R&ac lecture 24

Lesson
24
Expansion Devices
Version 1 ME, IIT Kharagpur 1

The specific objectives of this lecture are to:
1. Discuss the basic functions of expansion devices used in refrigeration systems
and their classification (Section 24.1)
2. Discuss the operating principle, concept of balance point, the effect of load
variation, selection of capillary tubes using analytical and graphical methods and
the advantages and disadvantages of capillary tubes (Section 24.2)
3. Explain the working principle of an automatic expansion valve, its performance
under varying loads and its applications (Section 24.3)
4. Present a simple analysis for fluid through orifices (Section 24.4)
5. Explain the working principle of a thermostatic expansion valve, its
performance under varying loads, variations available such as cross-charging,
external equalizer and limit charging, advantages and disadvantages of TEVs
(Section 24.5)
6. Explain the working principle of low-side and high-side float valves (Section
24.6)
7. Explain the working principle of an electronic expansion valve (Section 24.7)
8. Discuss briefly some of the practical problems with expansion devices (Section
24.8)
At the end of the lecture, the student should be able to:
1. Explain the basic functions of expansion devices in refrigeration systems
2. Explain the working principle and salient features of capillary tube, automatic
expansion valve, thermostatic expansion valve, float type expansion valve and
electronic expansion valve
3. Estimate the required length of capillary tubes using analytical and graphical
methods
4. Describe advantages, disadvantages and applications of different types of
expansion valves, and
5. Discuss some of the practical problems encountered in the operation of
various types of expansion devices in refrigeration systems
24.1. Introduction
An expansion device is another basic component of a refrigeration
system. The basic functions of an expansion device used in refrigeration systems
are to:
1. Reduce pressure from condenser pressure to evaporator pressure, and
2. Regulate the refrigerant flow from the high-pressure liquid line into the
evaporator at a rate equal to the evaporation rate in the evaporator
Under ideal conditions, the mass flow rate of refrigerant in the system should
be proportional to the cooling load. Sometimes, the product to be cooled is such

that a constant evaporator temperature has to be maintained. In other cases, it is
desirable that liquid refrigerant should not enter the compressor. In such a case,
the mass flow rate has to be controlled in such a manner that only superheated
vapour leaves the evaporator. Again, an ideal refrigeration system should have
the facility to control it in such a way that the energy requirement is minimum and
the required criterion of temperature and cooling load are satisfied. Some
additional controls to control the capacity of compressor and the space
temperature may be required in addition, so as to minimize the energy
consumption.
The expansion devices used in refrigeration systems can be divided into
fixed opening type or variable opening type. As the name implies, in fixed
opening type the flow area remains fixed, while in variable opening type the flow
area changes with changing mass flow rates. There are basically seven types of
refrigerant expansion devices. These are:
1. Hand (manual) expansion valves
2. Capillary Tubes
3. Orifice
4. Constant pressure or Automatic Expansion Valve (AEV)
5. Thermostatic Expansion Valve (TEV)
6. Float type Expansion Valve
a) High Side Float Valve
b) Low Side Float Valve
7. Electronic Expansion Valve
Of the above seven types, Capillary tube and orifice belong to the fixed
opening type, while the rest belong to the variable opening type. Of the above
seven types, the hand operated expansion valve is not used when an automatic
control is required. The orifice type expansion is used only in some special
applications. Hence these two are not discussed here.
24.2 Capillary Tube
A capillary tube is a long, narrow tube of constant diameter. The word
“capillary” is a misnomer since surface tension is not important in refrigeration
application of capillary tubes. Typical tube diameters of refrigerant capillary tubes
range from 0.5 mm to 3 mm and the length ranges from 1.0 m to 6 m.
The pressure reduction in a capillary tube occurs due to the following two
factors:
1. The refrigerant has to overcome the frictional resistance offered by tube
walls. This leads to some pressure drop, and

2. The liquid refrigerant flashes (evaporates) into mixture of liquid and vapour
as its pressure reduces. The density of vapour is less than that of the
liquid. Hence, the average density of refrigerant decreases as it flows in
the tube. The mass flow rate and tube diameter (hence area) being
constant, the velocity of refrigerant increases since = ρVA. The
increase in velocity or acceleration of the refrigerant also requires
pressure drop.
m
Several combinations of length and bore are available for the same mass flow
rate and pressure drop. However, once a capillary tube of some diameter and
length has been installed in a refrigeration system, the mass flow rate through it
will vary in such a manner that the total pressure drop through it matches with the
pressure difference between condenser and the evaporator. Its mass flow rate is
totally dependent upon the pressure difference across it; it cannot adjust itself to
variation of load effectively.
24.2.1. Balance Point of Compressor and Capillary Tube
The compressor and the capillary tube, under steady state must arrive at
some suction and discharge pressures, which allows the same mass flow rate
through the compressor and the capillary tube. This state is called the balance
point. Condenser and evaporator pressures are saturation pressures at
corresponding condenser and evaporator temperatures. Figure 24.1 shows the
variation of mass flow rate with evaporator pressure through the compressor and
the capillary tube for three values of condenser temperatures namely, 30, 40 and
50o
C.
The mass flow rate through the compressor decreases if the pressure ratio
increases since the volumetric efficiency of the compressor decreases with the
increase of pressure ratio. The pressure ratio increases when either the
evaporator pressure decreases or the condenser pressure increases. Hence, the
mass flow rate through the compressor decreases with increase in condenser
pressure and/or with decrease in evaporator pressure.

The pressure difference across the capillary tube is the driving force for
the refrigerant to flow through it, hence mass flow rate through the capillary tube
increases with increase in pressure difference across it. Thus the mass flow rate
through the capillary tube increases as the condenser pressure increases and/or
the evaporator pressure decreases. The variation of mass flow rate through
capillary tube is shown for three condenser temperatures, namely, 30, 40 and
50o
C in Figure 24.1. This is the opposite of the effect of pressures on the
compressor mass flow rate. Hence, for a given value of condenser pressure,
there is a definite value of evaporator pressure at which the mass flow rates
through the compressor and the evaporator are the same. This pressure is the
balance point that the system will acquire in steady state. Hence, for a given
condenser temperature, there is a definite value of evaporator temperature at
which the balance point will occur. Figure 28.1 shows a set of three balance
points A, B and C for the three condenser temperatures. These balance points
occur at evaporator temperatures of Te,A , Te,B and Te,C . It is observed that the
evaporator temperature at balance point increases with increase of condenser
temperature.
24.2.2. Effect Of load variation
The situation described above is in steady state. However, in practice the
refrigeration load may vary due to several reasons, such as the variation of
ambient temperatures etc. It is possible for the load to increase or decrease. This
variation of load affects the operation of compressor and capillary tube and
affects the balance point between them.
Te
TB
cB=30P
o
PC
Tc=50o
C
Tc=40 C
A
BT
TB
c
B B P
o
P
c=30o
C
Tc=40o
C
B=50P
o
PC
mr
Compressor
Capillary
Fig.24.1: Variation of refrigerant mass flow rate through compressor and capillary tube
with evaporator and condenser temperatures (A,B & C are the balance points)
Te,A Te,B Te,C

Increase in refrigeration Load:
If the refrigeration load increases, there is a tendency for the evaporator
temperature to increase due to higher rate of evaporation. This situation is shown
in Figure 24.2 for a condenser temperature of 40o
C. The balance point for design
load is shown by point B. As the load increases, the evaporator temperature rises
to C. At point C the mass flow rate through compressor is more than the mass
flow rate through the capillary tube. In such a situation, the compressor will draw
more refrigerant through the evaporator than the capillary tube can supply to it.
This will lead to starving of the evaporator. However, emptying of evaporator
cannot continue indefinitely. The system will take some corrective action since
changes are occurring in the condenser also. Since the capillary tube feeds less
refrigerant to the evaporator, the refrigerant accumulates in the condenser. The
accumulation of refrigerant in the condenser reduces the effective area of the
condenser that is available for heat transfer. The condenser heat transfer rate is
given by, Qc = U A ( Tc c c-T∞ ). If heat transfer coefficient U and Tc ∞ are constant,
then for same heat transfer rate a decrease in area Ac will lead to a higher
condenser temperature Tc. It is observed from Figure 24.1 that an increase in
condenser temperature leads to a decrease in compressor mass flow rate and an
increase in capillary mass flow rate. Hence, the system will find a new balance
point at higher condenser temperature.
The second possibility is that at lower evaporator mass flow rate, the
Reynolds number decreases and as a result, the heat transfer coefficient of
evaporator decreases. Or in a flooded evaporator, the reduction in mass flow rate
reduces the wetted surface area and the heat transfer coefficient. Therefore,
larger temperature difference is required in the evaporator for the same amount
of heat transfer. This decreases the evaporator temperature and corresponding
pressure to the previous values.
Decrease In refrigeration Load
If the refrigeration load decreases, there is a tendency for the evaporator
temperature to decrease, say to state A as shown in Figure 28.2. In this condition
the capillary tube feeds more refrigerant to the evaporator than the compressor
can remove. This leads to accumulation of liquid refrigerant in the evaporator
causing flooding of the evaporator. This may lead to dangerous consequences if
the liquid refrigerant overflows to the compressor causing slugging of the
compressor. This has to be avoided at all costs; hence the capillary tube based
refrigeration systems use critical charge as a safety measure. Critical charge is a
definite amount of refrigerant that is put into the refrigeration system so that in
the eventuality of all of it accumulating in the evaporator, it will just fill the
evaporator up to its brim and never overflow from the evaporator to compressor.
The flooding of the evaporator is also a transient phenomenon, it cannot continue
indefinitely. The system has to take some corrective action. Since the capillary
tube feeds more refrigerant from the condenser, the liquid seal at the condenser-

exit breaks and some vapour enters the capillary tube. The vapour has a very
small density compared to the liquid; as a result the mass flow rate through the
capillary tube decreases drastically. This situation is shown in Figure 28.2. This is
not desirable since the refrigeration effect decreases and the COP also
decreases. Hence, attempts are made in all the refrigeration plants to subcool
the refrigerant before entry to the expansion device. A vapour to liquid subcooling
heat exchanger is usually employed, wherein the low temperature refrigerant
vapour leaving the evaporator subcools the liquid leaving the condenser.
Te
mr
BA
C
Compressor
Capillary
Fig.24.2: Effect of load variation on capillary tube based refrigeration
systems. B: Design point; A: At low load; C: At high load
24.2.3. Selection of Capillary Tube
For any new system, the diameter and the length of capillary tube have to
be selected by the designer such that the compressor and the capillary tube
achieve the balanced point at the desired evaporator temperature. There are
analytical and graphical methods to select the capillary tube. The fine-tuning of
the length is finally done by cut-and-try method. A tube longer than the design
(calculated) value is installed with the expected result that evaporating
temperature will be lower than expected. The tube is shortened until the desired
balance point is achieved. This is done for mass production. If a single system is
to be designed then tube of slightly shorter length than the design length is
chosen. The tube will usually result in higher temperature than the design value.
The tube is pinched at a few spots to obtain the required pressure and
temperature.

Analytical Method
The analysis of flow through a capillary tube is one of the interesting
problems that illustrate how a simple one-dimensional analysis yields good
results. In a capillary tube the flow is actually compressible, three-dimensional
and two-phase flow with heat transfer and thermodynamic meta-stable state at
the inlet of the tube. However, in the simplified analysis, the flow is assumed to
be steady, one-dimensional and in single phase or a homogenous mixture. One-
dimensional flow means that the velocity does not change in the radial direction
of the tube. Homogeneous means annular flow or plug flow model etc. or not
considered for the two-phase flow. Figure 28.3 shows a small section of a vertical
capillary tube with momentum and pressure at two ends of an elemental control
volume.
Δyτw τw
g
ρV.V+ρV(∂V/∂Y)Δy
ρV.V
P+ (∂P/∂Y)Δy
P
Fig.24.3: A small section of a capillary tube considered for analysis
Applying mass and momentum conservation for a control volume shown in
Fig. 24.3, we get:
Mass Conservation:
0VAΔyA
y
)V(
VA =ρ−
∂
ρ∂
+ρ (24.1)

0.0
y
)V(
=
∂
ρ∂
∴ ρV = constant
Momentum Conservation:
The momentum theorem is applied to the control volume. According to this,
[Momentum] – [Momentum]out in = Total forces on control volume
y
V
∂
∂
y
p
∂
∂
πR2
[ρVV + ρV Δy] - πR2
[ρVV] = - πR2
Δy - ρavggπR2
Δy - 2πRΔyτw (24.2)
At the face y + Δy, Taylor series expansion has been used for pressure and
momentum and only the first order terms have been retained. The second order
terms with second derivatives and higher order terms have been neglected. If the
above equation is divided by πR2
Δy and limit Δy→ 0 is taken; then all the higher
order terms will tend to zero if these were included since these will have Δy or its
higher power of Δy multiplying them. Also, ρavg will tend to ρ since the control
volume will shrink to the bottom face of the control volume where ρ is defined.
Further, neglecting the effect of gravity, which is very small, we obtain:
y
p
∂
∂
R
wτ
y
V
∂
∂
ρV = - – 2 (24.3)
The wall shear stress may be written in terms of friction factor. In fluid flow
through pipes the pressure decreases due to shear stress. This will be referred to
as frictional pressure drop and a subscript ‘f’ will be used with it and it will be
written in terms of friction factor. The Darcy’s friction factor is for fully developed
flow in a pipe. In fully developed flow the velocity does not change in the flow
direction. In case of a capillary tube it increases along the length. Still it is good
approximation to approximate the shear stress term by friction factor. For fully
developed flow the left hand side of Equation (28.3) is zero, hence the frictional
pressure drop Δpf may be obtained from the following equation:
τw = R Δpf /( 2Δy ) (24.4)
The friction factor is defined as
2
V
D
Δy 2
Δpf = ρ f (24.5)
Substituting Eqn.(28.5) in Eqn.(28.4) we get
= ρ f V2
τ / 8 (24.6)w

Substituting for τ in Eqn.(28.3) we have:w
D2
fV
y
p 2
ρ
−
∂
∂
y
V
∂
∂
ρV = - (24.7)
Mass conservation Eqn.(28.1) indicates that the product ρV is constant in the
tube. In fact it is called mass velocity and is denoted by G,
G = ρV
We have mass flow rate = [πD2
m /4] ρV
∴ρV = /A = G = constant (24.8)m
Hence Eqn.(28.7) is rewritten as follows
D2
GVf
y
p
−
∂
∂
y
V
∂
∂
G = - (24.9)
In this equation the term on the left hand side is the acceleration of fluid. The
first term on the right hand side is the pressure drop required to accelerate the
fluid and to overcome the frictional resistance. The second term on the right hand
side is the frictional force acting on the tube wall. The friction factor depends
upon the flow Reynolds number and the wall roughness for the fully developed
flow. For the developing flow it is function of distance along the tube also in
addition to Reynolds number. The flow accelerates along the tube due to vapour
formation, as a result, the Reynolds number increases along the tube. The
velocity and Reynolds number vary in a complex manner along the tube and
these are coupled together. Hence, an exact solution of Eqn.(24.9) is not
possible. To a good approximation the integral of product f V, that is, ∫f V dy can
be calculated by assuming average value of the product f V over a small length
ΔL of the capillary tube.
Accordingly, integrating Equation (24.9) over a small length ΔL of the capillary
tube we obtain
G ΔV = -Δp –[fV]mean GΔL/2D (24.10)
Δp = G ΔV + [G / 2D] [f V]mean ΔL (24.11)
Where, ΔV = Vi+1 – V and Δp = pi i+1 - pi
Δp is negative since p > pi i+1.

Equation (24.11) may be expressed as follows
Δp = Δp + Δpfaccln
This means that total pressure drop over a length ΔL is the sum of that required
for acceleration and that required to overcome frictional resistance.
For laminar flow the effect of wall roughness in negligible and friction factor is
given by
f = 64/Re (24.12)
For turbulent flow the friction factor increases with increase in roughness
ratio. Moody’s chart gives the variation of friction factor with Reynolds numbers
for various roughness ratios. A number of empirical expressions are also
available for friction factor in standard books on Fluid Mechanics. One such
expression for the smooth pipe, known as Blasius Correlation is as follows:
– 0.25 – 0.25
f = 0.3164 Re ≈ 0.32 Re : for Re < 10 5
(24.13)
The solution procedure for Eqn.(24.11) as suggested by Hopkins and Copper
and Brisken is as follows:
The condenser and evaporator temperatures Tc and Te, the refrigerant and its
mass flow rate are usually specified and the length and bore of capillary tube are
required. Eqn.(24.11) is valid for a small length of the tube. Hence, the tube is
divided into small lengths ΔLi such that across each incremental length a
temperature drop Δti of say 1 or 2 degrees takes place depending upon the
accuracy of calculation required. The length of the tube ΔLi for temperature to
drop by say, 1o
C is found from Eqn.(24.11). The temperature base is taken for
calculations instead of pressure base since the refrigerant properties are
available on basis of temperature.
1. Assume an appropriate diameter D for the tube. At condenser exit and inlet to
capillary tube point “0” shown in Figure 24.4, say the state is saturated liquid
state hence,
= v , h = hv , μ = μ andf f f0 0 0
m is known from thermodynamic cycle calculation for the given cooling capacity.
∴Re = 4m /(πDμ),
G = m /A = ρ V = V/v
The constants in Eqn.(24.11) G, G/(2D) and 4 /πD required for solution are then
calculated.
m

0
1
2
3
h
P
Fig.24.4: Step-wise calculation procedure for capillary tube length on p-h
diagram
– 0.25
2. At inlet i = 0 : Re = 4 /(πDμ ), f and V = v G= 0.32 Rem0 0 0 0 0
3. At i = 1 in Figure 10.6: t = t - Δt , find the saturation pressure p at tc1 1 1 1. The
saturation properties v v , h , h are obtained at tand μ and μ1f, 1g 1f 1g 1f 1g 1. It is
assumed that the enthalpy remains constant during expansion as shown in
Figure 28.5.
is the dryness fraction at i = 1, then4. If x1
h h = x h + (1 – x ) h= (24.14)1g 1f0 1 1 1
= [h - h ] / [h - h∴x ]1f 1g 1f1 0
5. Find v = x v + (1 – x ) v1g 1f1 1 1
Assuming that viscosity of mixture can be taken as weighted sum of viscosity of
saturated liquid and vapour we get,
= xμ1 1μ + (1 – x ) μ1g 1f1
– 0.25
= 4m /(πDμ ), f and V = v GRe = 0.32 Re1 1 1 1 1
ΔV = V – V1 0ΔV = V – V1 0
Δp = p – p0 1Δp = p – p0 1

[fV] = [ f V + f V ]/2mean 0 0 1 1
Hence, from Eqn.(24.11) the incremental length of capillary tube for the first step,
ΔL is,1
mean)fV()D2/G(
ΔVGp −Δ−
ΔL =1
6. For the next section i = 2 : t = t - Δt , find the saturation pressure p at t2 1 2 2 2.
The saturation properties v v , h , h and μ and μ2f, 2g 2f 2g 2f 2g are obtained at
temperature t2.
7. Assuming the enthalpy to remain constant, that is h = h = h , the quality x2 1 0 2 is
found and steps 4 and 5 are repeated to find the incremental length ΔL .2
Steps 4 and 5 are repeated for all the intervals up to evaporator
temperature and all the incremental lengths are summed up to find the total
length of the capillary tube.
It is observed from Eqn.(24.11) that the total pressure drop is the sum of
pressure drops due to acceleration that is, Δpaccln = G ΔV and the pressure drop
due to friction, that is, Δp = [G/2D] [fV]f mean ΔL. It may so happen under some
conditions that after a few steps of calculation, the total pressure drop required
for a segment may become less than the pressure drop required for acceleration
alone, Δp < Δpaccln. The increment length ΔL for this segment will turn out to be
negative which has no meaning. This condition occurs when the velocity of
refrigerant has reached the velocity of sound (sonic velocity). This condition is
called choked flow condition. The velocity of fluid cannot exceed the velocity of
sound in a tube of constant diameter, hence the calculation cannot proceed any
further. The flow is said to be choked-flow and the mass flow rate through the
tube has reached its maximum value for the selected tube diameter. For a
capillary tube of constant diameter, choked flow condition represents the
minimum suction pressure that can be achieved. If further pressure drop is
required a tube of larger diameter should be chosen in which the velocity of
sound occurs at larger length.
Figure 24.5 shows the variation mass flow rate with suction pressure for
fixed condenser pressure. The mass flow rate through the capillary tube
increases as the evaporator pressure decreases. However at a pressure of p*
the
flow is choked. If the choking occurs at some interior point of the tube, the length
of the tube from this point to the exit will offer frictional resistance to the flow and
the pressure must decrease to overcome this. The pressure however cannot
decrease since the flow is choked. Hence, adjustment in the inlet conditions
occurs and the mass flow rate is reduced so that the flow will (always) be choked
at the exit of the tube with reduced mass flow rate. This is typical of compressible
sonic flow where upstream influence occurs; otherwise the downstream pressure
decides the mass flow rate.

At fixed Tc
Te or Pe
mr
Choked flow
Pe
*
Fig.24.5: Variation mass flow rate with suction pressure for fixed condenser
pressure
Shortcomings of the above analysis
It is assumed in the above analysis that the expansion is a constant
enthalpy process. This is strictly not true inside a capillary tube since there is a
large change in kinetic energy due to change in velocity along the length due to
flashing of refrigerant liquid. In fact kinetic energy increases at a very fast rate as
the velocity becomes sonic and the flow becomes choked. First law of
thermodynamics indicates that in absence of heat transfer, work done and
change in potential energy for a system in steady state, the sum of enthalpy and
the kinetic energy must remain constant. Hence, if the kinetic energy increases
the enthalpy must decrease, as a result the quality of the refrigerant will be lower
than calculated by assuming constant enthalpy. The actual state of refrigerant in
a constant diameter adiabatic tube is represented by Fanno line, which is shown
in Fig.24.6 on h–s diagram along with the saturation curve. Fanno line is the
solution of steady, compressible adiabatic flow with friction through a tube of
constant diameter.
It is observed that in the early part of the capillary tube, the constant
enthalpy line does not deviate very much from the Fanno line. In the latter part,
the deviation from the Fanno line increases. Most of the length of the capillary
tube happens to be in the latter portion where quality and velocity changes are
very significant; hence constant enthalpy approximation may introduce significant
error.

Saturation
curve
h = const.
s
h
Fanno Line
A
Fig.24.6: Fanno line for capillary tube on h-s diagram
Point A on the Fanno line is the point where the entropy is maximum. This
point corresponds to choked flow condition. Pressure cannot drop below this
value since it will require a decrease in entropy under adiabatic condition, which
is not possible in a real system. This would mean violation of second law of
thermodynamics.
Modified Procedure
It is observed that the Kinetic energy changes significantly in the latter part
of the capillary tube. In step 4 of the calculation procedure enthalpy was
assumed to be constant. To improve upon it, the quality is calculated by
considering energy balance, that is, the sum of enthalpy and kinetic energy is
assumed to remain constant. The quality of the mixture is not found from
Eqn.(24.14). Instead, sum of enthalpy and kinetic energy is taken as constant.
For the first segment we get
h0 + Vo
2 2 2 2
h + V = h + G v/2 = /2 /2 (24.15)1 1 1 1
Substituting for h and v in terms of quality x1 1 1 and properties at saturation, we
get
2
x1h1g + (1 – x1) h1f + G [x1v1g + (1 – x1) v1f ]2
/2 = h0 + Vo
2
/2 , orx 2
h1f + x1h1fg + G2
[v1f + x1v1fg ]2
/2 = h0 + Vo
2
/2, orh
x1
2
[v1fg
2
G2
/2] + x1[G2
v1f v1fg + h1fg ] + (h1f – h0) + (G2
/2) v1f
2
- Vo
2
/2 = 0x
1h1g + (1 – x1) h1f + G [x1v1g + (1 – x1) v1f ]2
/2 = h0 + Vo
2
/2 , or
1f + x1h1fg + G2
[v1f + x1v1fg ]2
/2 = h0 + Vo
2
/2, or
2 2 2
1 [v1fg G /2] + x1[G2
v1f v1fg + h1fg ] + (h1f – h0) + (G2
/2) v1f
2
- Vo
2
/2 = 0

This is a quadratic equation for x that can be solved to find x1 1. The
positive root of this equation is taken as the value of x1. The enthalpy is usually
given in kJ/kg and velocity in m/s, hence to make the equation dimensionally
consistent, the enthalpy is multiplied by 1000, that is,
2 2 2 2
x1 [v1fg G /2]+x1[G v1f v1fg+1000h1fg]+1000(h1f –h0)+(G2
/2)v1f
2
-Vo
2
/2 =0 (24.16)
The remaining part of the procedure from step 5 to 6 remains the same.
For all subsequent steps, the quality is calculated from Eqn.(24.1).
If the entry state of refrigerant to the capillary tube is subcooled, then
length required for the pressure to drop from the condenser pressure to the
saturated state (which occurs at an intermediate pressure) is calculated and is
added to the length required to reduce the pressure from the intermediate
saturated pressure to the final evaporator pressure. Calculation of the length for
the first part (i.e., in the subcooled liquid region) can be done in a single step as
there is no change of phase. For this single phase region, the enthalpy can be
assumed to be constant as the change in kinetic energy is negligible. Thus from
the known inlet enthalpy corresponding to the subcooled state at condenser
pressure, drawing an isenthalpic line, gives the intermediate saturation pressure.
For the two-phase region, the above procedure has to be used with the inlet
conditions corresponding to the saturated intermediate pressure.
Graphical Procedure
A graphical procedure for capillary tube selection has been presented in
ASHRAE Handbook. A representative Figure 24.7 gives the mass flow rate of
refrigerant through capillary tube at various inlet pressures, sub-cooling and
dryness fraction through a capillary tube of 1.63 mm diameter and 2.03 m length.
The companion Figure 24.8 gives the flow correction factor φ for diameters and
lengths different from that used in Fig.24.8. The mass flow rate for any diameter
d and length L is given by:i c
mdi,Lc = m1.63 mm, 2.03 m.φ (24.17)
These plots are for choked flow conditions. Corrections for non-choked
flow conditions are given in ASHRAE Handbook.

Pinlet = Pc
mr
10 C subcoolingo
o
5 C subcooling
saturated
xi = 0.05
xi = 0.10
di = 1.63 mm
Lc= 2.03 m
Fig.24.7: Variation of refrigerant mass flow rate with inlet state for the standard
capillary tube (Choked flow condition)
Lcapillary
φ
0.2
10
Fig.24.8: Variation of flow correction factor φ with capillary tube length and
diameter (Choked flow condition)
di=3 mm
di=2.5 mm
di = 2 mm
di=1.63 mm
d =1 mmi

24.2.4. Advantages and disadvantages of capillary tubes
Some of the advantages of a capillary tube are:
1. It is inexpensive.
2. It does not have any moving parts hence it does not require maintenance
3. Capillary tube provides an open connection between condenser and the
evaporator hence during off-cycle, pressure equalization occurs between
condenser and evaporator. This reduces the starting torque requirement
of the motor since the motor starts with same pressure on the two sides of
the compressor. Hence, a motor with low starting torque (squirrel cage
Induction motor) can be used.
4. Ideal for hermetic compressor based systems, which are critically charged
and factory assembled.
Some of the disadvantages of the capillary tube are:
1. It cannot adjust itself to changing flow conditions in response to daily and
seasonal variation in ambient temperature and load. Hence, COP is
usually low under off design conditions.
2. It is susceptible to clogging because of narrow bore of the tube, hence,
utmost care is required at the time of assembly. A filter-drier should be
used ahead of the capillary to prevent entry of moisture or any solid
particles
3. During off-cycle liquid refrigerant flows to evaporator because of pressure
difference between condenser and evaporator. The evaporator may get
flooded and the liquid refrigerant may flow to compressor and damage it
when it starts. Therefore critical charge is used in capillary tube based
systems. Further, it is used only with hermetically sealed compressors
where refrigerant does not leak so that critical charge can be used.
Normally an accumulator is provided after the evaporator to prevent
slugging of compressor
24.3. Automatic Expansion Valve (AEV)
An Automatic Expansion Valve (AEV) also known as a constant pressure
expansion valve acts in such a manner so as to maintain a constant pressure
and thereby a constant temperature in the evaporator. The schematic diagram of
the valve is shown in Fig. 24.9. As shown in the figure, the valve consists of an
adjustment spring that can be adjusted to maintain the required temperature in
the evaporator. This exerts force Fs on the top of the diaphragm. The
atmospheric pressure, Po also acts on top of the diaphragm and exerts a force of
F = P A , A being the area of the diaphragm. The evaporator pressure Po o d d e acts
below the diaphragm. The force due to evaporator pressure is F = P Ae e d. The
net downward force F + F - F is fed to the needle by the diaphragm. This nets o e

force along with the force due to follow-up spring Ffs controls the location of the
needle with respect to the orifice and thereby controls the orifice opening.
Adjustable screw
Adjustable spring
Diaphragm
Needle
Strainer
Follow-up spring
To evaporator
From condenser
Fo
Fs
Ffs
Fe
orifice
Fig.24.9: Schematic of an Automatic Expansion Valve
If F + F > F + Fe fs s o the needle will be pushed against the orifice and the valve
will be fully closed.
On the other hand if F + F < F + Fe fs s o, the needle will be away from the orifice
and the valve will be open. Hence the relative magnitude of these forces controls
the mass flow rate through the expansion valve.
The adjustment spring is usually set such that during off-cycle the valve is
closed, that is, the needle is pushed against the orifice. Hence,
Feo + Ffso > Fso + Fo
Where, subscript o refers to forces during off cycle. During the off-cycle, the
refrigerant remaining in the evaporator will vaporize but will not be taken out by
the compressor, as a result the evaporator pressure rises during the off-cycle as
shown in Fig.24.10.
When the compressor is started after the off-cycle period, the evaporator
pressure Pe starts decreasing at a very fast rate since valve is closed; refrigerant
is not fed to evaporator while the compressor removes the refrigerant from the
evaporator. This is shown in Fig.24.10. As P decreases the force Fe e decreases
from F to (F - ΔF ). At one stage, the sum F + F becomes less than F + F ,eo eo e e fs s o

as a result the needle stand moves downwards (away from the needle stand)
and the valve opens. Under this condition,
(Feo - ΔF ) + Fe fso < Fso + Fo
Time
Pe
Off On
Fig.24.10: Variation of evaporator pressure during on- and off-cycles of an
AEV based refrigeration system
When the refrigerant starts to enter the evaporator, the evaporator pressure
does not decrease at the same fast rate as at starting time. Thus, the movement
of the needle stand will slow down as the refrigerant starts entering. As the
needle moves downwards, the adjustment spring elongates, therefore the force
F decreases from its off-cycle value of Fs s0, the decrease being proportional to
the movement of the needle.
As the needle moves downwards, the follow-up spring is compressed; as a
result, Ffs increases from its off-cycle value. Hence, the final equation may be
written as,
(Feo - ΔF ) + (F + ΔF ) = (Fe fso fs so - ΔF ) + Fs o or
+ F = F + FFe fs s o = constant (24.18)
The constant is sum of force due to spring force and the atmospheric
pressure, hence it depends upon position of adjustment spring. This will be the
equilibrium position. Then onwards, the valve acts in such a manner that the

evaporator pressure remains constant as long as the refrigeration load is
constant. At this point, the mass flow rate through the valve is the same as that
through the compressor.
24.3.1. Effect of Load Variation
The mass flow rate through the valve is directly proportional to the
pressure drop through the orifice (P –Pc e) and the area of the orifice opening
(needle position). At constant condenser pressure the mass flow rate will
decrease if the evaporator pressure pe increases or as the orifice opening
becomes narrower.
Decrease In Load
If the refrigeration load decreases, there is a tendency in the evaporator
for the evaporator temperature to decrease and thereby the evaporator pressure
(saturation pressure) also decreases. This decreases the force Fe. The sum
F +Fe fs will become less than the sum on right hand side of Equation (28.18) and
the needle stand will be pushed downwards opening the orifice wider. This will
increase the mass flow rate through the valve. This is opposite of the
requirement since at lower load, a lower mass flow rate of the refrigerant is
required. This is the drawback of this valve that it counteracts in an opposite
manner since it tries to keep the evaporator pressure at a constant value. In
Figure 24.11, point A is the normal position of the value and B is the position at
reduced load and wider opening. It is observed that both these are at same
evaporator pressure. The compressor capacity remains the same as at A. The
valve feeds more refrigerant to the evaporator than the compressor can remove
from the evaporator. This causes accumulation of liquid refrigerant in the
evaporator. This is called “flooding” of the evaporator. The liquid refrigerant may
fill the evaporator and it may overflow to the compressor causing damage to it.
Increase In Load
On the other hand if the refrigeration load increases or the evaporator heat
transfer rate increases, the evaporator temperature and pressure will increase for
a flooded evaporator. This will increase Fe. A look at the schematic diagram
reveals that this will tend to move the needle stand upwards, consequently
making the orifice opening narrower and decreasing the mass flow rate. Again
the valve counteracts in a manner opposite to what is required. This shifts the
operating point from A to point C where the compressor draws out more
refrigerant than that fed by the expansion valve leading to starving of the
evaporator.
The adjustment of evaporator pressure and temperature is carried out by
adjustment spring. An increase in the tension of adjustment spring increases Fs

so that the evaporator pressure at which balance occurs, increases. That is, the
regulated temperature increases.
Te
mr
Compressor
Flooding
Balanced
Starving Wider opening
Normal opening
Narrow opening
Fig.24.11: Effect of load variation on balance point of the system using AEV
24.3.2. Applications of automatic expansion valve
The automatic expansion valves are used wherever constant temperature is
required, for example, milk chilling units and water coolers where freezing is
disastrous. In air-conditioning systems it is used when humidity control is by DX
coil temperature. Automatic expansion valves are simple in design and are
economical. These are also used in home freezers and small commercial
refrigeration systems where hermetic compressors are used. Normally the usage
is limited to systems of less than 10 TR capacities with critical charge. Critical
charge has to be used since the system using AEV is prone to flooding. Hence,
no receivers are used in these systems. In some valves a diaphragm is used in
place of bellows.
24.4. Flow Rate through orifice
In variable area type expansion devices, such as automatic and
thermostatic expansion valves, the pressure reduction takes place as the fluid
flows through an orifice of varying area. Let A and A1 2 be the areas at the inlet
and the outlet of the orifice where, A > A . Let V and V be the velocities, P and1 2 1 2 1

P are the pressures and ρ and ρ2 1 2 be the densities at the inlet and outlet
respectively of the orifice as shown in Figure 24.12.
P1,V1,ρ
P2,V2,ρ2
A1 A2
Fig.24.12: Fluid flow through an orifice
Then assuming steady, incompressible, inviscid flow and neglecting
gravity, Bernoulli’s equation may be used to write the flow rate through the orifice
as follows.
Mass Conservation:
A V Aρ = ρV (24.19)1 1 1 2 2 2
Assuming ρ = ρ we get1 2
V / V = A / A1 2 2 1
Bernoulli’s Equation:
2
VP
2
VP
2
2
2
2
2
1
1
1
+
ρ
=+
ρ
(24.20)
Therefore,
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−=
ρ
−
2
1
2
2
2
2
2
2
2
1
2
2
1
21
A
A
0.1
2
V
V
V
0.1
2
VPP
(24.21)

Ideal Flow Rate :
( )2
12
1
21
2
A/A0.1
0.1)PP(2
A
−ρ
−
= A VQ = (24.22)ideal 2 2
Defining
( )
2
12 A/A0.1
0.1
−
M = , we get
1
21
2
)PP(2
A
ρ
−
Q = M (24.23)ideal
The actual flow through the orifice is less than ideal flow because viscous
effects are not included in the above treatment. An empirical coefficient CD, called
discharge coefficient is introduced to account for the viscous effects.
1
21
2D
)PP(2
MAC
ρ
−
Q = C Q = (24.24)Dactual ideal
Introducing flow coefficient K = CD M
1
21
2
)PP(2
KA
ρ
−
Q =actual
To account for compressibility another empirical constant Y is introduced for
actual mass flow rate. Hence, the mass flow rate is expressed as,
1
21
21
)PP(2
AYK
ρ
−
ρm = (24.25)
The area of the orifice opening is usually controlled to control the mass flow
rate through the expansion valve. It is observed that the mass flow rate depends
upon the difference between the condenser and evaporator pressures also. It is
curious that single phase relations have been given above while it was shown
that during expansion of high pressure liquid, the refrigerant flashes into a low
pressure mixture of liquid and vapour as it flows through the expansion valve.
Actually, studies show that the refrigerant remains in a thermodynamic
metastable liquid state as it flows through the orifice of the expansion valve. That
is, it remains a liquid at a lower pressure and temperature during its passage
through the orifice. It flashes into a mixture of liquid and vapour as soon as it
emerges out of the orifice of the valve. This kind of phenomenon has been
observed in the initial sections of transparent capillary tubes also.

24.5. Thermostatic Expansion Valve (TEV)
Thermostatic expansion valve is the most versatile expansion valve and is
most commonly used in refrigeration systems. A thermostatic expansion valve
maintains a constant degree of superheat at the exit of evaporator; hence it is
most effective for dry evaporators in preventing the slugging of the compressors
since it does not allow the liquid refrigerant to enter the compressor. The
schematic diagram of the valve is given in Figure 24.13. This consists of a feeler
bulb that is attached to the evaporator exit tube so that it senses the temperature
at the exit of evaporator. The feeler bulb is connected to the top of the bellows by
a capillary tube. The feeler bulb and the narrow tube contain some fluid that is
called power fluid. The power fluid may be the same as the refrigerant in the
refrigeration system, or it may be different. In case it is different from the
refrigerant, then the TEV is called TEV with cross charge. The pressure of the
power fluid Pp is the saturation pressure corresponding to the temperature at the
evaporator exit. If the evaporator temperature is Te and the corresponding
saturation evaporator pressure is Pe, then the purpose of TEV is to maintain a
temperature T +ΔT at the evaporator exit, where ΔTe s s is the degree of superheat
required from the TEV. The power fluid senses this temperature T +ΔTe s by the
feeler bulb and its pressure Pp is the saturation pressure at this temperature. The
force F exerted on top of bellows of area A due to this pressure is given by:p b
Fp = Ab P (24.26)p
The evaporator pressure is exerted below the bellows. In case the evaporator is
large and has a significant pressure drop, the pressure from evaporator exit is
fed directly to the bottom of the bellows by a narrow tube. This is called pressure-
equalizing connection. Such a TEV is called TEV with external equalizer,
otherwise it is known as TEV with internal equalizer. The force Fe exerted due to
this pressure P on the bottom of the bellows is given bye
(24.27)= AFe b Pe
The difference of the two forces F and Fp e is exerted on top of the needle
stand. There is an adjustment spring below the needle stand that exerts an
upward spring force Fs on the needle stand. In steady state there will be a force
balance on the needle stand, that is,
F = Fs p - Fe (24.28)
During off-cycle, the evaporator temperature is same as room temperature
throughout, that is, degree of superheat ΔTs is zero. If the power fluid is the same
as the refrigerant, then P = P and F = Fp e p e. Therefore any arbitrarily small spring
force Fs acting upwards will push the needle stand against the orifice and keep
the TEV closed. If it is TEV with cross charge or if there is a little degree of

superheat during off-cycle then for TEV to remain closed during off-cycle, Fs
should be slightly greater than (F - F ).p e
Evaporator
Feeler
bulbCapillary tube
Superheated
refrigerant to
compressor
Suction line
Needle
stand
Bellows
Adjustable
spring
Screw
High pressure
liquid
Needle
stand
F Fp p
F Fs e
Fig.24.13: Schematic of a Thermostatic Expansion Valve (TEV)
As the compressor is started, the evaporator pressure decreases at a very
fast rate hence the force Fe decreases at a very fast rate. This happens since
TEV is closed and no refrigerant is fed to evaporator while compressors draws
out refrigerant at a very fast rate and tries to evacuate the evaporator. The force
Fp does not change during this period since the evaporator temperature does not
change. Hence, the difference F -Fp e, increases as the compressor runs for some
time after starting. At one point this difference becomes greater than the spring
force Fs and pushes the needle stand downwards opening the orifice. The valve
is said to open up. Since a finite downward force is required to open the valve, a
minimum degree of superheat is required for a finite mass flow rate.
As the refrigerant enters the evaporator it arrests the fast rate of decrease of
evaporator pressure. The movement of needle stand also slows down. The
spring, however gets compressed as the needle stand moves downward to open

the orifice. If Fs0 is the spring force in the rest position, that is, off-cycle, then
during open valve position
+ ΔFF = Fs s0 s
Eventually, the needle stand reaches a position such that,
F = Fs p - F = Ae b ( Pp – P ) (24.29)e
That is, F is greater than F or P is greater than P . The pressure P and Pp e p e p e
are saturation pressures at temperature (T + ΔTe s) and Te respectively. Hence,
for a given setting force Fs of the spring, TEV maintains the difference between
F and F or the degree of superheat ΔT constant.p e s
ΔT ∝ (Fs p - F ) (24.30)e
∝ Fs
This is irrespective of the level of Pe, that is, evaporator pressure or
temperature, although degree of superheat may be slightly different at different
evaporator temperatures for same spring force, Fs. It will be an ideal case if the
degree of superheat is same at all evaporator temperatures for a given spring
force.
24.5.1. Effect of Load Variation
If the load on the plant increases, the evaporation rate of liquid refrigerant
increases, the area available for superheating the vapour increases. As the
degree of superheat increases, pressure of power fluid Pp increases, the needle
stand is pushed down and the mass flow rate of refrigerant increases. This is the
ideal case. The evaporation rate of refrigerant is proportional to the load and the
mass flow rate supplied through the expansion valve is also proportional to the
load.
On the other hand, if the load on the plant decreases, the evaporation rate
of refrigerant decreases, as a result the degree of superheat decreases. The
thermostatic expansion valve reacts in such a way so as to reduce the mass flow
rate through it. The flow rate of refrigerant in this valve is proportional to the
evaporation rate of refrigerant in the evaporator. Hence, this valve always
establishes balanced flow condition of flow between compressor and itself.
24.5.2. TEV with cross charge
Figure 24.14 shows the saturated vapour line with pressure along the
ordinate. The difference between P and P is proportional to the spring force, Fp e s
and their corresponding projection from the saturated vapour line is the degree of
superheat given by a set of P and P The figure shows three sets of P and Pp e. p e

o
for the same spring force at three evaporator temperatures say –40 C, -20o
C and
5o
C. It is observed that at location A, the degree of superheat is very large
whereas at location C the degree of superheat is very small for the same spring
force setting proportional to (P –Pp e). This would not have been the case if the
saturated vapour line was a straight line. It is observed that if the spring is set for
say a superheat of 10o o
C at –40 C evaporator temperature, the degree of
superheat will become almost zero at higher temperature (Fig.24.14). As a result;
when the plant is started at warm temperature, there is a possibility of flooding of
evaporator. If degree of superheat is set to avoid flooding at say 5o
C, then at the
design point of say – 40o
C, the superheat will be very large and it will starve the
evaporator. This can be corrected if a fluid different from refrigerant is used in the
feeler bulb as power fluid. Such a TEV is called TEV with cross charge. Figure
24.15 shows the saturated vapour line for the power fluid as well as the
refrigerant in the system. The projection for Pp is taken from the saturation line for
power fluid and it shows the temperature at the exit of the evaporator. The power
fluid is such that at any temperature it has lower saturation pressure than that of
the refrigerant in the system, so that as the evaporator temperature increases the
degree of superheat increases. The projection for Pe is taken from the saturation
line of refrigerant and it indicates the evaporator temperature. It is observed that
for the two different locations A and B, the degree of superheat is almost same
for all evaporator temperatures. Hence cross charge helps in maintaining the
same degree of superheat at all evaporator temperatures. Cross-charged valves
perform satisfactorily in a narrow range of temperatures that must be specified
while ordering a valve.
10K
3K
7K
0.3 bar
0.3 bar
0.3 bar
T
P
e
A
-40o
C
B
-20o
C
C
5o
C
Pp
Pe
Pp
Pe
Pp
Pe
Fig.24.14: Vapour pressure curve of refrigerant and power fluid

24.5.3. TEV with External Pressure Equalizer
The pressure drop of the refrigerant is quite significant in large evaporators,
for example in direct expansion coils with a single long tube. Thermostatic
expansion valve maintains Fp – Fe = Ab(Pp – Pe) at a constant value equal to
spring force. The pressure Pp is the saturation pressure at (Te + ΔTs) while Pe is
saturation pressure at Te. In a large evaporator, due to pressure drop ΔPe, the
pressure at exit is say, Pe - ΔPe and corresponding saturation temperature at exit
of evaporator is Te-ΔTe. The superheat ΔTs corresponds to evaporator pressure
Pe and temperature TE. Therefore, effective superheat at evaporator exit is ΔTs +
ΔTe. This may become very large and may result in low COP and lower
volumetric efficiency of compressor. To correct for this, TEV is provided with a
tapping, which feeds the pressure Pe - ΔPe from evaporator exit to the bottom of
bellows. This will result in a degree of superheat equal to the set value ΔTs. A
TEV with this provision is called TEV with External Pressure Equalizer. In this
TEV a stuffing box is provided between pushpins and the valve body so that
evaporator inlet pressure is not communicated to the bottom of bellows. Figure
24.16 shows a TEV with an external equalizer arrangement with pressure
tapping.
ΔTs,A
ΔTs,B
ΔPs
ΔPs
Refrigerant
Power fluid
Te
P
A B
Fig.24.15: Vapour pressure curves of refrigerant and power fluid (cross-
charged TEV)

Pressure tapping
Evaporator
Feeler
bulb
TEV
Fig.24.16: A Thermostatic Expansion Valve with an external equalizer
In any case a large evaporator pressure drop leads to a lower COP; hence a
number of parallel paths or circuits are provided in the evaporator. The
refrigerant is fed to these paths by a single TEV fitted with a distributor. In such a
case, it is recommended that external pressure equalizer be used and care taken
to ensure that all the paths are symmetric and have the same length.
24.5.4. Fade-out point and pressure limiting characteristics of TEV:
The volume of power fluid in the feeler bulb and the connecting tube is
constant, therefore heating and cooling of power fluid is a constant specific
volume process. Figure 24.17 shows the pressure-temperature variation of the
power fluid. The bulb usually has a mixture of liquid and vapour and the pressure
exerted by power fluid corresponds to its saturation pressure. The pressure of
the power fluid increases rather rapidly as its temperature increases since the
liquid evaporates and it has to be accommodated in fixed volume. This sharp rise
in pressure with temperature continues until point B on the saturation curve,
where no liquid is left. Since the pressure of the power fluid does not increase
significantly beyond B, the valve does not open any wider, pp ≈ constant, hence
for a fixed spring setting pe remains almost constant and thereby limits the
pressure in the evaporator to Maximum Operating pressure. It was observed in
an earlier lecture on reciprocating compressors that the power requirement of a
reciprocating compressor is maximum at a certain evaporator pressure. The air-
conditioning systems usually operate near the peak while the refrigeration
systems such as those for ice cream or frozen food operate on the left side of the

peak power. It was shown that during pull-down, the power requirement would
pass through the power peak if the evaporator were kept fully supplied with
liquid. It is however uneconomical to provide a large electric motor to meet the
power requirement of the peak for small times during pull-down. The power
requirement at the design point on the left leg is small. A motor capable of
providing normal power can be used if the TEV makes the evaporator starve
(reduces mass flow rate to it) and limits the pressure during pull-down when the
load is high. Charging the bulb with limited mass of power fluid so that it is
entirely vapour above a maximum evaporating pressure and temperature
achieves this purpose. If rapid cooling is required from the refrigeration system
then this cannot be used.
The limit charged valve is prone to failure known as reversal. The feeler bulb
has vapour only. The head of the feeler bulb is usually colder than the rest of it,
as a result a small amount of vapor can condense in this region. This colder
region will have lower saturation pressure that will decide the pressure of the
feeler bulb and this low pressure may be insufficient to open the valve. This is
avoided by keeping the head of the valve warm by internal circulation.
ΔTe
ΔTe
ΔP1
ΔP2
B
C
D
T
P
Fig.24.17: Variation of power fluid pressure with temperature in a limit
charged TEV

24.4.5. Advantages, disadvantages and applications of TEV
The advantages of TEV compared to other types of expansion devices are:
1. It provides excellent control of refrigeration capacity as the supply of
refrigerant to the evaporator matches the demand
2. It ensures that the evaporator operates efficiently by preventing starving
under high load conditions
3. It protects the compressor from slugging by ensuring a minimum degree
of superheat under all conditions of load, if properly selected.
However, compared to capillary tubes and AEVs, a TEV is more
expensive and proper precautions should be taken at the installation. For
example, the feeler bulb must always be in good thermal contact with the
refrigerant tube. The feeler bulb should preferably be insulated to reduce the
influence of the ambient air. The bulb should be mounted such that the liquid is
always in contact with the refrigerant tubing for proper control.
The use of TEV depends upon degree of superheat. Hence, in
applications where a close approach between the fluid to be cooled and
evaporator temperature is desired, TEV cannot be used since very small extent
of superheating is available for operation. A counter flow arrangement can be
used to achieve the desired superheat in such a case. Alternately, a subcooling
HEX may be used and the feeler bulb mounted on the vapour exit line of the
HEX. The valves with bellows have longer stroke of the needle, which gives extra
sensitivity compared to diaphragm type of valve. But valves with bellows are
more expensive.
Thermostatic Expansion Valves are normally selected from manufacturers’
catalogs. The selection is based on the refrigeration capacity, type of the working
fluid, operating temperature range etc. In practice, the design is different to suit
different requirements such as single evaporators, multi-evaporators etc.
24.6.Float type expansion valves:
Float type expansion valves are normally used with flooded evaporators in
large capacity refrigeration systems. A float type valve opens or closes
depending upon the liquid level as sensed by a buoyant member, called as float.
The float could take the form of a hollow metal or plastic ball, a hollow cylinder or
a pan. Thus the float valve always maintains a constant liquid level in a chamber
called as float chamber. Depending upon the location of the float chamber, a float
type expansion valve can be either a low-side float valve or a high-side float
valve.

24.6.1. Low-side float valves:
A low-side float valve maintains a constant liquid level in a flooded
evaporator or a float chamber attached to the evaporator. When the load on the
system increases, more amount of refrigerant evaporates from the evaporator.
As a result, the refrigerant liquid level in the evaporator or the low-side float
chamber drops momentarily. The float then moves in such a way that the valve
opening is increased and more amount of refrigerant flows into the evaporator to
take care of the increased load and the liquid level is restored. The reverse
process occurs when the load falls, i.e., the float reduces the opening of the
valve and less amount of refrigerant flows into the evaporator to match the
reduced load. As mentioned, these valves are normally used in large capacity
systems and normally a by-pass line with a hand-operated expansion is installed
to ensure system operation in the event of float failure.
24.6.2. High-side float valves:
Figure 24.18 shows the schematic of a high-side float valve. As shown in
the figure, a high-side float valve maintains the liquid level constant in a float
chamber that is connected to the condenser on the high pressure side. When the
load increases, more amount of refrigerant evaporates and condenses. As a
result, the liquid level in the float chamber rises momentarily. The float then
opens the valve more to allow a higher amount of refrigerant flow to cater to the
increased load, as a result the liquid level drops back to the original level. The
reverse happens when the load drops. Since a high-side float valve allows only a
fixed amount of refrigerant on the high pressure side, the bulk of the refrigerant is
stored in the low-pressure side (evaporator). Hence there is a possibility of
flooding of evaporator followed by compressor slugging. However, unlike low-
side float valves, a high-side float valve can be used with both flooded as well as
direct expansion type evaporators.
From
condenser
To
evaporator
High side float
chamber
Float valve
Fig.24.18: Schematic of a high-side float valve

24.7. Electronic Type Expansion Valve
The schematic diagram of an electric expansion valve is shown in Fig.24.19.
As shown in the figure, an electronic expansion valve consists of an orifice and a
needle in front it. The needle moves up and down in response to magnitude of
current in the heating element. A small resistance allows more current to flow
through the heater of the expansion valve, as a result the valve opens wider. A
small negative coefficient thermistor is used if superheat control is desired. The
thermistor is placed in series with the heater of the expansion valve. The heater
current depends upon the thermistor resistance that depends upon the
refrigerant condition. Exposure of thermistor to superheated vapour permits
thermistor to selfheat thereby lowering its resistance and increasing the heater
current. This opens the valve wider and increases the mass flow rate of
refrigerant. This process continues until the vapour becomes saturated and some
liquid refrigerant droplets appear. The liquid refrigerant will cool the thermistor
and increase its resistance. Hence in presence of liquid droplets the thermistor
offers a large resistance, which allows a small current to flow through the heater
making the valve opening narrower. The control of this valve is independent of
refrigerant and refrigerant pressure; hence it works in reverse flow direction also.
It is convenient to use it in year-round-air-conditioning systems, which serve as
heat pumps in winter with reverse flow. In another version of it the heater is
replaced by stepper motor, which opens and closes the valve with a great
precision giving a proportional control in response to temperature sensed by an
element.
Evaporator
Heater
Liquid sensing
thermistor
Applied voltage
EEV
Refrigerant
out
Needle
Refrigerant
in Fig.24.19: Schematic of an electronic expansion valve

24.8. Practical problems in operation of Expansion valves
Certain practical problems are encountered with expansion devices if
either the selection and/or its operation are not proper. An oversized expansion
device will overfeed the refrigerant or hunt (too frequent closing and opening)
and not achieve the balance point. It may allow more refrigerant to flow to the
evaporator and cause flooding and consequent slugging of the compressor with
disastrous results.
A small valve on the other hand passes insufficient quantity of the
refrigerant so that balance point may occur at a lower temperature. The mass
flow rate through the expansion valve depends upon the pressure difference
between condenser and evaporator. The condenser temperature and
consequently the pressure decrease during winter for air-cooled as well as water-
cooled condensers. As a result, the pressure difference is not sufficient for
balance of flow between compressor and the expansion valve. Hence, the
evaporator temperature and pressure decrease during winter months. This
decreases the volumetric efficiency of the compressor and results in lower mass
flow rate and lower cooling capacity. This may lead to disastrous results for
hermetic compressors, which rely upon refrigerant flow rate for cooling of motor.
At lower mass flow rates hermetic compressor may not be cooled sufficiently and
may burn out. Hence, sometimes the condenser pressure must be kept artificially
high so that adequate supply of refrigerant is achieved. Thus the natural
advantage of lower condenser pressure is lost due to the need for maintaining
the condenser pressure artificially high for proper functioning of the expansion
device.
During summer months, the mass low rate through expansion valve is
large because of large pressure difference. The corrective action taken by the
system is to pass vapour through the expansion valve. This problem can occur if
there is insufficient charge of refrigerant in the system so that the liquid seal at
condenser exit is broken and vapour enters the expansion valve. It can occur
because of higher elevation of expansion valve over the condenser so that there
is static pressure drop to overcome gravitational force to reach the expansion
valve, which causes flashing of refrigerant into a mixture of liquid and vapour.
This is however not advisable since it leads to lower COP. Hence, it is advisable
to use a liquid to vapour subcooling heat exchanger so that the liquid is
subcooled and will not flash before entry into expansion valve.
Since the area available for refrigerant flow in the expansion device is
normally very small, there is a danger of valve blockage due to some impurities
present in the system. Hence, it is essential to use a filter/strainer before the
expansion device, so that only refrigerant flows through the valve and solid
particles, if any, are blocked by the filter/strainer. Normally, the automatic
expansion valve and thermostatic expansion valves consist of in-built
filter/strainers. However, when a capillary tube is used, it is essential to use a

filter/dryer ahead of the capillary to prevent entry of any solid impurities and/or
unbound water vapour into the capillary tube.
Questions and answers:
1. Which of the following statements are TRUE?
a) A capillary tube is a variable opening area type expansion device
b) In a capillary tube pressure drop takes place due to fluid friction
c) In a capillary tube pressure drop takes place due to fluid acceleration
d) In a capillary tube pressure drop takes place due to fluid friction and
acceleration
Ans.: d)
a) The refrigerant mass flow rate through a capillary tube increases as condenser
pressure decreases and evaporator pressure increases
b) The refrigerant mass flow rate through a capillary tube increases as condenser
pressure increases and evaporator pressure decreases
c) A capillary tube tends to supply more mass flow rate as refrigeration load
increases
c) A capillary tube tends to supply more mass flow rate as refrigeration load
decreases
Ans.: b) and d)
a) A capillary tube based refrigeration system is a critically charged system
b) A capillary tube based refrigeration system does not use a receiver
c) Capillary tube based refrigeration systems employ open type compressors
d) In capillary tube based systems, pressure equalization takes place when
compressor is off
Ans.: a), b) and d)
a) The mass flow rate through a capillary is maximum under choked flow
conditions
b) The mass flow rate through a capillary is minimum under choked flow
conditions
c) The enthalpy of refrigerant remains constant as it flows through a capillary
tube

d) The enthalpy of refrigerant in a capillary tube decreases in the flow direction
Ans.: a) and d)
5. For a given refrigerant mass flow rate, the required length of a capillary tube
increases as:
a) The degree of subcooling at the inlet decreases
b) The diameter of the capillary tube increases
c) The diameter of capillary tube decreases
d) Inlet pressure increases
Ans.: b) and d)
a) An automatic expansion valve maintains a constant pressure in the condenser
b) An automatic expansion valve maintains a constant pressure in the evaporator
c) In an automatic expansion valve, the mass flow rate of refrigerant increases as
the refrigeration load increases
d) Automatic expansion valve based systems are critically charged
Ans.: b) and d)
7. A thermostatic expansion valve:
a) Maintains constant evaporator temperature
b) Maintains a constant degree of superheat
c) Increases the mass flow rate of refrigerant as the refrigeration load increases
d) Prevents slugging of compressor
Ans.: b), c) and d)
a) Cross-charging is used in TEV when the pressure difference across the
evaporator is large
b) Cross-charging is used in TEV when the evaporator has to operate over a
large temperature range
c) An external equalizer is used when pressure drop in evaporator is large
d) By limiting the amount of power fluid, the power peak during pull-down period
can be avoided
Ans.: b), c) and d)

a) A float valve maintains a constant level of liquid in the float chamber
b) A float valve maintains a constant pressure in the float chamber
c) Low-side float valves are used with direct expansion type evaporators
d) High-side float valves are used in flooded type evaporators
Ans.: a)
a) An electronic expansion valve is bi-directional
b) In an electronic expansion valve, the refrigerant mass flow rate increases as
the amount of liquid at evaporator exit increases
c) In an electronic expansion valve, the refrigerant mass flow rate increases as
the temperature of refrigerant at evaporator exit increases
d) Electronic expansion valves are used in all-year air conditioning systems
Ans.: a), c) and d)
11. A thermostatic expansion valve uses R12 as the power fluid, and is used in a
R12 based system operating at an evaporator temperature of 4o
C. The
adjustable spring is set to offer a resistance equivalent to a pressure of 60 kPa.
What is the degree of superheat?
Ans.: From the properties of R12, at 4o
is 350 kPa.C, the saturation pressure Pe
Hence the pressure acting on the bellows/diaphragm due to the power fluid P is:p
Pp = P +P = 350 + 60 = 410 kPae s
The saturation temperature corresponding to a pressure of 410 kPa is 9o
C
Hence the degree of superheat = 9 – 4 = 5o
C (Ans.)
12. For the above thermostat, what is the actual degree of superheat if there is a
pressure drop of 22 kPa in the evaporator?
Ans.: The pressure of refrigerant at the exit of evaporator, Pe,exit is:
Pe,exit = Pe,inlet - ΔP = 350 – 22 = 328 kPae
The saturation temperature corresponding to 328 kPa is: 1.9o
C
Hence the actual degree of superheat = 9 – 1.9 = 7.1o
C (Ans.)
This implies that a TEV with external equalizer is preferable to reduce the
superheat

13. A straight-charged Thermostatic Expansion Valve (TEV) is designed to
operate at an evaporator temperature of 7o
C with a degree of superheat of 5 K.
R 134a is the refrigerant used in the refrigeration system as well as the bulb. Find
a) The required spring pressure at the design condition; b) Assuming the spring
pressure to remain constant, find the degree of superheat, if the same TEV
operates at an evaporator temperature of –23o
C. The saturation pressure of
R134a can be estimated using Antoine’s equation given by:
KinisTandkPainispwhereexpp sat
06.33T
2094
41.14
sat
⎟
⎠
⎞
⎜
⎝
⎛
−
−
=
o
Ans.: At the design conditions the evaporator temperature is 7 C and degree of
superheat is 5 K.
Hence the required adjustable spring pressure, Ps is:
Ps = Psat(12o
C) – Psat(7o
C)
Using Antoine’s equation given above, we find that:
o
Psat(12 C) = 445.2 kPa, and
Psat(7o
C) = 376.2 kPa
Hence, Ps = 445.2 – 376.2 = 69 kPa
o
If the above TEV is operated at –23 C evaporator temperature, then the pressure
exerted by the power fluid is:
Pp = Psat(-23o
C) + P = 116.5 + 69 = 185.5 kPas
The corresponding saturation temperature is Tsat(189.5 kPa) = 261 K = -12o
C
Hence the degree of superheat at –23o
C = -12 – (-23) = 13 K (Ans.)
This example shows that when the same TEV operates at a lower
evaporator temperature, then the required degree of superheat increases
implying improper utilization of evaporator area. Hence, it is better to use cross-
charging (power fluid is another fluid with a higher boiling point than refrigerant).

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