**4. Thermodynamic analysis of the studied combined system**

For the following analysis of steam and air flow through the plant condenser, it is assumed that both fluids are ideal gases. Since the steam and air flow inside the condenser are at relatively very low pressure, they can be considered behaving to acceptable accuracy as ideal gases. Referring to **Figures 1** and **2**, the steam exhausting the plant turbine (it is usually slightly wet) enters the condenser with temperature *Tci* and dryness fraction *x*ci. Knowing the temperature *Tci*, both the saturation pressure *p*s,ci (it equals the partial pressure of the steam) and specific volume *v*s,ci of the saturated steam at condenser inlet can be fixed. Given the steam mass flow rate *m*\_ *st,t* entering the turbine, the mass flow rate *m*\_ st*,* ci of the steam at condenser entry can be calculated by:

$$
\dot{m}\_{\text{st,ci}} = \propto\_{\text{ci}} \dot{m}\_{\text{st,t}} \tag{1}
$$

Hence, the mass flow rate *m*\_ st*,* ce of steam associated with the air is assessed by:

*Air Cooling in Steam Plant Condenser Using Refrigeration System for Improving Vacuum Pump…*

*v*s*,* ce

<sup>¼</sup> *<sup>β</sup>Ra* ð Þ *<sup>T</sup>*ce <sup>þ</sup> <sup>273</sup>*:*<sup>15</sup> *p*a*,* ce *v*s*,* ce

at inlet of the vacuum pump can be

*p*a*,*vpi ¼ *pc,t* � *p*s*,*vpi (10)

In the case of screening the steam condenser and cooling the air, the temperature *T*vpi of the air and water vapor mixture sucked by the vacuum pump is Δ*T*vpi lower than the condensate temperature *T*ce at steam condenser outlet (i.e.,*T*vpi = *T*ce�Δ*T*vpi). Knowing the temperature *T*vpi, the corresponding saturation pressure *p*s,vpi and specific volume *v*s,vpi can be fixed. The partial pressure *p*a,vpi and volume flow rate

determined using Eqs. (6), (7) and (9), respectively, by replacing the subscripts ce by vpi and *γ* by *δ*. Accordingly, it follows that *p*a,vpi, *V*\_ <sup>a</sup>*,*vpi, and *δ* are given by:

*<sup>V</sup>*\_ <sup>a</sup>*,*vpi <sup>¼</sup> *<sup>m</sup>*\_ *<sup>a</sup> Ra <sup>T</sup>*vpi <sup>þ</sup> <sup>273</sup>*:*<sup>15</sup>

*p*a*,*vpi

<sup>¼</sup> *<sup>β</sup>Ra <sup>T</sup>*vpi <sup>þ</sup> <sup>273</sup>*:*<sup>15</sup> *p*a*,*vpi *v*s*,*vpi

Regarding the VCRS, the *p-h* diagram of its cycle is illustrated in **Figure 4**. The numerals of **Figure 4** correspond to the points 1–10 given in **Figure 3**. It is to be considered here that the refrigerant condenser is cooled exactly as it is conducted with the steam plant condenser. Consequently, it is assumed here that the refrigerant leaving the refrigerant condenser has a temperature equal to that of the condensate in the steam plant condenser (i.e.,*T*<sup>5</sup> = *T*ce). Considering this fact and

(8)

(9)

(11)

(12)

*<sup>m</sup>*\_ st*,* ce <sup>¼</sup> *<sup>V</sup>*\_ <sup>a</sup>*,* ce

Dividing both sides of Eq. (8) by *m*\_ st*,*<sup>t</sup> and inserting Eq. (7) into Eq. (8), it

*<sup>γ</sup>* <sup>¼</sup> *<sup>m</sup>*\_ st*,* ce *m*\_ st*,*<sup>t</sup>

*<sup>δ</sup>* <sup>¼</sup> *<sup>m</sup>*\_ st*,*vp *m*\_ st*,*<sup>t</sup>

p*-*h *diagram of the VCRS cycle of the studied refrigeration system.*

*V*\_ <sup>a</sup>*,*vpi of the air and mass ratio *δ m*\_ st*,*vpi*=m*\_ *st,t*

*DOI: http://dx.doi.org/10.5772/intechopen.83787*

follows that:

and

**Figure 4.**

**229**

The volume flow rate *V*\_ st*,* ci at inlet to the condenser, by Dalton's law, is equal to the volume flow rate *V*\_ <sup>a</sup>*,* ci of the associated air [20] and is obtained from the following equation:

$$
\dot{V}\_{\text{st,ci}} = \dot{V}\_{\text{a,ci}} = \dot{m}\_{\text{st,ci}} v\_{\text{s,ci}} \tag{2}
$$

The partial pressure *p*a,ci of the air at entry to the condenser is calculated by:

$$p\_{\text{a,ci}} = \frac{\dot{m}\_a R\_a \left(T\_{\text{ci}} + 273.15\right)}{\dot{V}\_{\text{a,ci}}} \tag{3}$$

Inserting Eqs. (1) and (2) into Eq. (3) and designating the mass ratio *m*\_ *<sup>a</sup>=m*\_ st*,*<sup>t</sup> by *β*, it follows that:

$$p\_{\text{a,ci}} = \frac{\beta R\_{\text{a}} \left(T\_{\text{ci}} + 273.15\right)}{\varkappa\_{\text{ci}} \upsilon\_{\text{s,ci}}} \tag{4}$$

The total pressure *pc,t* at condenser entry is equal to the sum of the partial pressure *p*a,ci of the air and the saturation pressure *p*s,ci of the steam entering the condenser. It is taken constant throughout the condenser, since the velocity of steam flow is small. Hence, the total absolute pressure *p*c,t inside the condenser is given as:

$$p\_{\text{c,t}} = p\_{\text{s,ci}} + p\_{\text{a,ci}} \tag{5}$$

The condensate temperature *T*ce at condenser outlet is usually Δ*T*ce lower than the steam temperature *T*ci at condenser inlet (i.e.,*T*ce = *T*ci-Δ*T*ce). Knowing the temperature *T*ce, the saturation pressure *p*s,ce and specific volume *v*s,ce of the steam corresponding to this temperature can be determined. If the condenser is not screened, then the partial pressure *p*a,ce of the air leaving the steam condenser with condensate is given as:

$$p\_{\text{a,ce}} = p\_{c,t} - p\_{\text{s,ce}} \tag{6}$$

The volume flow rate *V*\_ <sup>a</sup>*,* ce of the air to be dealt by the vacuum pump at the exit of the steam condenser can be determined by:

$$\dot{V}\_{\text{a, ce}} = \frac{\dot{m}\_a R\_a \left(T\_{\text{ce}} + 273.15\right)}{p\_{\text{a, ce}}} \tag{7}$$

*Air Cooling in Steam Plant Condenser Using Refrigeration System for Improving Vacuum Pump… DOI: http://dx.doi.org/10.5772/intechopen.83787*

Hence, the mass flow rate *m*\_ st*,* ce of steam associated with the air is assessed by:

$$
\dot{m}\_{\text{st,ce}} = \frac{\dot{V}\_{\text{a,ce}}}{v\_{\text{s,ce}}} \tag{8}
$$

Dividing both sides of Eq. (8) by *m*\_ st*,*<sup>t</sup> and inserting Eq. (7) into Eq. (8), it follows that:

$$\gamma = \frac{\dot{m}\_{\text{st, ce}}}{\dot{m}\_{\text{st, t}}} = \frac{\beta R\_a \left(T\_{\text{ce}} + 273.15\right)}{p\_{\text{a, ce}} v\_{\text{s, ce}}} \tag{9}$$

In the case of screening the steam condenser and cooling the air, the temperature *T*vpi of the air and water vapor mixture sucked by the vacuum pump is Δ*T*vpi lower than the condensate temperature *T*ce at steam condenser outlet (i.e.,*T*vpi = *T*ce�Δ*T*vpi). Knowing the temperature *T*vpi, the corresponding saturation pressure *p*s,vpi and specific volume *v*s,vpi can be fixed. The partial pressure *p*a,vpi and volume flow rate *V*\_ <sup>a</sup>*,*vpi of the air and mass ratio *δ m*\_ st*,*vpi*=m*\_ *st,t* at inlet of the vacuum pump can be determined using Eqs. (6), (7) and (9), respectively, by replacing the subscripts ce by vpi and *γ* by *δ*. Accordingly, it follows that *p*a,vpi, *V*\_ <sup>a</sup>*,*vpi, and *δ* are given by:

$$p\_{\text{a,vpi}} = p\_{c,t} - p\_{\text{s,vpi}} \tag{10}$$

$$\dot{V}\_{\text{a, vpi}} = \frac{\dot{m}\_a R\_a \left( T\_{\text{vpi}} + 273.15 \right)}{p\_{\text{a, vpi}}} \tag{11}$$

and

**4. Thermodynamic analysis of the studied combined system**

condenser entry can be calculated by:

*Low-temperature Technologies*

following equation:

by *β*, it follows that:

condensate is given as:

**228**

of the steam condenser can be determined by:

For the following analysis of steam and air flow through the plant condenser, it is assumed that both fluids are ideal gases. Since the steam and air flow inside the condenser are at relatively very low pressure, they can be considered behaving to acceptable accuracy as ideal gases. Referring to **Figures 1** and **2**, the steam exhausting the plant turbine (it is usually slightly wet) enters the condenser with temperature *Tci* and dryness fraction *x*ci. Knowing the temperature *Tci*, both the saturation pressure *p*s,ci (it equals the partial pressure of the steam) and specific volume *v*s,ci of the saturated steam at condenser inlet can be fixed. Given the steam mass flow rate *m*\_ *st,t* entering the turbine, the mass flow rate *m*\_ st*,* ci of the steam at

The volume flow rate *V*\_ st*,* ci at inlet to the condenser, by Dalton's law, is equal to

The partial pressure *p*a,ci of the air at entry to the condenser is calculated by:

*<sup>p</sup>*a*,* ci <sup>¼</sup> *<sup>m</sup>*\_ *<sup>a</sup> Ra* ð Þ *<sup>T</sup>*ci <sup>þ</sup> <sup>273</sup>*:*<sup>15</sup> *V*\_ <sup>a</sup>*,* ci

Inserting Eqs. (1) and (2) into Eq. (3) and designating the mass ratio *m*\_ *<sup>a</sup>=m*\_ st*,*<sup>t</sup>

*<sup>p</sup>*a*,* ci <sup>¼</sup> *<sup>β</sup>Ra* ð Þ *<sup>T</sup>*ci <sup>þ</sup> <sup>273</sup>*:*<sup>15</sup> *x*ci *v*s*,* ci

Hence, the total absolute pressure *p*c,t inside the condenser is given as:

The total pressure *pc,t* at condenser entry is equal to the sum of the partial pressure *p*a,ci of the air and the saturation pressure *p*s,ci of the steam entering the condenser. It is taken constant throughout the condenser, since the velocity of steam flow is small.

The condensate temperature *T*ce at condenser outlet is usually Δ*T*ce lower than the steam temperature *T*ci at condenser inlet (i.e.,*T*ce = *T*ci-Δ*T*ce). Knowing the temperature *T*ce, the saturation pressure *p*s,ce and specific volume *v*s,ce of the steam corresponding to this temperature can be determined. If the condenser is not screened, then the partial pressure *p*a,ce of the air leaving the steam condenser with

The volume flow rate *V*\_ <sup>a</sup>*,* ce of the air to be dealt by the vacuum pump at the exit

*p*a*,* ce

*<sup>V</sup>*\_ <sup>a</sup>*,* ce <sup>¼</sup> *<sup>m</sup>*\_ *<sup>a</sup> Ra* ð Þ *<sup>T</sup>*ce <sup>þ</sup> <sup>273</sup>*:*<sup>15</sup>

the volume flow rate *V*\_ <sup>a</sup>*,* ci of the associated air [20] and is obtained from the

*m*\_ st*,* ci ¼ *x*ci *m*\_ st*,*<sup>t</sup> (1)

*<sup>V</sup>*\_ st*,* ci <sup>¼</sup> *<sup>V</sup>*\_ <sup>a</sup>*,* ci <sup>¼</sup> *<sup>m</sup>*\_ st*,* ci *<sup>v</sup>*s*,* ci (2)

*pc,t* ¼ *p*s*,* ci þ *p*a*,* ci (5)

*p*a*,* ce ¼ *pc,t* � *p*s*,* ce (6)

(3)

(4)

(7)

$$\delta = \frac{\dot{m}\_{\text{st, vp}}}{\dot{m}\_{\text{st, t}}} = \frac{\beta \, R\_d \left( T\_{\text{vpi}} + 273.15 \right)}{p\_{\text{a, vpi}} v\_{\text{s, vpi}}} \tag{12}$$

Regarding the VCRS, the *p-h* diagram of its cycle is illustrated in **Figure 4**. The numerals of **Figure 4** correspond to the points 1–10 given in **Figure 3**. It is to be considered here that the refrigerant condenser is cooled exactly as it is conducted with the steam plant condenser. Consequently, it is assumed here that the refrigerant leaving the refrigerant condenser has a temperature equal to that of the condensate in the steam plant condenser (i.e.,*T*<sup>5</sup> = *T*ce). Considering this fact and

**Figure 4.** p*-*h *diagram of the VCRS cycle of the studied refrigeration system.*

knowing the subcooling Δ*T*rc,sub of the refrigerant condenser, the pressure of the refrigerant in the condenser (e) can be fixed. The evaporator temperature *T*<sup>9</sup> = *T*<sup>10</sup> is defined according to the temperature required by the chilled water at inlet to the air cooler of the steam condenser. *T*<sup>9</sup> as well as *T*<sup>10</sup> is Δ*T*<sup>e</sup> less than the temperature *T*cw,aci (i.e.,*T*<sup>9</sup> = *T*<sup>10</sup> = *T*cw,aci � Δ*T*e) of the chilled water entering the steam condenser air cooler. Hence, the pressure of the refrigerant in the evaporator is the saturated one corresponding to the temperature *T*9/*T*10. Knowing the refrigerant pressures in the evaporator (a) and condenser (e), the adiabatic efficiencies *η*rco,I and *η*rco,II and mechanical efficiencies *η*m,rco,I and *η*m,rco,II of the compressor I (c) and II (d), respectively, and the effectiveness *ε*LLSL of the LLSL-HE, the states of the different points of the VCRS cycle can be determined as explained in any refrigeration text book (e.g., [21]).

From which it follows that:

*DOI: http://dx.doi.org/10.5772/intechopen.83787*

(*m*\_ <sup>r</sup>*,*I*=m*\_ st*,*t) is worked out as:

It follows from Eq. (18) that:

flow rate of the steam turbine is given by:

*<sup>ξ</sup>II* <sup>¼</sup> *<sup>m</sup>*\_ <sup>r</sup>*,*II *m*\_ st*,*<sup>t</sup>

*<sup>w</sup>*rco*,*<sup>I</sup> <sup>¼</sup> *<sup>ξ</sup><sup>I</sup>*

*<sup>w</sup>*rco*,*II <sup>¼</sup> *<sup>ξ</sup>II*

*η*m*,* co*,*<sup>I</sup>

*η*m*,*rco*,*II

¼ *ξIxξII* ¼ *ζ*

*<sup>ξ</sup><sup>t</sup>* <sup>¼</sup> *<sup>m</sup>*\_ <sup>r</sup>*,*<sup>t</sup> *m*\_ st*,*<sup>t</sup>

cycle are given as:

**231**

(**Figure 3**) yields:

*m*\_ <sup>r</sup>*,*<sup>I</sup> *m*\_ cw

*<sup>ξ</sup><sup>I</sup>* <sup>¼</sup> *<sup>m</sup>*\_ <sup>r</sup>*,*<sup>I</sup> *m*\_ st*,*<sup>t</sup>

<sup>¼</sup> *Cw* ð Þ *<sup>T</sup>*cw*,* ace � *<sup>T</sup>*cw*,* aci ð Þ *h*<sup>10</sup> � *h*<sup>9</sup>

<sup>¼</sup> *<sup>ζ</sup> Cw* ð Þ *<sup>T</sup>*cw*,* ace � *<sup>T</sup>*cw*,* aci ð Þ *h*<sup>10</sup> � *h*<sup>9</sup>

*m*\_ <sup>r</sup>*,*II *h*<sup>6</sup> þ *m*\_ <sup>r</sup>*,*<sup>I</sup> *h*<sup>2</sup> ¼ *m*\_ <sup>r</sup>*,*<sup>I</sup> *h*<sup>7</sup> þ *m*\_ <sup>r</sup>*,*II *h*<sup>3</sup> (18)

Multiplying both sides of Eq. (16) by the mass ratio *m*\_ *cw=m*\_ st*,*t, the mass ratio *ξ<sup>I</sup>*

*Air Cooling in Steam Plant Condenser Using Refrigeration System for Improving Vacuum Pump…*

The mass ratio ζ is obtained from Eq. (14). A heat balance of the flash chamber

<sup>¼</sup> ð Þ *<sup>h</sup>*<sup>2</sup> � *<sup>h</sup>*<sup>7</sup> ð Þ *h*<sup>3</sup> � *h*<sup>6</sup>

Multiplying both sides of Eq. (19) by *m*\_ *r,II=m*\_ *r,I*, it follows that the mass ratio *ξII* (*m*\_ *r,II=m*\_ *st,t*) of the refrigerant flow rate through the compressor II to the steam

¼ *ξ<sup>I</sup>*

*Cw* ð Þ *t*cw*,* ace � *t*cw*,* aci ð Þ *h*<sup>10</sup> � *h*<sup>9</sup>

> *<sup>ξ</sup><sup>t</sup>* <sup>¼</sup> *<sup>m</sup>*\_ <sup>r</sup>*,*<sup>t</sup> *m*\_ st*,*<sup>t</sup>

The characteristic parameters describing the performance of the refrigeration

ð Þ¼ *h*<sup>2</sup> � *h*<sup>1</sup>

ð Þ¼ *h*<sup>4</sup> � *h*<sup>3</sup>

COP <sup>¼</sup> *<sup>ξ</sup>II*ð Þ *<sup>h</sup>*<sup>10</sup> � *<sup>h</sup>*<sup>9</sup> *<sup>=</sup> <sup>ξ</sup>I*ð Þ *<sup>h</sup>*<sup>2</sup> *<sup>s</sup>* � *<sup>h</sup>*<sup>1</sup> *<sup>=</sup>η*co*,*<sup>I</sup> *<sup>η</sup>*m*,* co*,*<sup>I</sup> <sup>þ</sup> *<sup>ξ</sup>II*ð Þ *<sup>h</sup>*4*<sup>s</sup>* � *<sup>h</sup>*<sup>3</sup> *<sup>=</sup>η*co*,*<sup>I</sup> *<sup>η</sup>*m*,* co*,*II (28)

The hybrid system proposed in the current work can lead to two benefits, the first benefit is a decrease in the mass flow rate of steam lost in venting the air from the SPC, and the second one is a reduction in mass flow rate of air and steam mixture drawn by the vacuum pump and hence the pump power is lowered.

*m*\_ <sup>r</sup>*,*II *m*\_ <sup>r</sup>*,*<sup>I</sup>

¼ *ξ<sup>I</sup>*

ð Þ *h*<sup>2</sup> � *h*<sup>7</sup> ð Þ *h*<sup>3</sup> � *h*<sup>6</sup>

<sup>1</sup> <sup>þ</sup> ð Þ *<sup>h</sup>*<sup>2</sup> � *<sup>h</sup>*<sup>7</sup> ð Þ *h*<sup>3</sup> � *h*<sup>6</sup>

*q*rc ¼ *ξII*ð Þ *h*<sup>4</sup> � *h*<sup>5</sup> (23)

*w*rco*,*<sup>t</sup> ¼ ð Þ *w*rco*,*<sup>I</sup> þ *w*rco*,*II (26) *qe* ¼ *ξII* ð Þ *h*<sup>10</sup> � *h*<sup>9</sup> (27)

*ξI η*m*,*rco*,*<sup>I</sup> *η*i*,*rco*,*<sup>I</sup>

*ξII η*m*,*rco*,*I I*η*i*,*rco*,*II

(21)

ð Þ *h*2*<sup>s</sup>* � *h*<sup>1</sup> (24)

ð Þ *h*4*<sup>s</sup>* � *h*<sup>3</sup> (25)

*m*\_ *r,II m*\_ *r,I*

<sup>¼</sup> *<sup>m</sup>*\_ <sup>r</sup>*,*II *m*\_ <sup>r</sup>*,*<sup>I</sup> *x m*\_ <sup>r</sup>*,*<sup>I</sup> *m*\_ st*,*<sup>t</sup>

From Eqs. (17) and (20), the mass ratio *ξ<sup>t</sup>* can be found as:

(16)

(17)

(19)

(20)

(22)

For obtaining the value of the mass ratio ζ *m*\_ cw*=m*\_ ð Þ st*,*<sup>t</sup> of the chilled water flow rate through the air cooling segment and steam flow rate crossing the turbine, **Figure 5** shows the mass flow rates of air mixture and chilled water, and their temperatures through this segment. An energy balance for the air cooler leads to the following equation:

$$\dot{m}\_{\text{a}}c\_{\text{p,a}}\left(T\_{\text{ce}} - T\_{\text{vpi}}\right) + \left(\dot{m}\_{\text{st, aci}} - \dot{m}\_{\text{st, vpi}}\right)LH\left[\text{at saturation pressure} p\_{\text{s, vpi}}\right] \tag{13}$$

$$= \dot{m}\_{\text{cw}}C\_{\text{w}}\left(T\_{\text{cw, ace}} - T\_{\text{cw, aci}}\right)$$

It is to be noticed here that the sensible heat of the condensed steam in the air cooler was neglected as it is relatively very small, and *m*\_ st*,* aci is equal to *m*\_ st*,,* ce.

Solving Eq. (13) to get *m*\_ cw*=m*\_ *<sup>a</sup>* and multiplying both sides of the resulted equation by *m*\_ <sup>a</sup>*=m*\_ st*,*t, the ratio *ζ* (*m*\_ cw*=m*\_ st*,*<sup>t</sup> ) is obtained as:

$$\zeta = \frac{\dot{m}\_{\text{cw}}}{\dot{m}\_{\text{st,t}}} = \frac{\beta c\_{\text{p,a}} \left(T\_{\text{ce}} - T\_{\text{vpi}}\right) + (\chi - \delta) \ge LH \left[\text{at saturation pressure } p\_{\text{s,vpi}}\right]}{c\_w \left(T\_{\text{cw,acc}} - T\_{\text{cw,aci}}\right)} \tag{14}$$

For determining the mass ratio *m*\_ <sup>r</sup>*,*I*=m*\_ cw of the refrigerant and cooling water, a heat balance is performed for the evaporator/water HE (a), which yields to:

$$
\dot{m}\_{\rm r,1}(h\_{10} - h\_{9}) = \dot{m}\_{\rm cw} C\_{\rm w} (T\_{\rm cw,acc} - T\_{\rm cw,aci}) \tag{15}
$$

**Figure 5.** *Mass flow and temperature of air, steam, and chilled water through the air-cooling segment.*

*Air Cooling in Steam Plant Condenser Using Refrigeration System for Improving Vacuum Pump… DOI: http://dx.doi.org/10.5772/intechopen.83787*

From which it follows that:

knowing the subcooling Δ*T*rc,sub of the refrigerant condenser, the pressure of the refrigerant in the condenser (e) can be fixed. The evaporator temperature *T*<sup>9</sup> = *T*<sup>10</sup> is defined according to the temperature required by the chilled water at inlet to the air cooler of the steam condenser. *T*<sup>9</sup> as well as *T*<sup>10</sup> is Δ*T*<sup>e</sup> less than the temperature

For obtaining the value of the mass ratio ζ *m*\_ cw*=m*\_ ð Þ st*,*<sup>t</sup> of the chilled water flow

It is to be noticed here that the sensible heat of the condensed steam in the air cooler was neglected as it is relatively very small, and *m*\_ st*,* aci is equal to *m*\_ st*,,* ce. Solving Eq. (13) to get *m*\_ cw*=m*\_ *<sup>a</sup>* and multiplying both sides of the resulted

� � <sup>þ</sup> ð Þ *<sup>γ</sup>* � *<sup>δ</sup> xLH at saturation pressure p*s*,*vpi

*m*\_ <sup>r</sup>*,*Ið Þ¼ *h*<sup>10</sup> � *h*<sup>9</sup> *m*\_ cw *Cw*ð Þ *T*cw*,* ace � *T*cw*,* aci (15)

*cw* ð Þ *T*cw*,* ace � *T*cw*,* ac*<sup>i</sup>*

For determining the mass ratio *m*\_ <sup>r</sup>*,*I*=m*\_ cw of the refrigerant and cooling water, a

heat balance is performed for the evaporator/water HE (a), which yields to:

*Mass flow and temperature of air, steam, and chilled water through the air-cooling segment.*

� �*LH at saturation pressure p*s*,*vpi

h i

h i

(13)

(14)

rate through the air cooling segment and steam flow rate crossing the turbine, **Figure 5** shows the mass flow rates of air mixture and chilled water, and their temperatures through this segment. An energy balance for the air cooler leads to the

¼ *m*\_ cw *Cw* ð Þ *T*cw*,* ac*<sup>e</sup>* � *T*cw*,* aci

*T*cw,aci (i.e.,*T*<sup>9</sup> = *T*<sup>10</sup> = *T*cw,aci � Δ*T*e) of the chilled water entering the steam condenser air cooler. Hence, the pressure of the refrigerant in the evaporator is the saturated one corresponding to the temperature *T*9/*T*10. Knowing the refrigerant pressures in the evaporator (a) and condenser (e), the adiabatic efficiencies *η*rco,I and *η*rco,II and mechanical efficiencies *η*m,rco,I and *η*m,rco,II of the compressor I (c) and II (d), respectively, and the effectiveness *ε*LLSL of the LLSL-HE, the states of the different points of the VCRS cycle can be determined as explained in any

refrigeration text book (e.g., [21]).

*Low-temperature Technologies*

� � <sup>þ</sup> *<sup>m</sup>*\_ st*,* ac*<sup>i</sup>* � *<sup>m</sup>*\_ st*,*vp*<sup>i</sup>*

*β c*p*,* <sup>a</sup> *T*ce � *T*vpi

equation by *m*\_ <sup>a</sup>*=m*\_ st*,*t, the ratio *ζ* (*m*\_ cw*=m*\_ st*,*<sup>t</sup> ) is obtained as:

following equation:

*<sup>ζ</sup>* <sup>¼</sup> *<sup>m</sup>*\_ cw *m*\_ st*,*<sup>t</sup> ¼

**Figure 5.**

**230**

*m*\_ *<sup>a</sup> c*p*,* <sup>a</sup> *T*ce � *T*vpi

$$\frac{\dot{m}\_{\text{r,l}}}{\dot{m}\_{\text{cw}}} = \frac{C\_w \left(T\_{\text{cw,acc}} - T\_{\text{cw,aci}}\right)}{\left(h\_{10} - h\_9\right)}\tag{16}$$

Multiplying both sides of Eq. (16) by the mass ratio *m*\_ *cw=m*\_ st*,*t, the mass ratio *ξ<sup>I</sup>* (*m*\_ <sup>r</sup>*,*I*=m*\_ st*,*t) is worked out as:

$$\xi\_{I} = \frac{\dot{m}\_{\text{r,l}}}{\dot{m}\_{\text{st,t}}} = \zeta \frac{\mathcal{C}\_{w} \left(T\_{\text{cw,acc}} - T\_{\text{cw,aci}}\right)}{\left(h\_{10} - h\_{9}\right)} \tag{17}$$

The mass ratio ζ is obtained from Eq. (14). A heat balance of the flash chamber (**Figure 3**) yields:

$$
\dot{m}\_{\rm r,II} h\_6 + \dot{m}\_{\rm r,I} h\_2 = \dot{m}\_{\rm r,I} h\_7 + \dot{m}\_{\rm r,II} h\_3 \tag{18}
$$

It follows from Eq. (18) that:

$$\frac{\dot{m}\_{r,II}}{\dot{m}\_{r,I}} = \frac{(h\_2 - h\_7)}{(h\_3 - h\_6)}\tag{19}$$

Multiplying both sides of Eq. (19) by *m*\_ *r,II=m*\_ *r,I*, it follows that the mass ratio *ξII* (*m*\_ *r,II=m*\_ *st,t*) of the refrigerant flow rate through the compressor II to the steam flow rate of the steam turbine is given by:

$$\xi\_{\rm II} = \frac{\dot{m}\_{\rm r, II}}{\dot{m}\_{\rm st, t}} = \frac{\dot{m}\_{\rm r, II}}{\dot{m}\_{\rm r, I}} \propto \frac{\dot{m}\_{\rm r, I}}{\dot{m}\_{\rm st, t}} = \xi\_{I} \frac{\dot{m}\_{\rm r, II}}{\dot{m}\_{\rm r, I}} = \quad \xi\_{I} \frac{(h\_{2} - h\_{7})}{(h\_{3} - h\_{6})} \tag{20}$$

From Eqs. (17) and (20), the mass ratio *ξ<sup>t</sup>* can be found as:

$$\xi\_{\rm t} = \frac{\dot{m}\_{\rm r,t}}{\dot{m}\_{\rm st,t}} = \xi\_I \chi \xi\_{II} = \zeta \frac{\mathcal{C}\_w \left( t\_{\rm cw,acc} - t\_{\rm cw,acc} \right)}{\left( h\_{10} - h\_{9} \right)} \left[ 1 + \frac{\left( h\_2 - h\_7 \right)}{\left( h\_3 - h\_6 \right)} \right] \tag{21}$$

$$
\xi\_t = \frac{\dot{m}\_{\text{r,t}}}{\dot{m}\_{\text{st,t}}} \tag{22}
$$

The characteristic parameters describing the performance of the refrigeration cycle are given as:

$$q\_{\rm rc} = \xi\_{\rm II} (h\_4 - h\_5) \tag{23}$$

$$\left(\omega\_{\text{rco,I}} = \frac{\xi\_I}{\eta\_{\text{m,co,I}}} \left(h\_2 - h\_1\right) = \frac{\xi\_I}{\eta\_{\text{m,rco,I}} \eta\_{\text{i,rco,I}}} \left(h\_{2s} - h\_1\right) \tag{24}$$

$$w\_{\rm rec, II} = \frac{\xi\_{\rm II}}{\eta\_{\rm m, reco, II}} \left( h\_4 - h\_3 \right) = \frac{\xi\_{\rm II}}{\eta\_{\rm m, reco, I} \ \eta\_{\rm i, reco, II}} \left( h\_{4s} - h\_3 \right) \tag{25}$$

$$
\boldsymbol{w}\_{\text{rco, t}} = (\boldsymbol{w}\_{\text{rco, I}} + \boldsymbol{w}\_{\text{rco, II}}) \tag{26}
$$

$$q\_{\epsilon} = \xi\_{II} \left( h\_{10} - h\_{9} \right) \tag{27}$$

$$\text{COP} = \xi\_{\text{II}} (h\_{10} - h\_9) / \left[ \xi\_{\text{I}} (h\_{2s} - h\_1) / \eta\_{\text{co,1}} \eta\_{\text{m,co,1}} + \xi\_{\text{II}} (h\_{4s} - h\_3) / \eta\_{\text{co,1}} \eta\_{\text{m,co,II}} \right] \tag{28}$$

The hybrid system proposed in the current work can lead to two benefits, the first benefit is a decrease in the mass flow rate of steam lost in venting the air from the SPC, and the second one is a reduction in mass flow rate of air and steam mixture drawn by the vacuum pump and hence the pump power is lowered.

However, a new energy consumption comes out, which is the total work (*w*rco,t) of the two compressors employed in the VCRS. To be capable to judge the goodness of the proposed hybrid system, both the energies used for venting the air from SPC and for operating the compressors of the refrigeration system should be determinable. The total work *w*rco,t of the two refrigerant compressors can be determined using Eqs. (24)–(26). As for the work consumed for venting process, there are some vacuum pumps that can be utilized for this function, among which centrifugal compressor is the most effective and efficient instrument for performing this task. It is selected here only for the sake of judgment of the hybrid system goodness. In venting the air and steam mixture out of the steam condenser without air cooling, the specific vacuum pump (compressor) work *w*vp,wac referred to each kilogram of steam flow through the steam turbine can be expressed by aid of any thermodynamics text book (e.g., [20]) as:

$$\mathbf{w}\_{vp, uac} = \frac{k\_m R\_m T\_{c\epsilon} (\beta + \gamma)}{(k\_m - 1)} \left[ \left( \frac{p\_{atm}}{p\_t} \right)^{\left(\frac{k\_m - 1}{k\_m}\right)} - 1 \right] \tag{29}$$

where *km* and *Rm* are the isentropic exponent and gas constant, respectively, of the air steam mixture. They are given by [20]:

$$\mathbf{k}\_m = \frac{\beta \mathbf{C}\_{p,a} + \chi \mathbf{C}\_{p,st}}{\beta \mathbf{C}\_{v,a} + \chi \mathbf{C}\_{v,st}} \tag{30}$$

$$R\_m = \frac{\beta R\_d + \chi R\_{st}}{\beta + \chi} \tag{31}$$

rate computed from the present model is displayed in **Figure 6**, which shows satisfactory agreement with the experimental data of Ref. [22] since the maximal

*Comparison of the predicted and experimental values of condensation rate for all the tests of Ref. [22].*

of a specific parameter is to be examined; it is handled as a variable.

[23], which is used for solving the equations of the analysis of Section 4.

The refrigerant of the refrigeration system is selected to be ammonia. The physical properties of air, water, steam, and ammonia needed for computation are predicted using the built-in functions of the commercial computing package EES

In **Figure 7**, the mass ratio *γ* is plotted versus the temperature *T*ci for values of Δ*T*ce of 1, 3, and 5°C. It is seen from **Figure 7** that *γ* runs linearly with very low rate with *T*ci. This can be explained as follows: since *β* is constant, the mass rate of steam condensed because cooling the air depends mainly on Δ*T*ce and it is very little dependent on *T*ci. Of course the condensed steam rate in the air cooler is a pit higher at higher *T*ci. For constant *β* and *T*ci, the amount of steam associated with the

The thermodynamic analysis developed in Section 4 for performance prediction of the combined system proposed in this work necessitates knowing some basic design and operational data, which is listed in **Table 2**. It is to be noticed here that the values of isentropic and mechanical efficiencies of the compressors involved in this study have been selected close to the practical values of compressors in use in industry [24]. The results presented hereafter are based on these data. All parameter values given in **Table 2** will be kept unchanged except for the case where the effect

discrepancy does not exceed 10%.

**Test Inlet humid air**

**Table 1.**

**Figure 6.**

**233**

**temperature** *Tha,in* **(°C)**

*DOI: http://dx.doi.org/10.5772/intechopen.83787*

*Experimental conditions from Ref. [22].*

**Velocity of humid air** *vha* **(m/s)**

 82.66 1.46 100 7.3 80.61 2.02 100 9.0 79.13 2.52 97.83 10 78.73 3.01 87.35 11.1 75.02 3.59 96.55 12.5

*Air Cooling in Steam Plant Condenser Using Refrigeration System for Improving Vacuum Pump…*

**Inlet relative humidity of humid air** *φ*

**Average cooling flux** *qc,av* **(kW/m<sup>2</sup>**

**)**

When the steam condenser is fitted with air cooler, the air extracting compressor work *w*vp is given by:

$$\mathbf{w}\_{vp,ac} = \frac{k\_m R\_m \, T\_{vpi} \left(\beta + \delta\right)}{\left(k\_m - 1\right) \, \eta\_{m,vp} \eta\_{i,vp}} \left[ \left(\frac{p\_{atm}}{p\_t}\right)^{\left(\frac{k\_m - 1}{k\_m}\right)} - 1 \right] \tag{32}$$

*km* and *Rm* are calculated in this case by aid of Eqs. (30) and (31), respectively, by replacing *γ* by *δ*.

The total specific work *wt* (*w*rco,t + *w*vp,ac) employed for cooling and driving out steam condenser air is calculated by summing up Eqs. (26) and (32).

#### **5. Results and discussion**

The thermodynamic analysis developed in Section 4 for predicting the condensation rate in the steam plant condenser due to air cooling is first validated with the experimental data of reference [22]. In this work, experiments were conducted in a 2-m-long square cross-sectional channel (0.34 m � 0.34 m) to study the heat and mass transfer in the condensation of water vapor from humid air. The air flowing inside the channel was cooled by cold water flowing outside and adjoining only one side (0.34 m � 2 m) of the channel. Experimental data were obtained from five tests at various operating conditions as shown in **Table 1**. The thermodynamic analysis in Section 4 was slightly modified to be adapted for using the data given in **Table 1** for computing the condensation rate. For solving the equations in this analysis and finding out the rate of condensation, the commercial computer package EES [23] was used. The thermal properties of the humid air at different conditions were found using the built-in functions available in the EES package. The condensation


*Air Cooling in Steam Plant Condenser Using Refrigeration System for Improving Vacuum Pump… DOI: http://dx.doi.org/10.5772/intechopen.83787*

#### **Table 1.**

However, a new energy consumption comes out, which is the total work (*w*rco,t) of the two compressors employed in the VCRS. To be capable to judge the goodness of the proposed hybrid system, both the energies used for venting the air from SPC and for operating the compressors of the refrigeration system should be determinable. The total work *w*rco,t of the two refrigerant compressors can be determined using Eqs. (24)–(26). As for the work consumed for venting process, there are some vacuum pumps that can be utilized for this function, among which centrifugal compressor is the most effective and efficient instrument for performing this task. It is selected here only for the sake of judgment of the hybrid system goodness. In venting the air and steam mixture out of the steam condenser without air cooling, the specific vacuum pump (compressor) work *w*vp,wac referred to each kilogram of steam flow through the steam turbine can be expressed by aid of any thermody-

namics text book (e.g., [20]) as:

*Low-temperature Technologies*

sor work *w*vp is given by:

by replacing *γ* by *δ*.

**232**

**5. Results and discussion**

<sup>w</sup>*vp,wac* <sup>¼</sup> *kmRm Tce* ð Þ *<sup>β</sup>* <sup>þ</sup> *<sup>γ</sup>*

<sup>w</sup>*vp,ac* <sup>¼</sup> *kmRm Tvpi*ð Þ *<sup>β</sup>* <sup>þ</sup> *<sup>δ</sup>*

ð Þ *km* � 1 *ηm, vpηi, vp*

steam condenser air is calculated by summing up Eqs. (26) and (32).

the air steam mixture. They are given by [20]:

ð Þ *km* � 1 *ηm, vpηi, vp*

where *km* and *Rm* are the isentropic exponent and gas constant, respectively, of

<sup>k</sup>*<sup>m</sup>* <sup>¼</sup> *<sup>β</sup>Cp,a* <sup>þ</sup> *<sup>γ</sup>Cp,st βCv,a* þ *γCv,st*

*Rm* <sup>¼</sup> *<sup>β</sup>Ra* <sup>þ</sup> *<sup>γ</sup> Rst β* þ *γ*

When the steam condenser is fitted with air cooler, the air extracting compres-

*km* and *Rm* are calculated in this case by aid of Eqs. (30) and (31), respectively,

The total specific work *wt* (*w*rco,t + *w*vp,ac) employed for cooling and driving out

The thermodynamic analysis developed in Section 4 for predicting the condensation rate in the steam plant condenser due to air cooling is first validated with the experimental data of reference [22]. In this work, experiments were conducted in a 2-m-long square cross-sectional channel (0.34 m � 0.34 m) to study the heat and mass transfer in the condensation of water vapor from humid air. The air flowing inside the channel was cooled by cold water flowing outside and adjoining only one side (0.34 m � 2 m) of the channel. Experimental data were obtained from five tests at various operating conditions as shown in **Table 1**. The thermodynamic analysis in Section 4 was slightly modified to be adapted for using the data given in **Table 1** for computing the condensation rate. For solving the equations in this analysis and finding out the rate of condensation, the commercial computer package EES [23] was used. The thermal properties of the humid air at different conditions were found using the built-in functions available in the EES package. The condensation

*patm pt* � � *km*�<sup>1</sup> *km* ð Þ

*patm pt* � � *km*�<sup>1</sup> *km* ð Þ

" #

" #

� 1

� 1

(29)

(30)

(31)

(32)

*Experimental conditions from Ref. [22].*

#### **Figure 6.**

*Comparison of the predicted and experimental values of condensation rate for all the tests of Ref. [22].*

rate computed from the present model is displayed in **Figure 6**, which shows satisfactory agreement with the experimental data of Ref. [22] since the maximal discrepancy does not exceed 10%.

The thermodynamic analysis developed in Section 4 for performance prediction of the combined system proposed in this work necessitates knowing some basic design and operational data, which is listed in **Table 2**. It is to be noticed here that the values of isentropic and mechanical efficiencies of the compressors involved in this study have been selected close to the practical values of compressors in use in industry [24]. The results presented hereafter are based on these data. All parameter values given in **Table 2** will be kept unchanged except for the case where the effect of a specific parameter is to be examined; it is handled as a variable.

The refrigerant of the refrigeration system is selected to be ammonia. The physical properties of air, water, steam, and ammonia needed for computation are predicted using the built-in functions of the commercial computing package EES [23], which is used for solving the equations of the analysis of Section 4.

In **Figure 7**, the mass ratio *γ* is plotted versus the temperature *T*ci for values of Δ*T*ce of 1, 3, and 5°C. It is seen from **Figure 7** that *γ* runs linearly with very low rate with *T*ci. This can be explained as follows: since *β* is constant, the mass rate of steam condensed because cooling the air depends mainly on Δ*T*ce and it is very little dependent on *T*ci. Of course the condensed steam rate in the air cooler is a pit higher at higher *T*ci. For constant *β* and *T*ci, the amount of steam associated with the


#### **Table 2.**

*Basic design and operational data of the proposed combined steam plant condenser and refrigeration system.*

and becomes immaterially small for values of Δ*T*vpi greater than 12°C. This is brought about due to the large drop in steam content in the air and likewise the rate of steam condensed as the temperature *T*vpi falls down. It is also seen from **Figure 8** that *T*ci has almost negligible effect on *δ* as the amount of steam mixed with the condenser air and in turn the rate of condensed steam for constant *β* and Δ*T*vpi are

*Dependence of the mass of steam associated with air on the air temperature at vacuum pump entrance. ———,*

*Air Cooling in Steam Plant Condenser Using Refrigeration System for Improving Vacuum Pump…*

**Figure 9** illustrates the saving percentage (*γ δ*) 100/*γ* in the steam amounts to be condensed in the air cooler and not sucked by the vacuum pump as steam. It is clear from **Figure 9** that this saving has a reversed trend to that of the mass ratio *δ*, it is equal to zero at Δ*T*vpi = 0, and it increases steeply with Δ*T*vpi. The rate of increase in this saving with Δ*T*vpi falls increasingly with the rise in Δ*T*vpi where it

*Saving percentage in steam mass associated with air when using air cooler. ———,*T*ci = 20°C; ———,*

almost invariable with *T*ci.

**Figure 8.**

**Figure 9.**

**235**

T*ci = 30°C; ………* T*ci = 40°C.*

becomes inconsiderably small at Δ*T*vpi of 12°C.

T*ci = 20°C; ———,* T*ci = 30°C; ………,* T*ci = 40°C.*

*DOI: http://dx.doi.org/10.5772/intechopen.83787*

**Figure 7.** *Effect of condensate temperature on the extracted steam mass rate by the vacuum pump without air cooler. ———, Δ*T*ce = 1°C; ———, Δ*T*ce = 3°C; ………, Δ*T*ce = 5°C.*

condenser air and, in turn, the rate of condensed steam decrease progressively with Δ*T*ce. This accounts for the remarkable drop in *γ* with an increase in Δ*T*ce as shown in **Figure 7**. In contrast, the amount of steam associated with the condenser air and consecutively the rate of condensed steam for constant *β* and Δ*T*ce are almost unvarying with *T*ci. This explains the very low rate of increase in *γ* with rising *T*ci.

It is worth noting here that in **Figures 8–14**, which will be displayed in this section, the small values of temperature difference Δ*T*vpi close to zero represent the case in which there is virtually no air cooler is employed. These values are not practical as the refrigeration system will be useless. Yet these values are included in these images just for illumination. In **Figure 8**, the mass ratio *δ* is drawn against the temperature difference Δ*T*vpi for temperature *T*ci of 20, 30, and 40°C. It is seen from **Figure 8** that *δ* declines with an increase in Δ*T*vpi where the rate of declination is relatively high at small values of Δ*T*vpi and it decreases progressively with Δ*T*vpi

*Air Cooling in Steam Plant Condenser Using Refrigeration System for Improving Vacuum Pump… DOI: http://dx.doi.org/10.5772/intechopen.83787*

#### **Figure 8.**

*Dependence of the mass of steam associated with air on the air temperature at vacuum pump entrance. ———,* T*ci = 20°C; ———,* T*ci = 30°C; ………,* T*ci = 40°C.*

and becomes immaterially small for values of Δ*T*vpi greater than 12°C. This is brought about due to the large drop in steam content in the air and likewise the rate of steam condensed as the temperature *T*vpi falls down. It is also seen from **Figure 8** that *T*ci has almost negligible effect on *δ* as the amount of steam mixed with the condenser air and in turn the rate of condensed steam for constant *β* and Δ*T*vpi are almost invariable with *T*ci.

**Figure 9** illustrates the saving percentage (*γ δ*) 100/*γ* in the steam amounts to be condensed in the air cooler and not sucked by the vacuum pump as steam. It is clear from **Figure 9** that this saving has a reversed trend to that of the mass ratio *δ*, it is equal to zero at Δ*T*vpi = 0, and it increases steeply with Δ*T*vpi. The rate of increase in this saving with Δ*T*vpi falls increasingly with the rise in Δ*T*vpi where it becomes inconsiderably small at Δ*T*vpi of 12°C.

#### **Figure 9.**

*Saving percentage in steam mass associated with air when using air cooler. ———,*T*ci = 20°C; ———,* T*ci = 30°C; ………* T*ci = 40°C.*

condenser air and, in turn, the rate of condensed steam decrease progressively with Δ*T*ce. This accounts for the remarkable drop in *γ* with an increase in Δ*T*ce as shown in **Figure 7**. In contrast, the amount of steam associated with the condenser air and consecutively the rate of condensed steam for constant *β* and Δ*T*ce are almost unvarying with *T*ci. This explains the very low rate of increase in *γ* with rising *T*ci. It is worth noting here that in **Figures 8–14**, which will be displayed in this section, the small values of temperature difference Δ*T*vpi close to zero represent the case in which there is virtually no air cooler is employed. These values are not practical as the refrigeration system will be useless. Yet these values are included in these images just for illumination. In **Figure 8**, the mass ratio *δ* is drawn against the temperature difference Δ*T*vpi for temperature *T*ci of 20, 30, and 40°C. It is seen from **Figure 8** that *δ* declines with an increase in Δ*T*vpi where the rate of declination is relatively high at small values of Δ*T*vpi and it decreases progressively with Δ*T*vpi

*Effect of condensate temperature on the extracted steam mass rate by the vacuum pump without air cooler.*

*———, Δ*T*ce = 1°C; ———, Δ*T*ce = 3°C; ………, Δ*T*ce = 5°C.*

**Parameter Value** Mass ratio (*β*) 0.0003 Compressor isentropic efficiency (*η*i,rco,I, *η*i,rco,II, *η*i,vp) 0.85 Compressor mechanical efficiency (*η*m,rco,I, *η*m,rco,II, *η*m,vp) 0.75 Dryness fraction of steam entering the SPC (*x*ci) 0.9 Effectiveness of the liquid suction HE (*ε*LLSL) 0.8 Temperature difference (*T*ci *T5*), °C 0 Temperature difference (*T*cw,ace *T*cw,aci), °C 4 Temperature difference (*T*cw,aci *T*10), °C 4 Temperature difference (*T*cw,ace *T*vpi), °C 4 Temperature difference Δ*T*ce, °C 3 Subcooling of the refrigerant condenser (Δ*T*rc,sub), °C 3

*Basic design and operational data of the proposed combined steam plant condenser and refrigeration system.*

**Table 2.**

*Low-temperature Technologies*

**Figure 7.**

**234**

It follows from **Figures 8** and **9** that the amount of steam to be condensed in the air cooler is relatively high at small values of Δ*T*vpi and the rate of increase in this amount falls progressively with Δ*T*vpi. Therefore, the amount of the cooling chilled water and in turn the refrigerant needed for chilling the cooling water takes the same trend of the percentage saving (*γ δ*) 100/*γ* (see **Figure 9**). **Figures 10** and **11** show the mass ratios *ζ* and *ξt*, respectively, as a function of Δ*T*vpi.

refrigeration system and the increasing temperature difference between the refrigerant condenser and the evaporator. The temperature *T*ci has almost a negligible effect on COP as the temperature difference between refrigerant condenser

lines for the sake of comparison. It can be seen from **Figure 13** that *w*vp,wac

increase in *w*rco,t is almost independent of the temperature *T*ci.

**Figure 12.**

**237**

The specific works *wvp,wac, wrco,t, wvp,ac* as well as *wt* are plotted in the diagrams of **Figure 13** versus Δ*T*vpi for temperature *T*ci of 20, 30, and 40°C. Although *w*vp,wac is independent of Δ*T*vpi, it is represented on the diagrams of **Figure 13** as horizontal

*Air Cooling in Steam Plant Condenser Using Refrigeration System for Improving Vacuum Pump…*

decreases with an increase in *T*ci, which is caused mainly due to the drop in pressure ratio of the vacuum pump. The specific work *w*vp,ac is reduced steeply with Δ*T*vpi until a value of Δ*T*vpi around 12°C; then, the rate of decrease in *w*vp,ac diminishes remarkably. This can be interpreted as follows: on the one hand, at low temperature difference Δ*T*vpi, the amount of steam mixed with air is relatively high as can be seen from **Figures 8** and **9**, which results in relatively high mass rate of the mixture of air and water vapor flowing through the vacuum pump, and therefore, greater pump work *w*vp,ac is obtained. As Δ*T*vpi is raised, the amount of steam flowing with air dwindles and so the mass flow rate through the pump declines, which gives rise to decreasing the pump work *w*vp,ac. On the other hand, the pressure ratio through the vacuum pump is raised with Δ*T*vpi and hence the work *w*vp,ac is increased. However, the increase in *w*vp,ac is relatively small at low values of Δ*T*vpi compared to the work decrease due to the drop in pump mass flow rate. Therefore, the pump work *w*vp,ac falls off with relatively high rate, as Δ*T*vpi grows. As the mass flow induced by the pump declines and the pressure ratio through the pump grows with increasing Δ*T*vpi, the effect of the former parameter diminishes, while the effect of the latter parameter grows up and the net result is a considerable drop in the rate of decrease in *w*vp,ac. The specific work *w*rco,t rises almost linearly with Δ*T*vpi. This is attributed mainly to the declination of the refrigeration system COP (see **Figure 12**). The rate of

The saving percentage (*w*vp,wac *wt*) 100/*w*vp,wac in work by using refrigera-

*Effect of the air temperature at vacuum pump entrance on coefficient of performance of the refrigeration system.*

*———,* T*ci = 20°C; ———,* T*ci = 30°C; ………,* T*ci = 40°C.*

tion system for cooling the air contained in the steam condenser is plotted in **Figure 14** versus Δ*T*vpi for *T*ci of 20, 30, and 40°C. It is seen from **Figures 13** and **14**

and evaporator alters with Δ*T*vpi and not with *T*ci.

*DOI: http://dx.doi.org/10.5772/intechopen.83787*

In **Figure 12**, the coefficient of performance COP of the refrigeration system is plotted versus the temperature difference Δ*T*vpi for *T*ci of 20, 30, and 40°C. **Figure 12** discloses distinctly that COP decreases sharply with Δ*T*vpi. This is ascribed mainly to the falling value of the evaporator temperature of the

**Figure 10.**

*Relationship between the mass of chilled cooling water required for steam condenser air cooler and the air temperature at vacuum pump entrance. ———,* T*ci = 20°C; ———,* T*ci = 30°C; ………,* T*ci = 40°C.*

#### **Figure 11.**

*Effect of the air temperature at vacuum pump entrance on refrigerant mass rate when using air cooler. ———,* T*ci = 20°C; ———,* T*ci = 30°C; ………,* T*ci = 40°C.*

*Air Cooling in Steam Plant Condenser Using Refrigeration System for Improving Vacuum Pump… DOI: http://dx.doi.org/10.5772/intechopen.83787*

refrigeration system and the increasing temperature difference between the refrigerant condenser and the evaporator. The temperature *T*ci has almost a negligible effect on COP as the temperature difference between refrigerant condenser and evaporator alters with Δ*T*vpi and not with *T*ci.

The specific works *wvp,wac, wrco,t, wvp,ac* as well as *wt* are plotted in the diagrams of **Figure 13** versus Δ*T*vpi for temperature *T*ci of 20, 30, and 40°C. Although *w*vp,wac is independent of Δ*T*vpi, it is represented on the diagrams of **Figure 13** as horizontal lines for the sake of comparison. It can be seen from **Figure 13** that *w*vp,wac decreases with an increase in *T*ci, which is caused mainly due to the drop in pressure ratio of the vacuum pump. The specific work *w*vp,ac is reduced steeply with Δ*T*vpi until a value of Δ*T*vpi around 12°C; then, the rate of decrease in *w*vp,ac diminishes remarkably. This can be interpreted as follows: on the one hand, at low temperature difference Δ*T*vpi, the amount of steam mixed with air is relatively high as can be seen from **Figures 8** and **9**, which results in relatively high mass rate of the mixture of air and water vapor flowing through the vacuum pump, and therefore, greater pump work *w*vp,ac is obtained. As Δ*T*vpi is raised, the amount of steam flowing with air dwindles and so the mass flow rate through the pump declines, which gives rise to decreasing the pump work *w*vp,ac. On the other hand, the pressure ratio through the vacuum pump is raised with Δ*T*vpi and hence the work *w*vp,ac is increased. However, the increase in *w*vp,ac is relatively small at low values of Δ*T*vpi compared to the work decrease due to the drop in pump mass flow rate. Therefore, the pump work *w*vp,ac falls off with relatively high rate, as Δ*T*vpi grows. As the mass flow induced by the pump declines and the pressure ratio through the pump grows with increasing Δ*T*vpi, the effect of the former parameter diminishes, while the effect of the latter parameter grows up and the net result is a considerable drop in the rate of decrease in *w*vp,ac. The specific work *w*rco,t rises almost linearly with Δ*T*vpi. This is attributed mainly to the declination of the refrigeration system COP (see **Figure 12**). The rate of increase in *w*rco,t is almost independent of the temperature *T*ci.

The saving percentage (*w*vp,wac *wt*) 100/*w*vp,wac in work by using refrigeration system for cooling the air contained in the steam condenser is plotted in **Figure 14** versus Δ*T*vpi for *T*ci of 20, 30, and 40°C. It is seen from **Figures 13** and **14**

**Figure 12.** *Effect of the air temperature at vacuum pump entrance on coefficient of performance of the refrigeration system. ———,* T*ci = 20°C; ———,* T*ci = 30°C; ………,* T*ci = 40°C.*

It follows from **Figures 8** and **9** that the amount of steam to be condensed in the air cooler is relatively high at small values of Δ*T*vpi and the rate of increase in this amount falls progressively with Δ*T*vpi. Therefore, the amount of the cooling chilled water and in turn the refrigerant needed for chilling the cooling water takes the same trend of the percentage saving (*γ δ*) 100/*γ* (see **Figure 9**). **Figures 10** and **11**

In **Figure 12**, the coefficient of performance COP of the refrigeration system is plotted versus the temperature difference Δ*T*vpi for *T*ci of 20, 30, and 40°C. **Figure 12** discloses distinctly that COP decreases sharply with Δ*T*vpi. This is ascribed mainly to the falling value of the evaporator temperature of the

*Relationship between the mass of chilled cooling water required for steam condenser air cooler and the air temperature at vacuum pump entrance. ———,* T*ci = 20°C; ———,* T*ci = 30°C; ………,* T*ci = 40°C.*

*Effect of the air temperature at vacuum pump entrance on refrigerant mass rate when using air cooler. ———,*

show the mass ratios *ζ* and *ξt*, respectively, as a function of Δ*T*vpi.

*Low-temperature Technologies*

**Figure 10.**

**Figure 11.**

**236**

T*ci = 20°C; ———,* T*ci = 30°C; ………,* T*ci = 40°C.*

It is to be mentioned here that the parameters *γ*, *δ*, *ζ*, *ξt*, *w*vp,wac, *w*vp,ac, *w*rco,t, and *wt* are displayed in **Figures 7, 8, 10, 11,** and **13** for the value for *β* of 0.0003. These parameters are directly proportional to the mass ratio *β*. This is explained as follows: the mass of steam mixed with each kilogram of air and condensed and in turn the amount of cooling normal/chilled water used for cooling a kilogram of air and condensing the steam as well as the amount of refrigerant utilized for chilling the cooling water are dependent only on the initial and final air temperatures of the cooling process. Therefore, the parameters mentioned above are directly propor-

*Air Cooling in Steam Plant Condenser Using Refrigeration System for Improving Vacuum Pump…*

tional to the mass ratio *β*. On the contrary to that, the saving percentages

and total work, respectively, are independent of *β*.

*DOI: http://dx.doi.org/10.5772/intechopen.83787*

**6. Conclusions**

condensate.

**Nomenclature**

**239**

and 90%, respectively.

(*γ δ*) 100/*γ* and (*wt we*) 100/*we* in the amount of steam to be condensed

The current work is concerned with the use of vapor compression refrigeration system (VCRS) for chilling cooling water used with the air cooler of the steam plant condenser (SPC). A thermodynamic analysis is developed for working out the performance of the hybrid system of VCRS and SPC. The results obtained using this analysis showed that subcooling of the SPC condensate can cause considerable reduction in steam rate associated with the air induced by the vacuum pump. However, this is possibly avoided as it represents heat loss in the condensate heat content, which should be compensated in the plant boiler. In addition, the results of this work led to drawing the following conclusions for condensate subcooling of 3°C, which represents a reasonable and practical subcooling of the condenser

1. Temperature reductions of the condenser air of 5, 10, and 15°C below the condensate temperature result in reducing steam rate lost in venting air from the condenser relative to the loss when using no air cooler, by around 69, 85,

2. The total work saving when using chilled water for cooling the air in the

lost in venting process amount to 87.7, 84, and 79.2%, respectively.

COP coefficient of performance of the refrigeration system *Cp* specific heat capacity at constant pressure (kJ/kg K)

range of 5–7 and maximally 3%, respectively.

*Cw* specific heat capacity of water (kJ/kg K)

*h* specific enthalpy (kJ/kg) *k* isentropic exponent

condenser air cooler from that in case of no air cooling is applied, has maximums of 38.5, 33.9, and 28.9% and occurs at temperature decrease below the condensate temperature of 12, 10, and 8°C when the temperature of steam admitted to the condenser is 20, 30, and 40°C, respectively. In these cases, the savings in steam

3. Selecting the reduction in condenser air temperature in the range of 4°C higher than that temperature reduction, at which the minimum total work occurs, is very advantageous where the saving in steam lost becomes fairly greater while the saving in total work is slightly lower than the minimum total works; in the

#### **Figure 13.**

*Specific work dependence on the air temperature at vacuum pump entrance.* **———,** wvp,wac*;* ———, wvp,ac*;* **………,** wrco,t*;* **—. —,** wt.

that the sum of the specific works *w*vp,ac and *w*rco,t (i.e., the total specific work *wt*) has a minimal value (maximum saving in the total work sum *wt*). This minimum value depends on the value of *T*ci and it is less than the corresponding *w*vp,wac according to the temperature *T*ci by 38.5, 33.9, and 28.9% at Δ*T*vpi of 12, 10, and 8°C for *T*ci of 20, 30, and 40°C, respectively. Also, it is seen from **Figures 13** and **14** that *wt* is maximally higher than the minimal value corresponding to *T*ci by 3% when Δ*T*vpi is 4°C higher than its value at which the minimal total specific work occurs. On the contrary, the saving in the steam lost increases depending on *T*ci in the range of 5–7%. Therefore, it is more advantageous to choose values for Δ*T*vpi higher than those at which the minimal total work occurs in the range of 4°C, as it results in fairly less lost steam rate to be drawn by the vacuum pump and inconsiderable increase in the total work. Higher values than 4°C cause inconsiderably small increase in saving the lost steam, but the total work is significantly raised.

#### **Figure 14.**

*Saving percent in specific work due to refrigeration cooling of steam condenser air cooler. ———,* T*ci = 20°C; ———,* T*ci = 30°C; ………* T*ci = 40°C.*

*Air Cooling in Steam Plant Condenser Using Refrigeration System for Improving Vacuum Pump… DOI: http://dx.doi.org/10.5772/intechopen.83787*

It is to be mentioned here that the parameters *γ*, *δ*, *ζ*, *ξt*, *w*vp,wac, *w*vp,ac, *w*rco,t, and *wt* are displayed in **Figures 7, 8, 10, 11,** and **13** for the value for *β* of 0.0003. These parameters are directly proportional to the mass ratio *β*. This is explained as follows: the mass of steam mixed with each kilogram of air and condensed and in turn the amount of cooling normal/chilled water used for cooling a kilogram of air and condensing the steam as well as the amount of refrigerant utilized for chilling the cooling water are dependent only on the initial and final air temperatures of the cooling process. Therefore, the parameters mentioned above are directly proportional to the mass ratio *β*. On the contrary to that, the saving percentages (*γ δ*) 100/*γ* and (*wt we*) 100/*we* in the amount of steam to be condensed and total work, respectively, are independent of *β*.
