Th,i < Th,i-1 Yes

p3,i-total, T4,total

Gas dynamics calculations

VT re-dimensioning

Evaluate alternative Refrigerants

No

Coupling successful, p3,final= p3,i-1, T5 = Th,i-1 T4, T8, p8 Th,i-1 CFD, established 2-D VT model T3,i = T4 – ΔTsh,i Refrigerant Th,i-1 > T7 Coupling unsuccessful p3,i, T3,i

p3,i is the saturated pressure at T3,i

Th,i Yes i=i+1 ΔTsh,i = ΔTsh,i-1 – B (B is a specified value) If i = 1

i=1, ΔTsh,1 = A, (0 < ΔTsh,1 < T4 – T8), A is an input variable )

No

Yes

It should be noted that the current proposed/developed VT closed system integration procedure is based on two specified VT systems. For both of them, the VT inlet temperature is a known value as it can be defined, though inlet pressure is usually unknown. The VT cold end outlet pressure can be controlled in the heating system while is unknown in the cooling system.

In other systems, two other situations are possible. First is when the cold end pressure is unknown in a heating system, and second the cold end pressure can be controlled to a required value for cooling system. The proposed procedure can be easily adapted for these two possibilities, with the same aim of identifying the VT inlet pressure (pin) at the specified inlet temperature (Tin) to meet the design cooling/heating requirement. For the adaptation, certain steps are revised as follow.

For an unknown VT cold end outlet pressure in a heating system, the VT entry point should be on the right side of the boundary line, with reasons previously explained. The range of ΔTsh,1 (Figure 3.21) should be changed to be larger than ΔTsh,min (Figure 3.8) but less than Tin, while other steps (Figure 3.21) remain unchanged.

For a known VT cold end outlet pressure of a cooling system, a VT inlet pressure pin is initially picked up at the position on the boundary line at Tin. If the CFD prediction of Tc is either equal to or smaller than the design cooling temperature, then pin should be progressively decreased to obtain the largest system performance, such as coefficient of performance (COP). If not, the pin is raised gradually to see whether Tc can attain the design temperature but at the same time to ensure that no liquification inside the nozzle occurs.

Following the successful integration of the system, optimization of the working conditions could be carried out by comparing COP and capacity values for different combinations of the required cooling/heating and VT inlet temperatures. This exercise can be repeated for different refrigerants and/or VT designs to achieve the optimum performance.

This chapter outlined the steps for establishing the VT CFD model and also a unique refrigerant screening methodology. This was followed by presenting a systematic coupling procedure for integrating a VT into thermal systems, comprising optimal matching of the VT geometry with the refrigerant choice and the operating conditions.

In the next chapter, the details of establishing the VT CFD model, including geometry definition, analysis on the appropriate choice of meshing element numbers, turbulence models consideration and model validation, are presented. This is followed by a preliminary examination of the influence of different VT operating conditions on the TSE for three chosen fluids (air, R134a and R600).

4 Establishment of the VT simulation model and preliminary

CFD runs

In the process of setting up the CFD model of the VT, the results are initially analysed to assess the influence of the meshing element number on the accuracy/stability of the numerical simulations and to aid the selection of the appropriate turbulence models. The model is validated by comparing the CFD results with other experimental and/or numerical results.

Using the established VT model, the cold mass flow ratio µc is adjusted to determine whether the VT is to be primarily used as a heating or a cooling device, and the influence of the inlet conditions, such as mass flow rates ṁin and inlet temperatures Tin, on the TSE are investigated. Air, refrigerants R134a and R600 are chosen as the working fluids to be examined.