Patent Publication Number: US-2023147134-A1

Title: Heat exchanger and air-conditioning apparatus

Description:
TECHNICAL FIELD 
     The present disclosure relates to a heat exchanger including heat transfer tubes, and also relates to an air-conditioning apparatus including the heat exchanger. 
     BACKGROUND ART 
     Some heat exchangers has been known that includes a plurality of heat transfer tubes, and a pair of headers into which opposite end portions of the heat transfer tubes are inserted. Patent Literature 1 discloses a heat exchanger in which a value of the ratio, obtained by dividing the cross-sectional area of flow passages of a single heat transfer tube by the cross-sectional area of the header per the single heat transfer tube, ranges from 3% to 30%. Patent Literature 1 applies this ratio to the heat exchanger to improve its heat exchange performance. 
     CITATION LIST 
     Patent Literature 
     
         
         Patent Literature 1: Japanese Patent No. 4686062 
       
    
     SUMMARY OF INVENTION 
     Technical Problem 
     However, as disclosed in Patent Literature 1, in the heat exchanger with a relatively large number of heat transfer tubes, when a low air conditioning load is applied to the heat exchanger, and thus a refrigerant flow rate is relatively low, then refrigerant in a two-phase gas-liquid state may not be able to flow upward inside the heat transfer tubes, but may flow backward. In Patent Literature 1, there is a possibility that this back flow may cause pressure loss inside the heat transfer tubes, and consequently heat exchange performance may be degraded. 
     The present disclosure has been achieved to solve the above problems, and it is an object of the present disclosure to provide a heat exchanger and an air-conditioning apparatus including the heat exchanger, in which the heat exchanger reduces the likelihood of the occurrence of pressure loss of refrigerant in heat transfer tubes to improve heat exchange performance. 
     Solution to Problem 
     A heat exchanger according to an embodiment of the present disclosure includes a main heat exchanger and a sub-heat exchanger connected to the main heat exchanger. The main heat exchanger includes a plurality of main heat transfer tubes extending in an up-down direction, each of the plurality of main heat transfer tubes having a flow passage inside which refrigerant flows, a first main header into which one end portion of each of the plurality of main heat transfer tubes is inserted, main fins provided to the plurality of main heat transfer tubes and helping heat exchange between air and refrigerant flowing inside the plurality of main heat transfer tubes, and a second main header into which an other end portion of each of the plurality of main heat transfer tubes is inserted, the second main header being opposite to the first main header. The sub-heat exchanger includes a plurality of sub-heat transfer tubes extending in an up-down direction, each of the plurality of sub-heat transfer tubes having a flow passage inside which refrigerant flows, sub-fins provided to the plurality of sub-heat transfer tubes and helping heat exchange between air and refrigerant flowing inside the plurality of sub-heat transfer tubes, a first sub-header into which one end portion of each of the plurality of sub-heat transfer tubes is inserted, and a second sub-header into which an other end portion of each of the plurality of sub-heat transfer tubes is inserted, the second sub-header being opposite to the first sub-header. The heat exchanger satisfies Expression (1) below, where the number of the plurality of main heat transfer tubes is represented as N 1 , and the number of the plurality of sub-heat transfer tubes is represented as N 2 . The heat exchanger satisfies Expressions (2) and (3) below, where a cross-sectional area of the flow passage of each of the plurality of main heat transfer tubes is represented as Ta 1 , a cross-sectional area of the flow passage of each of the plurality of sub-heat transfer tubes is represented as Ta 2 , a cross-sectional area of the first main header per each of the plurality of main heat transfer tubes is represented as Ha 1 , and a cross-sectional area of the first sub-header per each of the plurality of sub-heat transfer tubes is represented as Ha 2 . The heat exchanger satisfies Expressions (4) and (5) below, where a sum total of cross-sectional areas of the flow passages of the plurality of main heat transfer tubes is represented as AT 1 , a sum total of cross-sectional areas of the flow passages of the plurality of sub-heat transfer tubes is represented as AT 2 , a flow rate [kG/h] of all refrigerant flowing through the main heat exchanger is represented as Gr 1 , a flow rate [kG/h] of all refrigerant flowing through the sub-heat exchanger is represented as Gr 2 , a gravitational acceleration [m/s 2 ] is represented as G, an equivalent diameter [m] of a cross-section of the flow passage of each of the plurality of main heat transfer tubes is represented as D 1 , an equivalent diameter [m] of a cross-section of the flow passage of each of the plurality of sub-heat transfer tubes is represented as D 2 , a density [kG/m 3 ] of liquid refrigerant flowing in the plurality of main heat transfer tubes is represented as ρL 1 , a density [kG/m 3 ] of liquid refrigerant flowing in the plurality of sub-heat transfer tubes is represented as ρL 2 , a density [kG/m 3 ] of gas refrigerant flowing in the plurality of main heat transfer tubes is represented as ρG 1 , a density [kG/m 3 ] of gas refrigerant flowing in the plurality of sub-heat transfer tubes is represented as ρG 2 , a quality [−] of refrigerant flowing in the main heat exchanger is represented as X 1 , and a quality [−] of refrigerant flowing in the sub-heat exchanger is represented as X 2.    
       0.1&lt; N   2 ( N   1   +N   2 )&lt;0.4  (1)
 
       0.03&lt; Ta   1   /Ha   1 &lt;0.3  (2)
 
       0.03&lt; Ta   2   /Ha   2 &lt;0.3  (3)
 
         AT   1   &lt;Gr   1 /( G×D   1 (ρ L   1   −ρG   1 )) (1/2) ×( X   1   (1/2)   ×ρG   1   (−1/4) +(1− X   1 ) (1/2)   ×ρL   1   (−1/4) ) 2   (4)
 
         AT   2   &lt;Gr   2 /( G×D   2 (ρ L   2   −ρG   2 )) (1/2) ×( X   2   (1/2)   ×ρG   2   (−1/4) +(1− X   2 ) (1/2)   ×ρL   2   (−1/4) ) 2   (5)
 
     Advantageous Effects of Invention 
     In the heat exchanger according to an embodiment of the present disclosure, the relationship between the number of the main heat transfer tubes and the number of the sub-heat transfer tubes satisfies Expression (1) below. In this heat exchanger, the main heat exchanger satisfies Expressions (2) and (4) below, while the sub-heat exchanger satisfies Expressions (3) and (5) below. The likelihood of stagnation and back flow of refrigerant is thus reduced when the refrigerant flows upward in the heat transfer tubes. Therefore, the heat exchanger has improved heat exchange performance without causing pressure loss of refrigerant in the heat transfer tubes. 
       0.1&lt; N   2 ( N   1   +N   2 )&lt;0.4  (1)
 
       0.03&lt; Ta   1   /Ha   1 &lt;0.3  (2)
 
       0.03&lt; Ta   2   /Ha   2 &lt;0.3  (3)
 
         AT   1   &lt;Gr   1 /( G×D   1 (ρ L   1   −ρG   1 )) (1/2) ×( X   1   (1/2)   ×ρG   1   (−1/4) +(1− X   1 ) (1/2)   ×ρL   1   (−1/4) ) 2   (4)
 
         AT   2   &lt;Gr   2 /( G×D   2 (ρ L   2   −ρG   2 )) (1/2) ×( X   2   (1/2)   ×ρG   2   (−1/4) +(1− X   2 ) (1/2)   ×ρL   2   (−1/4) ) 2   (5)
 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG.  1    is a circuit diagram illustrating an air-conditioning apparatus  1  according to Embodiment 1. 
         FIG.  2    is a perspective view illustrating a heat exchanger  7  according to Embodiment 1. 
         FIG.  3    is a plan view illustrating the heat exchanger  7  according to Embodiment 1. 
         FIG.  4    is a configuration diagram illustrating main heat transfer tubes  31  and a first main header  33  according to Embodiment 1. 
         FIG.  5    is a configuration diagram illustrating sub-heat transfer tubes  41  and a first sub-header  43  according to Embodiment 1. 
         FIG.  6    is a graph illustrating heat exchange performance of the heat exchanger  7  according to Embodiment 1. 
         FIG.  7    is a graph illustrating the conditions under which flooding occurs according to Embodiment 1. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Embodiment 1 
     An air-conditioning apparatus  1  according to Embodiment 1 is described hereinafter with reference to the drawings.  FIG.  1    is a circuit diagram illustrating the air-conditioning apparatus  1  according to Embodiment 1. As illustrated in  FIG.  1   , the air-conditioning apparatus  1  includes an outdoor unit  2 , an indoor unit  3 , and a refrigerant pipe  4 . Note that  FIG.  1    illustrates an example in which one indoor unit  3  is provided, however, two or more indoor units  3  may be provided. 
     (Outdoor Unit  2 , Indoor Unit  3 , and Refrigerant Pipe  4 ) 
     The outdoor unit  2  includes a compressor  5 , a flow switching device  6 , a heat exchanger  7 , an outdoor fan  8 , and an expansion unit  9 . The indoor unit  3  includes an indoor heat exchanger  11  and an indoor fan  12 . The refrigerant pipe  4  connects the compressor  5 , the flow switching device  6 , the heat exchanger  7 , the expansion unit  9 , and the indoor heat exchanger  11  to form a refrigerant circuit in which refrigerant flows. 
     (Compressor  5 , Flow Switching Device  6 , Heat Exchanger  7 , Outdoor Fan  8 , and Expansion Unit  9 ) 
     The compressor  5  is configured to suck refrigerant in a low-temperature and low-pressure state, compress the sucked refrigerant into a high-temperature and high-pressure state, and discharge the compressed refrigerant. The flow switching device  6  is configured to change the flow directions of refrigerant in the refrigerant circuit. For example, the flow switching device  6  is a four-way valve. The heat exchanger  7  is configured to exchange heat between refrigerant and outdoor air. The heat exchanger  7  operates as a condenser during cooling operation, and operates as an evaporator during heating operation. The outdoor fan  8  is a device to deliver outdoor air to the heat exchanger  7 . The expansion unit  9  is a pressure reducing valve or an expansion valve to reduce the pressure of refrigerant and expand the refrigerant. 
     (Indoor Heat Exchanger  11  and Indoor Fan  12 ) 
     The indoor heat exchanger  11  is configured to exchange heat between room air and refrigerant. The indoor heat exchanger  11  operates as an evaporator during cooling operation, and operates as a condenser during heating operation. The indoor fan  12  is a device to deliver room air to the indoor heat exchanger  11 . 
     (Cooling Operation) 
     Operation of the air-conditioning apparatus  1  is described below. First, cooling operation is described. During cooling operation, refrigerant sucked into the compressor  5  is compressed by the compressor  5  into a high-temperature and high-pressure gas state and then discharged. The gas refrigerant in a high-temperature and high-pressure state discharged from the compressor  5  passes through the flow switching device  6  and flows into the heat exchanger  7 , which operates as a condenser. Refrigerant flowing into the heat exchanger  7  exchanges heat with outdoor air delivered by the outdoor fan  8 , and condenses into liquid. The refrigerant in a liquid state flows into the expansion unit  9 , and is reduced in pressure and expanded, so that the refrigerant is brought into a low-temperature and low-pressure two-phase gas-liquid state. The refrigerant in the two-phase gas-liquid state flows into the indoor heat exchanger  11 , which operates as an evaporator. Refrigerant flowing into the indoor heat exchanger  11  exchanges heat with room air delivered by the indoor fan  12 , and evaporates into gas. At this time, the room air is cooled and thus cooling is performed in the room. Thereafter, the gas refrigerant having evaporated into a low-temperature and low-pressure state passes through the flow switching device  6  and is sucked into the compressor  5 . 
     (Heating Operation) 
     Next, heating operation is described. During heating operation, refrigerant sucked into the compressor  5  is compressed by the compressor  5  into a high-temperature and high-pressure gas state and then discharged. The high-temperature and high-pressure gas refrigerant discharged from the compressor  5  passes through the flow switching device  6  and flows into the indoor heat exchanger  11 , which operates as a condenser. Refrigerant flowing into the indoor heat exchanger  11  exchanges heat with room air delivered by the indoor fan  12 , and condenses into liquid. At this time, the indoor air is heated and thus heating is performed in the room. The refrigerant in a liquid state flows into the expansion unit  9 , and is reduced in pressure and expanded, so that the refrigerant is brought into a low-temperature and low-pressure two-phase gas-liquid state. The refrigerant in the two-phase gas-liquid state flows into the heat exchanger  7 , which operates as an evaporator. Refrigerant flowing into the heat exchanger  7  exchanges heat with outdoor air delivered by the outdoor fan  8 , and evaporates into gas. Thereafter, the gas refrigerant having evaporated into a low-temperature and low-pressure state passes through the flow switching device  6  and is sucked into the compressor  5 . 
     (Heat Exchanger  7 ) 
       FIG.  2    is a perspective view illustrating the heat exchanger  7  according to Embodiment 1.  FIG.  3    is a plan view illustrating the heat exchanger  7  according to Embodiment 1. The open arrows illustrated in  FIG.  2    represent the flow of refrigerant when the heat exchanger  7  operates as an evaporator. The hatched arrow represents the flow of air passing through the heat exchanger  7 . The configuration of the heat exchanger  7  is described below in detail. Note that the configuration equivalent to that of the heat exchanger  7  may be applied to the indoor heat exchanger  11 . As illustrated in  FIG.  2   , the heat exchanger  7  includes a main heat exchanger  21  and a sub-heat exchanger  22 . When the heat exchanger  7  operates as a condenser, the main heat exchanger  21  is located upstream of the sub-heat exchanger  22 . When the heat exchanger  7  operates as a condenser, the sub-heat exchanger  22  operates as a subcooling device. Note that the heat exchanger  7  may be formed into an L-shape in top view such that the heat exchanger  7  extends along the back face and the side face of the housing of the outdoor unit  2 . In this case, a portion of the heat exchanger  7  located beside the back face of the housing, and another portion of the heat exchanger  7  located beside the side face of the housing may be connected through a connection pipe, or may be formed integrally with each other. 
     (Main Heat Exchanger  21 ) 
     As illustrated in  FIG.  2   , the main heat exchanger  21  includes main heat transfer tubes  31 , main fins  32 , a first main header  33 , a second main header  34 , and a third main header  35 . Each of the main heat transfer tubes  31  has a plurality of flow passages inside which refrigerant flows. For example, the main heat transfer tubes  31  are flat tubes. The main heat transfer tubes  31  extend in the up-down direction. The number of the main heat transfer tubes  31  provided in the main heat exchanger  21  is N 1 . In the present Embodiment 1, the main heat transfer tubes  31  are arranged in two parallel lines, which are a first line and a second line. Note that the main heat transfer tubes  31  may be arranged only in a single line. Each of the main fins  32  is, for example, a corrugated fin, and the main fins  32  are provided to the main heat transfer tubes  31  and help heat exchange between air and refrigerant flowing inside the main heat transfer tubes  31 . 
     One end portion of each of the main heat transfer tubes  31  arranged in the first line is inserted into the first main header  33 . The refrigerant pipe  4  is connected to the first main header  33 . When the heat exchanger  7  operates as a condenser, the first main header  33  distributes refrigerant flowing from the refrigerant pipe  4  to the main heat transfer tubes  31  arranged in the first line. When the heat exchanger  7  operates as an evaporator, the first main header  33  allows refrigerant, having joined together from the main heat transfer tubes  31  arranged in the first line, to flow out to the refrigerant pipe  4 . 
     The second main header  34  is provided to be opposite to the first main header  33  and the third main header  35 . The other end portion of each of the main heat transfer tubes  31  arranged in the first line and the second line is inserted into the second main header  34 . When the heat exchanger  7  operates as a condenser, the second main header  34  distributes refrigerant, having joined together from the main heat transfer tubes  31  arranged in the first line, to the main heat transfer tubes  31  arranged in the second line. When the heat exchanger  7  operates as an evaporator, the second main header  34  distributes refrigerant, having joined together from the main heat transfer tubes  31  arranged in the second line, to the main heat transfer tubes  31  arranged in the first line. 
     The third main header  35  is provided parallel to the first main header  33 . One end portion of each of the main heat transfer tubes  31  arranged in the second line is inserted into the third main header  35 . When the heat exchanger  7  operates as a condenser, the third main header  35  allows refrigerant, flowing from the main heat transfer tubes  31  arranged in the second line, to flow into the third sub-header  45  of the sub-heat exchanger  22 , which is described later. When the heat exchanger  7  operates as an evaporator, the third main header  35  distributes refrigerant flowing from the third sub-header  45  to the main heat transfer tubes  31  arranged in the second line. Note that, in the main heat exchanger  21 , the first main header  33  and the third main header  35  may be integrated into one header, and the main heat exchanger  21  may include a partition portion (not illustrated) at the central portion of the one header to partition the internal space into sub-spaces. 
       FIG.  4    is a configuration diagram illustrating the main heat transfer tubes  31  and the first main header  33  according to Embodiment 1.  FIG.  4    illustrates the cross-section of the first main header  33  taken along the A-A direction illustrated in  FIG.  3   . With reference to  FIG.  4   , dimensions of the parts of the main heat exchanger  21 , properties of refrigerant flowing in the main heat transfer tubes  31 , and other specifications are explained below. Note that, in the explanations below, the term “cross-section” refers to a cross-section perpendicular to the direction in which the flow passage formed in the main heat transfer tube  31  extends. As illustrated in  FIG.  4   , the equivalent diameter [m] of the cross-section of the flow passage of each of the main heat transfer tubes  31  is represented as D 1 . The cross-sectional area of the flow passages of each of the main heat transfer tubes  31  is represented as Ta 1 . The cross-sectional area Ta 1  of the flow passages is the sum of the cross-sectional areas of the plurality of flow passages formed in the main heat transfer tube  31 . 
     The sum total of the cross-sectional areas of the flow passages of the main heat transfer tubes  31  is represented as AT 1 . The sum total AT 1  of the cross-sectional areas of the flow passages refers to a value obtained by multiplying the cross-sectional area Ta 1  of the flow passages of a single main heat transfer tube  31  by the number N 1  of the main heat transfer tubes  31 . The cross-sectional area of the first main header  33  per each of the main heat transfer tubes  31  is represented as Ha 1 . The cross-sectional area Ha 1  of the first main header  33  per each of the main heat transfer tubes  31  refers to a value obtained by dividing the cross-sectional area of the interior space of the first main header  33  by the number N 1  of the main heat transfer tubes  31 . The cross-sectional area Ha 1  of the first main header  33  per each of the main heat transfer tubes  31  refers to the area of the region illustrated in  FIG.  4    that is hatched laterally to the sheet plane. The main heat exchanger  21  satisfies Expression (2) below. 
       [Expression 6] 
       0.03&lt; Ta   1   /Ha   1 &lt;0.3  (2)
 
     The main heat exchanger  21  also satisfies Expression (4) below, where the flow rate [kG/h] of all refrigerant flowing through the main heat exchanger  21  is represented as Gr 1 , the density [kG/m 3 ] of liquid refrigerant flowing in the main heat transfer tubes  31  is represented as ρL 1 , the density [kG/m 3 ] of gas refrigerant flowing in the main heat transfer tubes  31  is represented as ρG 1 , the quality [−] of refrigerant flowing in the main heat exchanger  21  is represented as X 1 , and the gravitational acceleration [m/s 2 ] is represented as G. 
       [Expression 7] 
         AT   1   &lt;Gr   1 /( G×D   1 (ρ L   1   −ρG   1 )) (1/2) ×( X   1   (1/2)   ×ρG   1   (−1/4) +(1− X   1 ) (1/2)   ×ρL   1   (−1/4) ) 2   (4)
 
     (Sub-Heat Exchanger  22 ) 
     As illustrated in  FIG.  2   , the sub-heat exchanger  22  includes sub-heat transfer tubes  41 , sub-fins  42 , a first sub-header  43 , a second sub-header  44 , and a third sub-header  45 . Each of the sub-heat transfer tubes  41  has a plurality of flow passages inside which refrigerant flows. For example, the sub-heat transfer tubes  41  are flat tubes. The sub-heat transfer tubes  41  extend in the up-down direction. The number of the sub-heat transfer tubes  41  provided in the sub-heat exchanger  22  is N 2 . In the present Embodiment 1, the sub-heat transfer tubes  41  are arranged in two parallel lines, which are a first line and a second line. Note that the sub-heat transfer tubes  41  may be arranged only in a single line. Each of the sub-fins  42  is, for example, a corrugated fin, and the sub-fins  42  are provided to the sub-heat transfer tubes  41  and help heat exchange between air and refrigerant flowing inside the sub-heat transfer tubes  41 . 
     One end portion of each of the sub-heat transfer tubes  41  arranged in the first line is inserted into the first sub-header  43 . The first sub-header  43  is connected to the first main header  33  through a first partition plate  23 . The first partition plate  23  partitions the internal space into the first main header  33  and the first sub-header  43 . The refrigerant pipe  4  is connected to the first sub-header  43 . When the heat exchanger  7  operates as an evaporator, the first sub-header  43  distributes refrigerant flowing from the refrigerant pipe  4  to the sub-heat transfer tubes  41  arranged in the first line. When the heat exchanger  7  operates as a condenser, the first sub-header  43  allows refrigerant, having joined together from the sub-heat transfer tubes  41  arranged in the first line, to flow out to the refrigerant pipe  4 . 
     The second sub-header  44  is provided to be opposite to the first sub-header  43  and the third sub-header  45 . The other end portion of each of the sub-heat transfer tubes  41  arranged in the first line and the second line is inserted into the second sub-header  44 . The second sub-header  44  is connected to the second main header  34  through a second partition plate  24 . The second partition plate  24  partitions the internal space into the second main header  34  and the second sub-header  44 . When the heat exchanger  7  operates as an evaporator, the second sub-header  44  distributes refrigerant, having joined together from the sub-heat transfer tubes  41  arranged in the first line, to the sub-heat transfer tubes  41  arranged in the second line. When the heat exchanger  7  operates as a condenser, the second sub-header  44  distributes refrigerant, having joined together from the sub-heat transfer tubes  41  arranged in the second line, to the sub-heat transfer tubes  41  arranged in the first line. 
     The third sub-header  45  is provided parallel to the first sub-header  43 . One end portion of each of the sub-heat transfer tubes  41  arranged in the second line is inserted into the third sub-header  45 . The third sub-header  45  is connected to the third main header  35  such that their internal spaces communicate with each other. When the heat exchanger  7  operates as an evaporator, the third sub-header  45  allows refrigerant, flowing from the sub-heat transfer tubes  41  arranged in the second line, to flow into the third main header  35  of the main heat exchanger  21 . When the heat exchanger  7  operates as a condenser, the third sub-header  45  distributes refrigerant flowing from the third main header  35  to the sub-heat transfer tubes  41  arranged in the second line. Note that, in the sub-heat exchanger  22 , the first sub-header  43  and the third sub-header  45  may be integrated into one header, and the sub-heat exchanger  22  may include a partition portion (not illustrated) at the central portion of the one header to partition the internal space into sub-spaces. 
       FIG.  5    is a configuration diagram illustrating the sub-heat transfer tubes  41  and the first sub-header  43  according to Embodiment 1.  FIG.  5    illustrates the cross-section of the first sub-header  43  taken along the A-A direction illustrated in  FIG.  3   . With reference to  FIG.  5   , dimensions of the parts of the sub-heat exchanger  22 , properties of refrigerant flowing in the sub-heat transfer tubes  41 , and other specifications are explained below. Note that, in the explanations below, the term “cross-section” refers to a cross-section perpendicular to the direction in which the flow passage formed in the sub-heat transfer tube  41  extends. In the explanations below, the configuration of the sub-heat exchanger  22  denoted with the suffix “2” is equivalent to the corresponding configuration of the main heat exchanger  21  denoted with the suffix “1” in place of the suffix “2.” The equivalent diameter [m] of the cross-section of the flow passage of each of the sub-heat transfer tubes  41  is represented as D 2 . The cross-sectional area of the flow passages of each of the sub-heat transfer tubes  41  is represented as Ta 2 . The cross-sectional area Ta 2  of the flow passages is the sum of the cross-sectional areas of the plurality of flow passages formed in the sub-heat transfer tube  41 . 
     The sum total of the cross-sectional areas of the flow passages of the sub-heat transfer tubes  41  is represented as AT 2 . The sum total AT 2  of the cross-sectional areas of the flow passages refers to a value obtained by multiplying the cross-sectional area Ta 2  of the flow passages of a single sub-heat transfer tube  41  by the number N 2  of the sub-heat transfer tubes  41 . The cross-sectional area of the first sub-header  43  per each of the sub-heat transfer tubes  41  is represented as Ha 2 . The cross-sectional area Ha 2  of the first sub-header  43  per each of the sub-heat transfer tubes  41  refers to a value obtained by dividing the cross-sectional area of the interior space of the first sub-header  43  by the number N 2  of the sub-heat transfer tubes  41 . The cross-sectional area Ha 2  of the first sub-header  43  per each of the sub-heat transfer tubes  41  refers to the area of the region illustrated in  FIG.  5    that is hatched laterally to the sheet plane. The sub-heat exchanger  22  satisfies Expression (3) below. 
       [Expression 8] 
       0.03&lt; Ta   2   /Ha   2 &lt;0.3  (3)
 
     The sub-heat exchanger  22  also satisfies Expression (5) below, where the flow rate [kG/h] of all refrigerant flowing through the sub-heat exchanger  22  is represented as Gr 2 , the density [kG/m 3 ] of liquid refrigerant flowing in the sub-heat transfer tubes  41  is represented as ρL 2 , the density [kG/m 3 ] of gas refrigerant flowing in the sub-heat transfer tubes  41  is represented as ρG 2 , and the quality [−] of refrigerant flowing in the sub-heat exchanger  22  is represented as X 2 . 
       [Expression 9] 
         AT   2   &lt;Gr   2 /( G×D   1 (ρ L   1   −ρG   2 )) (1/2) ×( X   2   (1/2)   ×ρG   2   (−1/4) +(1− X   2 ) (1/2)   ×ρL   2   (−1/4) ) 2   (5)
 
       FIG.  6    is a graph illustrating heat exchange performance of the heat exchanger  7  according to Embodiment 1. The vertical axis illustrated in  FIG.  6    represents heat exchange performance of the heat exchanger  7 . The horizontal axis illustrated in  FIG.  6    represents the ratio of the sub-heat exchanger  22  in the heat exchanger  7 . The ratio of the sub-heat exchanger  22  refers to the ratio of the number N 2  of the sub-heat transfer tubes  41  to the total number N 1 +N 2  of the main heat transfer tubes  31  and the sub-heat transfer tubes  41 . As illustrated in  FIG.  6   , the heat exchanger  7  has high heat exchange efficiency when the ratio of the sub-heat exchanger  22  ranges from 10% to 40%. The heat exchanger  7  satisfies Expression (1) below for the number of the main heat transfer tubes  31  and the number of the sub-heat transfer tubes  41 . Because of this expression, the heat exchanger  7  achieves high heat exchange performance. 
       [Expression 10] 
       0.1&lt; N   2 ( N   1   +N   2 )&lt;0.4  (1)
 
       FIG.  7    is a graph illustrating the conditions under which flooding occurs according to Embodiment 1. The flooding is a phenomenon in which when refrigerant in a two-phase gas-liquid state flows upward inside the heat transfer tubes, portion of the refrigerant in a liquid state in the vicinity of the gas-liquid interface flows backward in the reverse direction to the flow of another portion of the refrigerant in a gas state, so that the refrigerant in a two-phase gas-liquid state stagnates in the heat transfer tubes. If the flooding has occurred in the heat transfer tubes, pressure loss of refrigerant flowing in the heat transfer tubes will be caused. With reference to  FIG.  7   , an explanation is given for the fact that the likelihood of stagnation and back flow of refrigerant is reduced when the refrigerant flows upward in the main heat transfer tubes  31  and the sub-heat transfer tubes  41  according to Embodiment 1. Note that, in the explanations below, the suffixes “1” and “2” are appropriately omitted. The description in which the suffixes “1” and “2” are omitted explains each of the main heat exchanger  21  and the sub-heat exchanger  22 . 
       FIG.  7    illustrates the results of the examination of the conditions under which the flooding occurs when the velocity of refrigerant flowing in the heat transfer tubes is varied in the heat exchanger  7  that satisfies Expressions (1) to (3). The vertical axis illustrated in  FIG.  7    represents the dimensionless quantity jG* (1/2)  derived from Expression (6) below, where the flow rate [m/s] of gas refrigerant flowing in the heat transfer tubes is represented as jG. The horizontal axis illustrated in  FIG.  7    represents the dimensionless quantity jL* (1/2)  derived from Expression (7) below, where the flow rate [m/s] of liquid refrigerant flowing in the heat transfer tubes is represented as jL. The point of intersection of the vertical line and the horizontal line represents the dimensionless quantity C=jG* (1/2) +jL* (1/2) . 
       [Expression 11] 
         jG*=jG ×(ρ G /( G×D ×(ρ L−ρG ))) (1/2)   (6)
 
       [Expression 12] 
         jL*=jL ×(ρ L /( G×D ×(ρ L−ρG ))) (1/2)   (7)
 
     The up-pointing triangle marks and the plus signs illustrated in  FIG.  7    represent the values of jG* (1/2)  and the values of jL* (1/2)  when the flooding has occurred. In addition, the square marks and the down-pointing triangle marks illustrated in  FIG.  7    represent the values of jG* (1/2)  and the values of jL* (1/2)  when the flooding has ended. That is,  FIG.  7    shows that the flooding occurs within the range of 0.88&lt;C≤1. It is also known that, in a case of C≤0.88, liquid refrigerant flows downward throughout the heat transfer tubes to the bottom. Therefore, where the heat exchanger  7  satisfies C&gt;1, that is, Expression (8) below, when refrigerant flows upward in the main heat transfer tubes  31  and the sub-heat transfer tubes  41 , the likelihood of stagnation and back flow of the refrigerant is reduced. 
       [Expression 13] 
         jG*   (1/2)   +jL*   (1/2) &gt;1  (8)
 
     Where the flow rate [kg/h] of liquid refrigerant flowing in the heat transfer tubes is represented as GL, and the flow rate [kg/h] of gas refrigerant flowing in the heat transfer tubes is represented as GG, Expressions (9) to (13) below are satisfied. 
       [Expression 14] 
         GG=G×X   (9)
 
       [Expression15] 
         GL=G ×(1− X )  (10)
 
       [Expression 16] 
         G=Gr/AT   (11)
 
       [Expression 17] 
         jG=GG/ρG   (12)
 
       [Expression 18] 
         jL=GL/ρL   (13)
 
     On the basis of Expressions (9) and (11), Expression (14) below is satisfied. On the basis of Expressions (10) and (11), Expression (15) below is satisfied. 
       [Expression 19] 
         GG =( Gr×X )/ AT   (14)
 
       [Expression 20] 
         GL =( Gr ×(1− X ))/ AT   (15)
 
     On the basis of Expressions (12) and (14), Expression (16) below is satisfied. On the basis of Expressions (13) and (15), Expression (17) below is satisfied. 
       [Expression 21] 
         jG =( Gr×X )/( AT×ρG )  (16)
 
       [Expression 22] 
         jL =( Gr ×(1− X ))/( AT×ρL )  (17)
 
     On the basis of Expressions (6) to (8), (16), and (17), Expression (18) below is satisfied. Expression (18) corresponds to Expressions (4) and (5). That is, the main heat exchanger  21  and the sub-heat exchanger  22  according to Embodiment 1 meet the configuration with C&gt;1 derived from the experiment illustrated in  FIG.  7   . Because of this configuration, the main heat exchanger  21  and the sub-heat exchanger  22  according to Embodiment 1 reduce the likelihood of stagnation and back flow of refrigerant when the refrigerant flows upward in the main heat transfer tubes  31  and the sub-heat transfer tubes  41 . 
       [Expression23] 
         AT&lt;Gr /( G×D (ρ L−ρG )) (1/2) ×( X   (1/2)   ×ρG   (−1/4) +(1− X ) (1/2)   ×ρL   (−1/4) ) 2   (18)
 
     In the heat exchanger according to the present disclosure, the relationship between the number of the main heat transfer tubes  31  and the number of the sub-heat transfer tubes  41  satisfies Expression (1) below. In this heat exchanger, the main heat exchanger  21  satisfies Expressions (2) and (4) below, while the sub-heat exchanger  22  satisfies Expressions (3) and (5) below. The likelihood of stagnation and back flow of refrigerant is thus reduced when the refrigerant flows upward in the heat transfer tubes. Therefore, the heat exchanger has improved heat exchange performance without causing pressure loss of refrigerant in the heat transfer tubes. 
       0.1&lt; N   2 ( N   1   +N   2 )&lt;0.4  (1)
 
       0.03&lt; Ta   1   /Ha   1 &lt;0.3  (2)
 
       0.03&lt; Ta   2   /Ha   2 &lt;0.3  (3)
 
         AT   1   &lt;Gr   1 /( G×D   1 (ρ L   1   −ρG   1 )) (1/2) ×( X   1   (1/2)   ×ρG   1   (−1/4) +(1− X   1 ) (1/2)   ×ρL   1   (−1/4) ) 2   (4)
 
         AT   2   &lt;Gr   2 /( G×D   2 (ρ L   2   −ρG   2 )) (1/2) ×( X   2   (1/2)   ×ρG   2   (−1/4) +(1− X   2 ) (1/2)   ×ρL   2   (−1/4) ) 2   (5)
 
     Since no flooding occurs in the main heat exchanger  21  and the sub-heat exchanger  22 , the flow rate of refrigerant does not decrease. This allows the heat exchanger  7  to have improved condensation performance of the sub-heat exchanger  22  even when the heat exchanger  7  operates as a condenser and the sub-heat exchanger  22  operates as a subcooling device. 
     REFERENCE SIGNS LIST 
       1 : air-conditioning apparatus,  2 : outdoor unit,  3 : indoor unit,  4 : refrigerant pipe,  5 : compressor,  6 : flow switching device,  7 : heat exchanger,  8 : outdoor fan,  9 : expansion unit,  11 : indoor heat exchanger,  12 : indoor fan,  21 : main heat exchanger,  22 : sub-heat exchanger,  23 : first partition plate,  24 : second partition plate,  31 : main heat transfer tube,  32 : main fin,  33 : first main header,  34 : second main header,  35 : third main header,  41 : sub-heat transfer tube,  42 : sub-fin,  43 : first sub-header,  44 : second sub-header,  45 : third sub-header