JP2021173428A - Evaluation method, evaluation device and evaluation program of heat exchanger core for air conditioning - Google Patents

Abstract

To provide a technology for calculation estimation of temperature changes and pressure losses of refrigerant and passing air from the shape of heat exchanger core for air conditioning and test conditions.SOLUTION: The present invention is a method for evaluating the performance of a heat exchanger core for air conditioning, which is provided with a plurality of fins and tubes, and air is circulated between the fins and the tubes to exchange heat between the medium and the fins. An air pressure loss and an average heat transfer rate are obtained. Under an assumption that a fin temperature distribution has a uniform average temperature, a fin temperature distribution is obtained from fin efficiency, fin root temperature, and outside air temperature. The temperature of the air is obtained by the difference method for each of divided regions of the fin in the air flow direction under a recognition that the tubes are one straight tube. Under an assumption that a relational expression that air wind speed×total fin area×input/output air temperature difference×specific heat=amount of medium×specific heat×input/output air temperature difference is reasonable, the amount of medium is obtained by solving the relational expression, and the air outlet temperature and the water outlet temperature are obtained.SELECTED DRAWING: Figure 1

Description

The present invention relates to an evaluation method, an evaluation device, and an evaluation program for an air conditioning heat exchanger core.

A heat exchanger for air conditioning is tested by passing wet air or dry air under predetermined conditions through a heat exchanger through which a predetermined cooled refrigerant or heated refrigerant has passed, and pressure loss, air inflow and outflow. ΔT and ΔT of the refrigerant are obtained, and it is evaluated whether or not the heat exchanger exhibits a predetermined performance.
As a means to improve the performance of the heat exchanger, the structure of the heat exchanger has been changed and the surface treatment of the fins has been performed, and lab-scale tests are conducted to evaluate the performance.
Since the data collected in the heat exchanger test usually varies, the test is performed multiple times and the results are compared, but there is a problem that it is difficult to judge what kind of conditions are good at present.

For example, in Patent Document 1 below, when designing an outdoor unit for air conditioning including a plate fin tube set, the relationship between the propeller fan of the fan and the plate fin is grasped, and the measurement on the suction side on the rotation axis of the propeller fan is performed. A design method for determining the installation position and front area of the plate fin tube set based on the flow rate and the average flow rate at two or more different flow rate measurement positions is disclosed.

Japanese Unexamined Patent Publication No. 2004-053044

The technique described in Patent Document 1 investigates the distribution of the flow strength of forced convection in a plate fin tube set in detail, defines a flow field length scale and a velocity scale in consideration of fan characteristics, and heat exchange. It is said that it will provide a forced convection model that can predict the heat transfer and flow loss performance of the vessel.
The technique described in Patent Document 1 states that structural calculation and flow prediction of an outdoor unit can be performed. However, in this technique, structural design is the main component, and the influence of temperature and humidity of the refrigerant flowing between fins is the main subject. Is not considered.

In the heat exchanger, in order to improve the performance, the surface of the fin material is surface-treated to impart hydrophilicity and water repellency.
The performance test of the heat exchanger is performed by the method specified by each heat exchanger manufacturer, and the temperature, pressure loss due to the heat exchanger core, etc. are measured for each of the inflow and outflow of the refrigerant (water) or air. ..
Further, in order to evaluate the defrosting performance of a heat exchanger, it is required that a small heat exchanger core can be used for evaluation due to the restrictions of the test equipment.

In the current technology, various techniques for measuring the heat exchanger core itself have been established, but there is no method that can estimate the temperature and pressure loss in advance, and whether or not the evaluation is valid for the small heat exchanger core. The reality is that there is no way to consider.

In view of these backgrounds, the present invention provides an evaluation method for an air conditioning heat exchanger core that can calculate temperature changes and pressure losses of a medium and passing air from the shape and test conditions of the air conditioning heat exchanger core. The purpose is to provide an evaluation device and an evaluation program.

"1" The method for evaluating the heat exchanger core for air conditioning according to the present invention includes a plurality of fins arranged side by side at predetermined intervals and a tube joined so as to be in contact with the plurality of fins. This is a performance evaluation method for an air-conditioning heat exchanger core in which air is circulated between the fins and the tube to exchange heat between the medium in the tube and the fins. The pressure loss and the average heat transfer rate when air flows along the fins are obtained, and it is assumed that the temperature distribution of the fins has a uniform average temperature, and the fins are obtained from the fin efficiency, the fin root temperature, and the outside air temperature. Assuming that the heat transfer between the medium and the tube has a turbulent heat transfer rate relationship, the fins are divided into a plurality of parts along the air flow direction, and the air division region is obtained. The temperature of the air is obtained by the difference method for each time, the tube is regarded as one straight tube, divided into the same number as the divided regions of the air, and the temperature of the medium is obtained for each divided region of the tube, and the air is obtained. Wind speed x total fin area x inlet / outlet air temperature difference x specific heat = medium amount x specific heat x inlet / outlet temperature difference It is characterized in that the water outlet temperature is obtained.

"2" In the performance evaluation method according to the present invention, it is assumed that the relational expression of the air velocity × total fin area × inlet / outlet air temperature difference × specific heat = amount of medium × specific heat × inlet / output medium temperature difference is established, and this relational expression is established. When solving, it is preferable to multiply the heat transfer coefficient of the medium by a coefficient to match the calculation result on the left side and the calculation result on the right side of the relational expression.

"3" In the performance evaluation method according to the present invention, as a pressure loss calculation model when air is circulated through the air conditioning heat exchanger core, the pressure loss Pc of the air conditioning heat exchanger core is as follows (1). It is preferable to assume that it is represented by the equation, the equation (2), and the equation (3).
However, in (1), (2), Pc: pressure loss in the heat exchanger core for air conditioning, _{C D:} flow loss coefficient, [rho: density _{^{(kg / m 3), U}} c: air conditioning heat exchanger core the wind passing through the air _{(m / sec), D ec} :( typical dimension: wetted perimeter: m), _{L t:} air conditioning heat exchanger core of the air flow direction length (m), Re: Yes Reynolds number , (3), _Ac : Free passage area (total area where fins and tubes do not exist when the air conditioning heat exchanger core is viewed along the air flow direction), A _o : Total heat transfer area be.

"4" In the performance evaluation method according to the present invention, as a temperature calculation model, the average heat transfer of the heat exchanger core for air conditioning is obtained as the Nusselt number Nu represented by the following equation (4), and the Nusselt number. Has a relationship expressed by the following equation (5) in relation to the heat transfer coefficient h.
However, in Eq. (4), Pr: Prandle number, _Ipt : Fin spacing (m), Nusselt number: Nu (non-dimensional number) = hL / λ, and h in Eq. (5) thermal conductivity, lambda: the thermal conductivity of the fin material (W / mK), L is the characteristic length or the _{D ec} (wetted perimeter).

"5" In the performance evaluation method according to the present invention, the temperature of the fin has a relationship represented by the following equations (6) and (7), and is passed through in order to obtain the heat conduction amount from the heat transfer rate. Assuming that the temperature of the air to be heated and the temperature of the fins are required, the temperature distribution of the fins has a uniform average temperature θm in the above equation (7), where θm is the fin efficiency ηf and the fin root temperature θ. It can be obtained from ₀ and the outside air temperature t _0.
However, in the equation (7), df is the tube height pitch, dc is the tube depth pitch (in the case of one tube, the depth dimension (m), and F ₁ is the fin thickness (m).

"6" In the performance evaluation method according to the present invention, the heat transfer between the medium and the tube has a relationship of the turbulent heat transfer coefficient shown in the following equation (8).

In the performance evaluation method according to "7" the present invention, the heat exchanger passing wind velocity U _c, compared face velocity U ₀ to the heat exchanger core the air conditioning, the free passage area A _c the frontal projected area A _f It is preferable to multiply the ratio and calculate using the relationship of _{U c} = ( _Ac / A _f).

"8" The performance evaluation device according to the present invention includes a plurality of fins arranged side by side at predetermined intervals and a tube joined so as to be in contact with the plurality of fins, and the plurality of fins and the tube. A performance evaluation device for an air-conditioning heat exchanger core that exchanges heat between the medium in the tube and the fins by allowing air to flow between them, along the fins of the air-conditioning heat exchanger core. The fins are calculated from the fin efficiency, the root temperature of the fins, and the outside air temperature, assuming that the first calculation means for obtaining the pressure loss and the average heat transfer coefficient when air flows and the temperature distribution of the fins have a uniform average temperature. Assuming that the second calculation means for obtaining the temperature distribution of the above and the heat transfer between the medium and the tube have a turbulent heat transfer coefficient relationship, the fins are divided into a plurality of parts along the air flow direction. A third calculation means for obtaining the temperature of the air by the difference method for each divided region of the air, and the tube is divided into the same number as the divided region of the air by regarding the tube as one straight pipe. It is assumed that the fourth calculation means for obtaining the temperature of the medium for each divided region and the relational expression of air wind velocity × total fin area × inlet / outlet air temperature difference × specific heat = medium amount × specific heat × inlet / outlet temperature difference are established. It is characterized by having a fifth calculation means for obtaining the amount of the medium by solving this relational expression, and further obtaining the air outlet temperature and the water outlet temperature.

The performance evaluation program according to the present invention includes a plurality of fins arranged side by side at predetermined intervals and a tube joined so as to be in contact with the plurality of fins, and air is provided between the plurality of fins and the tube. This is a performance evaluation program for an air-conditioning heat exchanger core that exchanges heat between the medium in the tube and the fins by circulating a computer.
It is assumed that the first calculation means for obtaining the pressure loss and the average heat transfer capacity when air flows along the fins of the heat exchanger core for air conditioning and the temperature distribution of the fins have a uniform average temperature. Assuming that the second calculation means for obtaining the temperature distribution of the fin from the fin efficiency, the fin root temperature, and the outside air temperature, and the heat transfer between the medium and the tube have a turbulent heat transfer rate relationship, the fin Is divided into a plurality of parts along the flow direction of the air, and the temperature of the air is obtained by the difference method for each divided region of the air. A fourth calculation means for obtaining the temperature of the medium for each divided region of the tube by dividing into the same number as the divided regions of the above, and air wind velocity × total fin area × inlet / outlet air temperature difference × specific heat = amount of medium × specific heat × Assuming that the relational expression of the temperature difference between inflow and outflow is established, it is characterized by solving this relational expression to obtain the amount of the medium, and further functioning as a fifth calculation means for obtaining the air outlet temperature and the water outlet temperature. do.

According to the present invention, it is possible to estimate the temperature change and pressure loss of the refrigerant and passing air from the estimation of the shape and test conditions of the heat exchanger core for air conditioning without conducting a model experiment or the like, and the heat exchanger core for air conditioning can be estimated. You can build a method to evaluate the performance of.

An example of the heat exchanger core for air conditioning applied in the performance evaluation method of the first embodiment according to the present invention is shown, where (A) is a front view and (B) is a side view. The explanatory view for demonstrating the state which carries out the test by passing water while sending air to the heat exchanger core for air conditioning in the performance evaluation method of 1st Embodiment which concerns on this invention. A graph showing the viscosity of water as a function of temperature. The block diagram which shows the main part of the performance evaluation apparatus used for carrying out the performance evaluation method of 1st Embodiment which concerns on this invention. Explanatory drawing in the case where the tube of the heat exchanger core is regarded as one straight tube and divided into 20 in the length direction of the straight tube for analysis. A flowchart showing the input step to the fifth step in step order in the first embodiment.

"First Embodiment (Embodiment in the case of no condensation)"
Hereinafter, the first embodiment of the performance evaluation method for the heat exchanger core for air conditioning according to the present invention will be described in detail based on the embodiment shown in the attached drawings.
FIG. 1 shows an example of an air conditioning heat exchanger core to which the performance evaluation method of the first embodiment according to the present invention is applied. The air-conditioning heat exchanger core 1 includes a plurality of rectangular plate-shaped fins 2 arranged side by side at predetermined intervals, and a tube 3 that penetrates the plurality of fins 2 and is joined so as to be in contact with each other. This is a device that allows air to flow between a plurality of fins 2 and the tube 3 to exchange heat with a medium (refrigerant) that flows in the tube 3.

The fin 2 is made of, for example, a vertically long rectangular fin material made of an aluminum alloy, and the tube 3 is made of a pipe material made of a copper alloy or an aluminum alloy. In the state of FIG. 1A, tens to hundreds of fins 2 are individually arranged vertically with an interval (fin pitch) of about 1/1 mm to several mm to form a fin group 2A. ing. The tube 3 is arranged so as to penetrate all of the fins 2 arranged vertically adjacent to each other.

As an example, the tube 3 of FIG. 1 is composed of a plurality of straight pipe portions 3A and a plurality of U-shaped elbow pipes 3B. A plurality of straight pipe portions 3A are horizontally arranged so as to penetrate each fin 2 in a right angle direction at a predetermined interval in the vertical direction (length direction of the fin 2) of FIG. 1 (A). Further, in the straight pipe portion 3A protruding to the outside of the fin group 2A, the vertically adjacent ends are connected by the elbow pipe 3B. Due to this structure, the tube 3 is arranged so as to repeatedly penetrate the plurality of fins 2 from the upper side to the lower side thereof in a meandering state as a whole. An inlet portion 3a of a medium (water) is formed at one end of a tube 3 located at the uppermost portion of the fin group 2A, and an outlet portion of the medium (water) is formed at the other end of the tube 3 located at the lowermost portion of the fin group 2A. 3b is formed.
A collar portion (not shown) formed by cutting up the fin 2 is formed around the portion where the straight pipe portion 3A of the tube 3 penetrates the fin 2.

In FIG. 1 (A), the air-conditioning heat exchanger core 1 (B), the fin pitch is denoted by F _P, it denoted the individual thickness of the fins 2 and F _1, the outer diameter of the fin collar portion FD The width along the direction in which the plurality of fins 2 are arranged (the width of the fin group 2A) is described as the core width (L ₃ ), and the height of the fin group 2A is referred to as the core height (L ₁ ). Notated, and the width of the fin group 2A is referred to as the core depth (L ₂ ).

Further, the outer diameter of the tube 3 is referred to as raw tube diameter, the tube inside diameter may be referred to as a mother pipe inner diameter, the tube stage pitch base pipe stage pitch (center-to-center distance between the blank pipe: S _1: FIG. 1 (B )), The number of fins can be calculated by (core width / fin pitch), and the number of tubes can be calculated by (core height ÷ raw tube pitch). A spreadsheet software program to be described later records a relational expression of the number of fins = core width / fin pitch, and the number of fins is automatically calculated from this relational expression and used in the performance evaluation method described later. be able to.

When evaluating the performance of the heat exchanger core 1 for air conditioning shown in FIG. 1, as shown in FIG. 2, the peripheral surfaces of the heat exchanger core 1 for air conditioning except for the front surface and the back surface are covered with a peripheral wall 4 such as a ventilation duct for air conditioning. The analysis is performed assuming that the front and back surfaces of the heat exchanger core 1 are open. By covering the circumference of the heat exchanger core 1 for air conditioning with the peripheral wall 4 of the ventilation duct so that air can be blown from the blower such as a fan to the ventilation duct, the air for cooling is blown from the blower at the target wind speed for air conditioning. It is assumed that it can be sent to the heat exchanger core 1.
In FIG. 2, in order to show and recognize the air-conditioning heat exchanger core 1, the peripheral wall 4, and the air-blowing direction in one figure, the air-conditioning heat exchanger core 1 is blown from an obliquely front direction. However, in the analysis described below, air is blown parallel to each fin 2 and parallel to each fin 2 from the front side to the back side of the heat exchanger core 1 for air conditioning shown in FIG. It is assumed that the air is blown so that the air can escape.

In the present embodiment, air is blown at a predetermined wind speed so as to escape from the front side to the back side of the fin group 2A, and water as a medium (refrigerant) is introduced into the tube 3 from the inlet portion 3a of the tube 3 to enter the outlet portion. The performance of the heat exchanger core 1 for air conditioning is evaluated by discharging water as a refrigerant from 3b.

When performing performance evaluation, as an example, the physical characteristics of air (atmosphere), water (refrigerant), and aluminum can be set as follows.
Atmospheric set temperature: 21 ° C, Atmospheric set relative humidity: 70%, Atmospheric pressure: 1 atm (fixed), Air density: 1.19289264 kg / m ³ , Air viscosity: 1.81819 x ^10-5 Pa · sec, Air The specific heat can be set to 1 kJ / kgK and the thermal conductivity of air can be set to 0.024702542 W / mK.
The density of water: 1000 kg / m ³ , the viscosity of water: 0.00052825 Pa · sec, the specific heat of water: 4.2 kJ / kgK, and the thermal conductivity of water: 0.6 W / mK can be set.
The density of aluminum ^{can be set to 2700 kg / m 3} , the specific heat of aluminum can be set to 0.88 kJ / kgK, and the thermal conductivity of aluminum can be set to 200 W / mK.

If necessary, the density of air, the viscosity of air, the thermal conductivity of air, and the viscosity of water are grasped as function values of temperature as described below, and the function values according to temperature are adopted.
The air density is based on the following equations (9), (10) and (11) (approximate equation of tea tins).
However, in the following equation, P indicates (pressure: Pa), e indicates (actual water vapor pressure: Pa), and e (T) is (water vapor pressure: Pa as a function of temperature T: K). e (SAT) indicates saturated water vapor pressure: Pa.

For the viscosity (viscosity coefficient) μ of air, the formula of Sutherland represented by the following formula (12) is applied, and for the thermal conductivity λ of air, the following formula (13) is applied.
In the following equation, T represents absolute temperature K. Since other physical properties of air are less affected by humidity, they are ignored and assumed to be affected only by temperature, and the density, specific heat, and thermal conductivity are set to the above-mentioned constant values. The physical characteristic value of aluminum is also set to the above-mentioned constant value.

Since the relationship between the viscosity of water and the temperature shown in FIG. 3 is known, it is calculated and used based on the following approximate formula (14) shown in FIG.

Approximately, the viscosity of water has the following relationship.
0 ° C: 1.792, 5 ° C: 1.52, 10 ° C: 1.307, 15 ° C: 1.138, 20 ° C: 1.002, 25 ° C: 0.89, 30 ° C: 0.797, 35 ℃: 0.719, 40 ℃: 0.653, 45 ℃: 0.598, 50 ℃: 0.548, 55 ℃: 0.505, 60 ℃: 0.467, 65 ℃: 0.434, 70 ℃ : 0.404, 75 ° C: 0.378, 80 ° C: 0.355, 85 ° C: 0.334, 90 ° C: 0.315, 95 ° C: 0.298, 100 ° C: 0.282.

FIG. 4 is a configuration diagram showing an example of a performance evaluation device for an air conditioning heat exchanger core used to carry out the performance evaluation method described below.
The performance evaluation device 23 shown in FIG. 4 is a so-called computer, and mainly includes an input means 24, a control unit 25, a storage means 26, and an output means 27.
The input means 24 is, for example, a keyboard for inputting characters and numbers, whereby various information can be input to the storage means 26 or the control unit 25.
The control unit 25 is composed of a so-called CPU (Central Processing Unit), RAM (Random Access Memory), ROM (Read Only Memory), etc., and performs various numerical calculations, information processing, device control, etc. by a program. Can be done.

The storage means 26 is, for example, an information recording medium such as an HDD (hard disk drive) or SSD (solid state drive), and is necessary for executing necessary programs, calculation means 28, and prediction means 29, for example, spreadsheet software. Various information such as processing and calculation by software and their results, and the results obtained by these can be stored, read, and calculated as needed.
The output means 27 is, for example, a monitor, a printer, or the like, and can display various information obtained from a necessary program as needed. The performance evaluation device 23 shown in FIG. 4 has a display monitor type display device as an output means 27.

In addition to the basic operating system (OS), the storage means 26 stores table calculation software, and further stores various information necessary for executing the calculation means 28 and the prediction means 29, which will be described later, for table calculation. Various information required in advance is stored in the software. The performance evaluation device 23 can arbitrarily read out these various types of information and calculate as described later. In addition, it is possible to store and read the calculation results obtained by the spreadsheet software as needed.

For example, Microsoft Excel (trade name) can be used as the spreadsheet software. The spreadsheet software shown here is an example applicable to the present embodiment, and is not limited to the spreadsheet software used in this example.

Using the above-mentioned table calculation software, set the above-mentioned air property value, water property value, and aluminum property value as basic conditions, input various parameters of the heat exchanger core 1 for air conditioning shown below, and enter the following. The performance of the heat exchanger core 1 for air conditioning is evaluated by performing calculations based on the relational expressions described below, which are incorporated in the table calculation software under the conditions described below.

When evaluating the performance of the heat exchanger core 1 for air conditioning, the parameters to be input to the table calculation software are fin pitch: Fp (mm), fin thickness: F ₁ (mm), and fin collar diameter: (mm). , Core width: L ₃ (mm), core height (fin height): L ₁ (mm), core depth: L ₂ (mm), raw tube diameter (diameter of tube 3 through which refrigerant passes): (Mm), inner diameter of raw pipe: (mm: inner diameter of tube 3), raw pipe step pitch (center distance between straight pipe portions 3A arranged above and below): S ₁ (mm), set wind speed (m) / Sec), the set amount of water (L / min), the set temperature (atmospheric temperature: ° C.), the set relative humidity (%), and the water temperature (° C.).

When evaluating the heat exchanger core 1 for air conditioning, as an example of actually inputting parameters into the table calculation software, fin pitch (Fp): 1.2 mm, fin thickness (F ₁ ): 0.1 mm, fins Collar diameter (outer diameter of collar part): 7.7 mm, core width (L ₃ ) 150 mm, core height (L ₁ ) 300 mm, core depth (L ₂ ) 13 mm, raw tube diameter: 7.7 mm, raw tube inner diameter : 6.7 mm, raw pipe stage pitch (S1): 25 mm, set wind speed: 1.5 m / sec, set water volume: 6 L / min, set temperature: 21 ° C, set relative humidity: 70%, water temperature: 50 ° C, etc. You can enter each value in.
As described above, the step of inputting and recording various parameters necessary for the subsequent calculations into the spreadsheet software is referred to as input step S0 in the present embodiment.

Furthermore, as an example of a case of numerical value input, the fin sheets (core width / fin pitch): 125 sheets, the number of tubes (fin height ÷ tube stage pitch = Number): 12, free passage cross-sectional area _A c: _{35339.66737mm} ^2, the representative wind speed: 1.910034956m / sec, Zenden'netsu area _a 0: _945064.549mm ^2, the typical dimension _D ec: _{1.944483797mm,} flow loss coefficient _C D: perform numerical either calculation input as such 0.176308214 , Pressure loss: 2.564871215 Pa can be obtained. The contents of each calculation will be described below.
In addition, the calculation formulas described below necessary for these calculations are individually incorporated in a plurality of cells of the spreadsheet software stored in the storage means 26. Then, as an example of the above-mentioned input values, fin pitch (Fp), fin thickness (F ₁ ), fin collar diameter, core width (L ₃ ), core height (L ₁ ), core depth (L ₂ ), By inputting the raw pipe diameter, raw pipe inner diameter, raw pipe stage pitch (S ₁ ), set wind speed, set water volume, set temperature, set relative humidity, and water temperature, calculate as described below to obtain the following values. be able to.

The free-passing cross-sectional area means an area through which air substantially passes, excluding the area occupied by the fins from the area on the front surface side of the fin group 2A shown in FIG. In other words, the free-passing cross-sectional area is the actual passing volume / apparent passing volume x front cross-sectional area = (actual gap x actual fin passing surface area) / (apparent gap x apparent fin passing surface area) x front cutting Area = (fin pitch-fin thickness) x (tube step pitch x core depth-π x (tube radius) ² ) / (tube step pitch x core depth x fin pitch) x core width x core height.
The typical wind speed means that even if air is blown at a set wind speed of 2.0 m / sec, the speed is reduced by the amount blocked by the fins and the tube. The representative wind speed is the set wind speed x front cross-sectional area / free passage cross-sectional area.
The total heat transfer area means the size of each fin × the number of fins × (the area of the reduction corresponding to the penetration of the tube on the front surface and the back surface of the fin) + the surface area of the tube.

The representative dimension D _ec (wet edge length) means which dimension should be taken when the fluid dimension is taken, and indicates the equivalent diameter (the number of circular tubes having a diameter equivalent to the set of tubes). ) = 4 × Flow path cross-sectional area / Wet edge length = 4 × Free-passing volume / Total heat transfer area = 4 × Free-passing cross-sectional area × Depth / Total heat transfer area. It is a value on the order of substantially the same as the fin pitch, which means that a fluidly equal gap is obtained.
The flow loss coefficient C _D indicates how much loss is generated per unit length, and can be calculated by the following equation (2). However, in (2), _{C D:} flow loss _{coefficient, D} ec :( typical dimension: wetted perimeter: m), _{L t:} air conditioning heat exchanger core of the air flow direction length (m), the above-mentioned air-conditioning in use heat exchanger core 1 core depth: corresponding to L _2.

(2) the L _t in equation assuming L ₂ In the air conditioning heat exchanger core 1 described above, in this case the flow loss coefficient can be derived the following equation (15) and is expressed as C _D.

Flow loss coefficient _{C D} is the (15), in one example described above, since a _{(0.43 + 35.1 × Re × D} ec / 13) -1.07 × D ec / 13, the typical dimension _{D ec:} It can be calculated by substituting 1.944438977 mm and Reynolds number Re: 35974.58645. In the case of the input value of the above example, it can be calculated as 0.176308214.
The pressure loss Δp due to friction can be expressed by the following equation (16). However, in equation (16), the unit of pressure loss Δp due to friction is Pa, ρ: the unit of fluid density (water density) is kg / m ² , f indicates the flow loss coefficient, and L ₂ is the core. indicates the depth _{(m), D ec} denotes wetted perimeter of (m), V represents a typical wind speed (m / sec).
In the various calculation examples described below based on each table described later, each size is displayed in mm, but in the calculation, it is calculated by converting it to m and inputting it.

For the pressure loss Pc of the heat exchanger core 1 for air conditioning, the following pressure loss calculation model can be set. The pressure loss Pc of the heat exchanger core 1 for air conditioning is given by the following equation (1) and the above equation (2). (1) and (2), Pc: pressure loss in the heat exchanger core for air conditioning, _{C D:} flow loss coefficient, [rho: density _{^{(kg / m 3), U}} c: air conditioning heat exchanger core There wind passing _{(m / sec), D ec} :( typical dimension: wetted perimeter: m), _{L t:} air conditioning heat exchanger core of the air flow direction length (m), Re: a Reynolds number. In addition, U _c is the total area where fins and tubes do not exist when the front projected area A _f and _Ac (free passage area: air conditioning heat exchanger core is viewed along the air flow direction) with respect to the front wind velocity U _0. Area) can be multiplied and U _c = U ₀ ( _Ac / A _f ) can be used.

Here, the typical dimension D _ec is wetted perimeter is the length given by the following equation (3). In equation (3), _Ac : free passage area, A _o : total heat transfer area.

In the relationship between the above equations (1), (2) and (3), the dimensions and the front wind speed of the heat exchanger core 1 for air conditioning can be easily obtained, so that the pressure loss Pc is these (1) to (3). ) Can be obtained from the equation.
As shown in Eq. (1), the pressure loss Pc is the flow loss coefficient ( _CD ) × {core depth (L2) / representative dimension (D _ec )} × (density (ρ) × representative wind speed ² ) / 2. Therefore, in the above example, it can be calculated as 2.564871215Pa. In the present specification, the execution of the calculation by the calculation model from the above relational expression to the calculation of the pressure loss Pc in the spreadsheet software is referred to as the first step performed by the first calculation means.

Next, the average heat transfer coefficient (h) in the tube of the heat exchanger core 1 for air conditioning can be obtained as the Nusselt number Nu. The Nusselt number Nu can be expressed by the following equations (4) and (5).
In the following equation (4), Re: Reynolds number, Pr: Prandle number, _Ipt : Fin spacing (m), Nusselt number: Nu (dimensionless number) = hL / λ, and (5) ), H is the thermal conductivity, λ: the thermal conductivity of the fin material (W / mK), and L is the representative length or the representative dimension: _Dec.

3.66 can be adopted when the flow of the refrigerant in the tube is laminar in the Nusselt number Nu, but in the case of the heat exchanger core 1 for air conditioning, the refrigerant (water) flowing inside the tube 3 is in a turbulent state. In the case of turbulent flow, it is considered that there is, and the following equation (8) is followed.
In the equation (8), as an example, the values of Re (bare tube Re) of the tube 3 = 35974.58645, Pr of water = 3.679775, Re of the core atmosphere = 243.6735586, Pr of the atmosphere = 0.73603242, and the like are used. It can be adopted after calculation.

Re can be obtained by the following formula (17), and Pr can be obtained by the following formula (18).
However, in equation (17), ρ indicates the density (kg / m ³ ), v indicates the average velocity (m ² / sec), L indicates the characteristic length (m), and μ indicates the viscosity of the air (m). Viscosity coefficient) is shown.
In equation (18), v indicates the average velocity (m ² / sec), α indicates the thermal diffusivity (m ² / sec), η indicates the viscosity (Pa · s), and Cp indicates the specific heat (J / sec). kg), where k represents the thermal conductivity of air (W / mK).

Further, regarding the root temperature of the fin 2, it is assumed that there is no thermal resistance due to the joining of the fin 2 and the tube 3, and the root temperature of the fin 2 is the same as the surface temperature of the tube 3.
In the present specification, the execution of the calculation by the calculation model from the above relational expression to the calculation of the average heat transfer coefficient h in the spreadsheet software is referred to as a second step performed by the second calculation means.

Next, regarding the heat transfer between the fin 2 and the air, the fin 2 is divided into 20 in the air flow direction, and the difference method is used on the assumption that the temperature of the air gradually rises.

As an example, when the above-mentioned Re and Pr are substituted into the above equation (8), the Nusselt number Nu = 156.9705096 and the heat transfer coefficient in the tube h = 14057.06056 are obtained in the heat transfer between the refrigerant (water) and the tube 3. be able to.
In the heat transfer between the fins 2 and the air, the Nusselt number Nu = 7.329502525 and the core heat transfer coefficient h = 93.11332245 can be obtained with respect to the above equation (4).
As for the refrigerant flowing inside the tube 3, 3.66 can be applied when the flow is a laminar flow, but since it can be clearly assumed to be a turbulent flow in this embodiment, the calculation is performed using the above equation (8). do.

Next, the fin efficiency ηf will be described.
When the fin efficiency ηf is 1, the fin has an ideal efficiency, but when the fin efficiency ηf decreases, a temperature difference occurs between one end and the other end of the fin, for example, 100: 1. The fin efficiency ηf has the relationship shown by the following equations (6) and (7).
In the equation (6), the temperature distribution of the fin has a uniform average temperature θm, and θm is the fin efficiency ηf, which can be obtained from the _{fin root temperature θ 0} and the outside air temperature t _0. Regarding the root temperature of the fins, it is assumed that there is no thermal resistance due to the joining of the fins 2 and the tube 3, and the surface temperature of the tube 3 and the root temperature of the fins 2 are assumed to be the same temperature.
In the equation (7), df is the tube height pitch, dc is the tube depth pitch (in the case of one tube, the depth dimension (m), and F ₁ is the fin thickness (mm).

Next, air passage time: 0.006806158 sec, unit time passage air weight: 0.080520253 kg / sec, water path length (core width x number): 1800 mm, water passage time (water path length ÷ flow velocity): 0. The amount of water in the raw pipe is 634617424 sec, 0.010576957 kg, and the amount of water passing through ΔT (divided by 20 because it is per element) 0.003173087.
The air passage time indicates how long the air passes through the fin group 2A according to the wind speed, and is the length of the straight pipe portion 3A except for the curved elbow pipe 3B portion of the tube 3 due to the water path length. Only used is used, and the amount of water in the raw tube indicates the amount of water present in the entire tube 3.

Next, when evaluating the performance of the heat exchanger core 1 for air conditioning shown in FIGS. 1 and 2, the region where the air flows from the upstream side to the downstream side of the air flow is divided into 20 regions excluding the inlet region and the outlet region. It will be described that the evaluation is performed by dividing the region where the water flows from the upstream side to the downstream side of the water flow into 20 parts excluding the inlet region and the outlet region.
When each parameter as an example described above is used, the region where the air flows is divided into 20 parts excluding the inlet region and the outlet region for evaluation. When analyzing the air flow region and the water flow region by dividing them into 20 parts excluding the inlet region and the outlet region, the tube 3 penetrates the fin group 2A in a meandering state, so that the calculation and analysis are simplified. As shown in FIG. 5, assuming that the tube 3 is one straight pipe 3C in the length direction, the straight pipe 3C is divided into 20 parts in the length direction excluding the inlet region and the outlet region for analysis. ..
If the straight pipe 3C 20 divides, as shown in FIG. 5, if the water T _{W1 (°} C.) from the inlet end 3a of the straight tube 3C has flowed, the water temperature T _W in a particular division region, T is in the following areas _W + ΔT _W (° C). On the other hand, the air flow is directed in the direction perpendicular to the water flow direction and flows along the fin 2 in the width direction thereof.

For each of the inlet region and the 20-divided region, the temperature Tf of the air, the temperature Te after passing through the fins of the air, the temperature T (° C.) of the water, and the time (time: sec) of passing through the 1-divided region for each of the above-mentioned conditions. Table 1 below shows the results of determining the heat removal amount q (W), the water temperature (° C.), and the temperature T _{c of the water after passing through the divided region by the difference method.}

The temperature Tf for each region shown in Table 1 is obtained by fin efficiency × (water temperature in Table 1 − inlet atmospheric temperature) + inlet atmospheric temperature. As explained in the above equation (6), the fin temperature distribution has a uniform average temperature θm, and θm is a function of the fin efficiency ηf, from the fin root temperature θ ₀ and the outside air temperature t _0. This is because it can be obtained.
Since water flows along the tube 3 while air flows along the fins 2, the direction in which water flows and the direction in which air flows differ by 90 °. Therefore, in the case of water, the tube 3 is regarded as one straight pipe, and the difference method is used in consideration of the case where air passes through each region of the straight pipe divided into 20. The fin 2 is calculated by the difference method for each region divided into 20 in the direction of air flow.

The temperature of the tube 3 is different for each region, and the temperature of the air is affected by the temperature of the tube 3. Taking this into consideration, Table 1 shows the corrected temperature (temperature after passing through the fins of air) Te after being affected by the temperature received from the tube 3 in each region divided into 20 by regarding the tube 3 as a straight pipe. It will be as described. When the influence of the temperature received from the tube 3 is taken into consideration, the following equation (19) can be used.
However, in the following equation (19), of the inlet region and each of the 20-divided regions, a _f indicates the fin heat transfer area _{per region, a p} indicates the tube heat transfer area per region, and Ts. Indicates the surface temperature of the fin, T _c indicates the root temperature of the fin, and a indicates ( _af + a _p ).

In Table 1, the temperature T of water has the relationship shown by the following equation (20). However, in the following (20), T ₁ is the inlet temperature, T ₂ is the temperature of the outlet, T _e is out of the 20 divided regions, showing temperature e th region, h is the water pipe tube Indicates the heat transfer coefficient with, a indicates ( _af + a _p ), g indicates the weight of air passing through in a unit time, and C _p indicates the specific heat of air.
The water temperature shown in Table 1 means that the water entering at 50 ° C. gradually decreases in the straight pipe. The water temperature was first obtained for each of the 20 divided regions, and then the temperature change of the air for each region was obtained. The results are the results in Table 1. The results in Table 1 will be described again with reference to Table 5 in association with the examples shown in Tables 2 to 5 which will be shown later as calculation examples.

In Table 1, the column described as time is the time required for water to pass through one of the 20 divided regions: Δt.
The amount of heat removed is calculated by multiplying the water temperature, the temperature difference, and the heat transfer coefficient of the heat exchanger core obtained earlier by Δt × area × time. The calculation for air also obtains how much heat is removed from each of the 20 divided regions according to the above equation (19).
Regarding the air flowing into each region, the water temperature is different for each region, so the air temperature will change. Therefore, if you take the average, you can see how much the air has dropped.
As shown in Table 1 in the spreadsheet software from the above relational expression, the third calculation means in the present specification performs the calculation by the calculation model until the temperature of the air is obtained by the difference method for each divided region of the air. It is called step 3.
In the present specification, the fourth calculation means performs the calculation by the calculation model from the above relational expression to the calculation of the water temperature by the difference method for each division region of the water as shown in Table 1 in the spreadsheet software. It is called step 4.

In the results shown in Table 1, if the temperature of the air at 37 ° C. becomes 53 ° C., the temperature rises by 16 ° C., and the amount of heat taken by the air can be obtained.
The average (ave.) Of the water temperatures shown in Table 1 is 37.03069261 ° C.
From the relationships shown in Table 1,
Air ΔT = 16.03069261, → Air endothermic: 1290.795428W
ΔT of water = -2.406538843, → Endothermic water: -1010.746163W
Can be calculated.
In the case shown in Table 1, the air temperature difference is 20 ° C., the calorific value is 1610.405604J, the water temperature difference is 5.2 ° C., and the calorific value is 2184J.

The air ΔT becomes 16.03069 on average (ave.): 37.03069261 ° C.-21 ° C. (set temperature). From here, the endothermic air is the unit time weight of the air passing through the heat exchanger core (calculation example described later, the value shown in the 26th row of the D column of Table 2) × air ΔT (16.03069) × specific heat of air × It becomes 1000 (mm).
The unit-time weight of air passing through the heat exchanger core (values shown in Table 2, column D, row 26) means the unit-time weight of air passing through the heat exchanger core at a set wind speed. The value of the unit time weight is a value such as 0.080520253 kg / sec as shown in the calculation example of Table 2 described later.
Therefore, when the above calculation is performed, the air ΔT becomes a value such as 1290.785428W as in the calculation example of Table 2 described later.

The ΔT of water is the temperature difference of 2.40645 between the temperature of the 20th region in Table 1 and the temperature of the first 50 ° C. The endothermic process of water is ΔT of water × specific heat × 1000 × (value obtained by converting the set flow rate of water from the flow velocity to the amount of water per unit time).
As a value obtained by converting the set flow rate of water from the flow velocity to the amount of water per unit time, it is a value such as 0.1 kg / sec in the calculation example of Table 2 described later.
Therefore, when the above calculation is performed, the value of ΔT of water becomes −1010.746163W as shown in the calculation example of Table 2 described later.

Originally, the values of air endothermic and water endothermic should match, but these values usually do not match. It is considered that this is because the relationship between the thermal resistance of the fin 2 and the tube 3, the thickness of the tube 3 is not uniform, or the various coefficients and theories set up to this point include some error components.
Therefore, in the present embodiment, among the variously set coefficients and theories, the heat transfer in the pipe is likely to include an error and the contact heat resistance between the fin and the tube is not taken into consideration. VBA (Visual Basic for) is a solver that comes with Microsoft Excel (trade name) to balance air heat absorption and water heat absorption by setting a coefficient for (heat absorption depending on the temperature) and increasing or decreasing this coefficient. Applications) It can be carried out by executing it internally, and the correct answer is obtained when the endothermic and water endothermic values are minimized by manually increasing or decreasing the water transfer coefficient in the pipe.

By adjusting under the conditions of the calculation example shown in Table 2 described later so that the values of air endothermic and water endothermic match.
Air outlet temperature: 37.03069261 ° C., dt: 16.03069261,
Water outlet temperature: 47.59346152 ° C., dt: -2.4565384883,
Pressure loss: 2.564871215 can be determined. From these, it is possible to know at what temperature the water comes out and at what temperature the air passes through the fin 2. In addition, it is possible to know what value the pressure loss of the heat exchanger core 1 before and after that is.
In the specification of the present application, the calculation of the calculation model is carried out from the above relational expression to increasing or decreasing the transmission rate in the pipe of water in the spreadsheet software and adjusting the numerical values so that the values of air endothermic and water endothermic match. This is referred to as a fifth step performed by the calculation means.

As described above, the fact that the air outlet temperature and the water outlet temperature of the heat exchanger core 1 for air conditioning can be calculated means that the fin pitch (Fp), fin thickness (F ₁ ), fin collar diameter, which were input at the beginning, Core width (L ₃ ), core height (L ₁ ), core depth (L ₂ ), raw tube (tube) diameter, raw tube (tube) inner diameter, raw tube (tube) step pitch (S ₁ ), set wind speed , It is equivalent to being able to calculate and understand how the air outlet temperature and the water outlet temperature are affected according to the set water volume, set temperature, set relative humidity, and water temperature value. That is, the temperature change of the refrigerant, the temperature change of the passing air, and the pressure loss are estimated and evaluated in the heat exchanger core 1 for air conditioning due to the influence of the size, wind speed, water volume, temperature, etc. of each part of the heat exchanger core 1 for air conditioning. be able to.

In the present embodiment, the performance evaluation device 23 of the heat exchanger core 1 for air conditioning stores the above-mentioned calculation formulas, various basic data, calculation parameters, and the like in the storage means 26, and these are input from the input means 24. The control unit 25 has a function of performing calculations on the above-mentioned table calculation software according to basic data and calculation parameters, and calculating pressure loss, air outlet temperature, and water outlet temperature.
The calculation performed as described above can be performed using, for example, general commercially available spreadsheet software for personal computers. The spreadsheet software used is not limited to the above.

The spreadsheet software can apply a calculation formula to each cell, and can apply the calculation result in each cell to a calculation formula in another cell as needed to perform another calculation.
In addition, it has a function of comparing the results obtained in each cell and recalculating the specific calculation result and the numerical value of the specific calculation result so as to be extremely close to 0 by executing the above-mentioned solver function with VBA.
By using the above-mentioned function, the performance evaluation device 23 can calculate so that the values of air endothermic and water endothermic match, and as a result, all the cases where the values of air endothermic process and water endothermic process match. The input conditions and necessary parameters are displayed on the output means 27 so that the user can grasp them.

Hereinafter, Tables 2 to 5 show an example of the result of laying out by substituting various numerical values and various calculation formulas as an example of the above into each cell shown by a matrix of spreadsheet software.
Table 2 shows a state in which each numerical value as an example described above is entered in each cell of the A column to the F column and the first row to the 43rd row of the spreadsheet software.

As shown in Table 2, the A column, second row C, the first row to the 43 row, as the core size, the fin pitch Fp: 1.2 mm, the fin thickness _F 1: 0.1 mm, fin collar diameter 7 .7 mm, core width L ₃ : 150 mm, core height L ₁ : 300 mm, core depth L ₂ : 13 mm, raw pipe diameter (raw pipe: pipe through which refrigerant passes) 7.7 mm, raw pipe inner diameter 6.7 mm, raw pipe stage Pitch (distance between centers of raw pipes) S ₁ : 25 mm, number of fins 125, number of raw pipes (height ÷ raw pipe pitch = number), free passage cross-sectional area 35339.66737 mm ² , representative wind speed 1.910034956 m / Sec, total heat transfer area 945064.549 mm ² , representative dimensions 1.944438977 mm, flow loss coefficient 0.176308214, pressure loss 2.564871215 Pa are entered.

As shown in Table 2, in columns D to F and rows 1 to 16, the atmospheric conditions are set temperature 21 ° C, set relative humidity 70%, atmospheric pressure 1 atm (fixed), water: water temperature 50 ° C. Is written.
In columns A to D, rows 26 to 43, set wind speed 1.5 m / sec → 0.080520253 kg / sec, set water volume 6 L / min → 0.1 kg / sec, convert water volume to in-pipe flow velocity → 2.833545522m / sec, air / water heat capacity 0.191714889, H11 × B33 / (B10 / 1000) × 3, area, k consideration 0.19008171, heat transfer in piping, Nu (not used because it is actually turbulent flow) 3 .66, flow layers (Re <2300), Nu156.9705096 turbulence, h; right in formula α14057.06056W ^{/ m} 2 K, the core heat transfer, Nu7.329502525, h; the right expression alpha, 93.11332245W Regarding / m ² K and fin efficiency ηf, φ, df = 0.015796683, φl, ηf = 0.928878624 are entered.

Further, as shown in Table 2, calculation buttons for performing calculations are arranged in columns D to F and rows 18 to 23. When this calculation button is clicked by mouse operation on the screen of a personal computer running spreadsheet software, the above-mentioned solver operates in VBA, and the air outlet temperature shown in Table 3 described below is displayed. The water outlet temperature and pressure loss are calculated and displayed.

Table 3 shows a state in which each numerical value as an example described above is entered in each cell of the A column to the C column and the 47th row to the 72nd row of the spreadsheet software.
Air passage time 0.006806158 sec, unit time passage air weight 0.080520253 kg / sec, ΔT passage air volume (B47 x B48 divided by 20 elements), 2.74017E-05 kg, water path length (core) Width x number) 1800 mm, water passage time (water path length ÷ flow velocity) 0.634617424 sec, water volume in raw pipe 0.0105676957 kg, ΔT passage water volume (divided by 20 because it is per element) 0.003173087, air outlet temperature 34 Enter .50516463 ° C, dt13.50516463, water outlet temperature 44.9431159 ° C, dt-5.56884914, pressure loss 2.564871215Pa, air temperature difference 20, calorific value 1610.405604J, water temperature difference 5.2,2184J. doing.

The amount of water passing through ΔT described in the 54th row of the A column of Table 3 is obtained by multiplying 0.1 kg / sec described in the 27th row of the D column by 0.031730871 described in the 55th row of the H column of Table 5. Can be obtained.
The dt of the air described in the 58th row of the A column of Table 3 is 37.03069261 described in the 57th row of the B column and the atmospheric set temperature of 21 ° C. described in the 2nd row of the E column of the table 2. It can be grasped as a temperature difference.
The dt of the water described in the 60th row of the A column of Table 3 is the temperature difference between 47.59346152 described in the 59th row of the B column and the water temperature of 50 ° C. described in the 16th row of the E column of Table 2. Can be grasped.

Table 4 shows a state in which each numerical value as an example described above is entered in each cell of the G column to the I column and the first row to the 27th row of the spreadsheet software.
As air physical characteristics, density 1.19289264 kg / m ³ , viscosity 1.81819E-05Pa · sec, specific heat 1: kJ / kgK, thermal conductivity 0.024702542 W / mK, water (refrigerator) physical properties, density 1000 kg / m ³ , Viscosity 0.00052825 Pa · sec, Specific heat 4.2 kJ / kgK, Thermal conductivity 0.6 W / mK, Al physical characteristics, Density 2700 kg / m ³ , Specific heat 0.88 kJ / kgK, Thermal conductivity 200 W / mK ing.
Further, the dimensionless numbers are displayed as Re (bare tube) 35974.58645, Pr (water) 3.69775, Re (core atmosphere) 243.6735586, and Pr (atmosphere) 0.73603242.

As shown in Table 5, in the cells of the spreadsheet software, the numerical values shown in Table 1 as an example of the above are entered in the cells of columns D to K and rows 52 to 76. Is shown.
The numerical values entered in these rows and columns are the temperature distribution of air by the difference method (Tf, Te) shown in Table 1 and the temperature distribution of water by the difference method (T2, time, heat removal amount, water temperature, color part temperature: It is equivalent to Tc). Tf indicates "((fin efficiency × (water temperature-inlet air temperature))-inlet air temperature)", and Te is the temperature of the e-th region (temperature after passing through the fins of air) in the 20-divided regions, T. ₁ is the inlet temperature, T ₂ is the outlet temperature, and time is the time for water to pass through one of the 20 divided regions.
As shown in Table 5, in the cells of the spreadsheet software, the states in which the numerical values indicating the calculation results as an example of the above are described in the cells from the D column to the K column and the 78th row to the 88th row are shown. show.
In these rows and columns are Ave37.03069261, Air ΔT: 16.03069261 → Air endothermic 1290.79543W, ↓↑ Sum 280.049652, Coefficient → 1, Water ΔT: -2.406538 Water endothermic, -1010.746163W, air test QfromCP-1290.795428W, water test Qfrom, 1010.746163W, af0.045257531, ap0.0019995697.

The values displayed in the above cells shown in Table 5 indicate that the values of air endothermic (air ΔT) and water endothermic (water ΔT) are different.
Therefore, it is recalculated so that the difference between air endothermic process and water endothermic process is eliminated or minimized by multiplying the calorific value of water described in column B, row 34, shown in Table 2 by a slight coefficient. By doing so, it is possible to evaluate the performance of the heat exchanger core 1 for air conditioning.
In the present embodiment, for example, the calculation can be completed when it becomes 0.000001 or less.

As a result of the calculation of each step described above, as shown in columns A to C and 57th to 61st rows of Table 3, the air outlet temperature: 37.03069261 ° C., the water outlet temperature 47.59346152 ° C., Pressure loss: 2.564871215 Pa can be determined.
The calculation described above assumes that the relational expression of air velocity x total fin area x inlet / outlet air temperature difference x specific heat = amount of medium x specific heat x inlet / outlet temperature difference holds, and the values on the left and right sides of the above equation When the value on the left side and the value on the right side are the smallest by repeating the method of selecting a condition that has a large effect in the calculation process (for example, the amount of heat of water), making fine adjustments, and recalculating when there is a deviation. It means that the calculation is completed under the condition of.

FIG. 6 shows the outlines performed in the first step S1 to the fifth calculation means by the first calculation means and the fifth step S5 by the fifth calculation means, starting from the input step S0 of various parameters according to the procedure described so far. It is a flowchart which shows.
In the present embodiment, the pressure loss when air flows is obtained in the first step S1 by the calculation model adopted in the first calculation means shown above, the average heat transfer rate is obtained, and the calculation means is adopted in the second calculation means. The temperature distribution of the fins was obtained in the second step S2 by the calculated calculation model, the temperature of the air in each divided region was obtained in the third step S3 by the calculation model adopted in the third calculation means, and the fourth calculation means was used. In the fourth step S4 of the adopted calculation model, the temperature of water for each divided region is obtained, and in the fifth step S5 of the calculation model adopted in the fifth calculation means, the amount of the medium, the air outlet temperature, and the water outlet temperature are determined. I was able to calculate and estimate the pressure loss.

"Calculation example 2"
In Tables 6 to 10, when the input step S0 and the first steps S1 to 5 in the first embodiment are carried out, the dimensions of each part of the heat exchanger core 1 for air conditioning and other input conditions are appropriately changed. The calculation example 2 in the case of the calculation is shown.

The set temperature, set relative humidity, atmospheric pressure, and water temperature described in the cells of columns D to I and rows 1 to 16 shown in Table 6 are the same as in the previous example, and the air density and air viscosity are the same. , Air specific heat, air heat conductivity, water density, water viscosity, water specific heat, water heat conductivity, aluminum density, specific heat, heat transfer rate are the same as the previous example.
In this example, the fin pitch, fin thickness, core width, core height, core depth, number of fins, number of raw pipes, raw pipe diameter, and raw material described in columns A to C and 1st to 27th rows. The inner diameter of the pipe and the pitch of the raw pipe are the same as in the previous example, but the input values of the set wind speed of 2 m / sec and the set water volume of 16 L / min are different.
Among the dimensionless numbers, Re (bare tube) 95932.23055, Pr (water) 3.69775, Re (core atmosphere) 326.2028897. It can be calculated as Pr (atmosphere) 0.73603242.

When these values are entered, the free passage cross-sectional area is 35339.66737 mm ² , the representative wind speed is 2.546713274 m / sec, the total heat transfer area is 945064.549 mm ² , the representative dimensions are 1.944438977 mm, the flow loss coefficient is 0.146636033, and the pressure loss is 3. It can be calculated as .792374293Pa.
When these values are input, the number of Nusselt numbers for heat transfer in the pipe Nu: 344.0274164, h: 1940930.797 W / m ² K, the number of Nusselt numbers for core heat transfer: Nu 8.201138032, h: 30808.42535 W / m ² With respect to K and fin efficiency ηf, it can be calculated as φ: 144.11316205, φl: 0.814343656, ηf: 0.825179927.

From these, as shown in Table 7, the root temperature (θ ₀ ), average temperature (θm), air passage time (), unit time passing air weight, ΔT passing air amount, water path length, water passing time, inside the pipe. The amount of water and the amount of water passing through ΔT can be obtained.
Further, as shown in columns D to G and rows 52 to 76 of Table 9, the temperature of the air passing through the fins is obtained for each region when divided into 20 regions, and the temperature of the air passing through the fins is obtained by the difference method, and the H in Table 9 is obtained. As shown in columns to columns I and 52 to 76, the temperature of water passing through a straight tube can be obtained by the difference method for each region when divided into 20 regions.

By the calculation of each of these steps, it can be calculated that air ΔT: -19.085823 → air endothermic: −2040.76814W, and water ΔT: −1.82211382 → water endothermic 2040.76748W.
Since the values of endothermic air and water and water absorption were almost the same, as shown in Table 7, the air outlet temperature: 40.585823 ° C., dt: 19.805823, the water outlet temperature 48.17787862 ° C., dt: -1. .822118, pressure loss: 3.79237429Pa could be determined.

Comparing the first calculation example described based on Tables 1 to 5 and the second calculation example described based on Tables 6 to 9, the size of the applied heat exchanger core 1 is the same. , The set wind speed is changed from 1.5 m / sec to 2.0 m / sec, and the set water volume is changed from 6 L / min to 16 L / min.
As a result, in the first calculation example, as shown in Table 3, the air outlet temperature: 37.03069261 ° C., the water outlet temperature: 47.59346152 ° C., and the pressure loss: 2.564871215Pa can be obtained, and the second calculation. In the example, as shown in Table 7, the air outlet temperature: 40.585823 ° C., the water outlet temperature: 48.17787862 ° C., and the pressure loss: 3.79237429Pa could be obtained.

From these contrasts, there is a feature that the air temperature and water temperature itself can be obtained under different conditions. The values of air temperature and water temperature obtained in this way are indicators of performance evaluation. In addition, it is possible to consider how much the influence will occur by changing each parameter used in the calculation as described above.
That is, it is possible to simulate which of the various conditions of the heat exchanger core 1 is changed and how the characteristics of the heat exchanger core 1 are affected by using the technique of the present embodiment. Recognize.

Further, according to the performance evaluation method according to the first to fifth steps described so far, for example, the heat exchanger core for air conditioning does not change the conditions of the wind speed and the refrigerant (water) added to the heat exchanger core for air conditioning. Only the size can be changed and calculated, and only the difference between the air outlet temperature, the water outlet temperature and the pressure loss can be calculated.
For example, when the size of the heat exchanger core for air conditioning is calculated as 150 mm (core width) x 300 mm (core height) x 13 mm (core depth), and the size of the heat exchanger core for air conditioning is 50 mm (core width) x When calculated as 100 mm (core height) × 13 mm (core depth), the difference between the air outlet temperature, the water outlet temperature, and the pressure loss alone can be calculated and compared.

As a result of calculation with a heat exchanger core having a size of 150 × 300 × 13 mm in the second calculation example, as shown in Table 7, the air outlet temperature: 40.585823 ° C., the water outlet temperature: 48.177882 ° C., and the pressure loss. : 3.79237429Pa could be obtained.
On the other hand, when calculated with a heat exchanger core having a size of 50 × 100 × 13 mm, the core dimensions are fin pitch Fp: 1.2 mm, fin thickness F ₁ : 0.1 mm, fin collar diameter 1 mm, and core width L _3. : 100 mm, core height L ₁ : 50 mm, core depth L ₂ : 13 mm, raw pipe diameter (raw pipe: pipe through which refrigerant passes) 7.7 mm, raw pipe inner diameter 6.7 mm, raw pipe step pitch (between the centers of the raw pipe) Distance) S ₁ : 25 mm, number of fins 84, number of raw pipes (height ÷ raw pipe pitch = number), free passage cross-sectional area 3926.629707 mm ² , representative wind speed 2.546713274 m / sec, total heat transfer area 104587 .1434 mm ² , representative dimensions 1.95222969 mm, flow loss coefficient 0.146519069, pressure loss 3.774191922 Pa, set wind speed 2 m / sec, set water volume 16 L / min.
By performing this calculation, it can be calculated that the air outlet temperature: 41.23052979 ° C., dt: 20.23059279, the water outlet temperature: 49.78452812 ° C., dt: −0.215471876, and the pressure loss: 3.774419922Pa.

From this result, it can be seen that even when the size of the heat exchanger core for air conditioning is changed from the size of 150 × 300 × 13 mm to the size of 50 × 100 × 13 mm, the similar air outlet temperature and water outlet temperature can be obtained. It can be calculated, and it can be seen that the set water volume and the set wind speed can be calculated in the same way.
As described above, by implementing this embodiment, the temperature of the air and the temperature of the water passing through the heat exchanger core for air conditioning are changed by changing the size of the heat exchanger core for air conditioning and other test conditions. It will be possible to understand how much the temperature will change and how much pressure loss will occur, and to estimate the temperature and water temperature of the air passing through the heat exchanger core for air conditioning.

Hereinafter, for the purpose of general explanation of the calculation example 2, in the calculation examples shown in Tables 6 to 9, the main parameters described in each cell can be obtained from the following simplified relational expressions.
In the following simplified relational expression, as an example, B2 means the numerical value written in the cell of the second row of the B column, and B11 means the numerical value written in the eleventh row of the B column. In each of the following equations, PI () indicates a function of pi in spreadsheet software, and substantially indicates 3.141592.
Free passage cross-sectional area = (B2-B3) x (B11 x B8-PI () x (B9 / 2) ² ) / (B2 x B8 x B11) x B6 x B7
Representative wind speed = B6 x B7 / B17 x B26
Total heat transfer area = B7 x B8 x B14 x 2-PI () x (B9 / 2) ² x B14 x B15 + PI () x B9 x (B2-B3) x B14 x B15
Representative dimensions = 4 x B17 x B8 / B19
Flow loss coefficient = (0.43 + 35.1 × (H26 × B21 / B8) ^-1.07 ) * B21 / B8
Pressure loss = B22 × B8 / B21 × H2 × B18 2/2

(Heat transfer in piping) Nu = 0.023 x H23 ^0.8 x H24 ^0.3333
h = H11 × B33 / (B10 / 1000)
(Core heat transfer) Nu = 2.1 × (H26 × H27 × B21 / B8) ^0.38
h = H5 x B37 / (B21 / 1000) x 2
φ = (2 × B38 / (H16 × (B3 / 1000))) ^0.5
φ1 = B41 × ((B8-B9) / 2+ (B11-B9) / 2) / 2/1000
ηf = 1 / B42 × (EXP (B42) -EXP (-B42)) / (EXP (B42) + EXP (-B42))
Average temperature = B43 x (E45-E2) + E2
Air passage time = B8 / B18 / 1000
Air volume passing per unit time = B17 / 1000/1000 x B18 x H2
Amount of air passing through ΔT = B48 × E55
Water path length = B6 x B15
Water transit time = B51 / D28 / 1000
Containing tube water ^{= PI () × (B10 /} 2) 2/1000/1000 × B6 × 2/1000 × H8
Amount of water passing through ΔT = D27 × H55

Air outlet temperature = G78
dt = B57-E2
Water outlet temperature = J74
dt = B59-E16
Pressure loss = B23
Calorific value = D26 x B68 x H4 x 1000
Water temperature difference (W) = D27 x H10 x B71 x 1000

Air ΔT = −E2 + G80
Water ΔT = −K54 + K74
Atmosphere QfromCP = (E2-B57) x B48 x H4 x 1000
Water test Qfromh = (E16-B59) x D27 x H10 x 1000
Air endothermic = D26 x G80 x H4 x 1000
Water endothermic = G83 x H10 x 1000 x D27
Sum = I80 + I83

1 ... Heat exchanger core for air conditioning, 2 ... Fins, 3 ... Tubes (bare pipes), 3A ... Straight pipes, 3a ... Inlets, 3B ... Elbow pipes, 3b ... Outlets, 23 ... Performance evaluation devices, 24 ... Input means, 25 ... Control unit, 26 ... Storage means, 27 ... Output means, 28 ... Calculation means, 29 ... Prediction means,
S0 ... Input step, S1 ... First step by the first calculation means, S2 ... Second step by the second calculation means, S3 ... Third step by the third calculation means, S4 ... Fourth calculation Fourth step by means, S5 ... Fifth step by means of fifth calculation means.

Claims (21)

A plurality of fins arranged side by side at predetermined intervals and a tube joined so as to be in contact with the plurality of fins are provided, and air is circulated between the plurality of fins and the tube to allow air to flow between the plurality of fins and the medium in the tube. This is a performance evaluation method for an air-conditioning heat exchanger core that exchanges heat between the fins and the fins.
Obtain the pressure loss and average heat transfer coefficient when air flows along the fins of the heat exchanger core for air conditioning, and assume that the temperature distribution of the fins has a uniform average temperature, and fin efficiency and fin roots. Obtain the temperature distribution of the fins from the temperature and the outside air temperature,
Assuming that the heat transfer between the medium and the tube has a turbulent heat transfer coefficient relationship,
The fin is divided into a plurality of parts along the flow direction of the air, and the temperature of the air is obtained by a difference method for each divided region of the air.
The tube was regarded as one straight pipe and divided into the same number as the divided regions of the air, and the temperature of the medium was obtained for each divided region of the tube.
Assuming that the relational expression of air wind velocity x total fin area x inlet / outlet air temperature difference x specific heat = medium amount x specific heat x inlet / water temperature difference holds, the amount of the medium is obtained by solving this relational expression, and the air outlet is further obtained. A method for evaluating the performance of an air conditioner core, which is characterized by obtaining the temperature and the water outlet temperature. Assuming that the relational expression of air velocity x total fin area x inlet / outlet air temperature difference x specific heat = amount of medium x specific heat x inlet / output medium temperature difference holds, when solving this relational expression, a coefficient is added to the heat transfer coefficient of the medium. The method for evaluating the performance of the heat exchanger core for air conditioning according to claim 1, wherein the calculation result on the left side and the calculation result on the right side of the above equation are combined by multiplying by. As a pressure loss calculation model when air is circulated through the air conditioning heat exchanger core, the pressure loss Pc of the air conditioning heat exchanger core is expressed by the following equations (1), (2), and (3). The method for evaluating the performance of an air conditioning heat exchanger core according to claim 1 or 2, wherein it is assumed to be represented.
However, in (1), (2), Pc: pressure loss in the heat exchanger core for air conditioning, _{C D:} flow loss coefficient, [rho: density _{^{(kg / m 3), U}} c: air conditioning heat exchanger core the wind passing through the air (heat exchanger passes wind _{speed: m / sec), D ec} :( typical dimension: wetted perimeter: m), _{L t:} air conditioning heat exchanger core of the air flow direction length (m), Re: Reynolds number, in equation (3), _Ac : free passage area (total area where fins and tubes do not exist when the air conditioning heat exchanger core is viewed along the air flow direction), A _o : Total heat transfer area.

As a temperature calculation model, the average heat transfer of the heat exchanger core for air conditioning is obtained in relation to the Nusselt number Nu represented by the following equation (4), and the Nusselt number is related to the heat transfer coefficient h. The method for evaluating the performance of a heat exchanger core for air conditioning according to any one of claims 1 to 3, wherein the method has a relationship represented by the following equation (5).
However, in Eq. (4), Pr: Prandle number, _Ipt : Fin spacing (m), Nusselt number: Nu (non-dimensional number) = hL / λ, and h in Eq. (5) Heat transfer coefficient, λ: Thermal conductivity of fin material (W / mK), L is a representative length or the _Dec.

The temperature of the fin has a relationship represented by the following equations (6) and (7), and the temperature of the passing air and the temperature of the fin are required in order to obtain the heat conduction amount from the heat transfer rate. Assuming that there is, in the above equation (7), the temperature distribution of the fin has a uniform average temperature θm, and θm can be obtained from _{the fin efficiency ηf, the fin root temperature θ 0} , and the outside air temperature t _0. The method for evaluating the performance of a heat exchanger core for air conditioning according to any one of claims 1 to 4, which is characterized.
However, in the equation (7), df is the tube height pitch, dc is the tube depth pitch (in the case of one tube, the depth dimension (m), and F ₁ is the fin thickness (m).

The heat exchange for air conditioning according to any one of claims 1 to 5, wherein the heat transfer between the medium and the tube has a turbulent heat transfer coefficient relationship shown in the following equation (8). How to evaluate the performance of the vessel core.

The heat exchanger passes through the wind velocity _{U c,} compared face velocity _{U 0} to the heat exchanger core the air conditioner, by multiplying the ratio of the free passage area _{A c} the frontal projected area _{A f, U c = (A} c / The performance evaluation method for an air conditioning heat exchanger core according to any one of claims 3 to 6, wherein the calculation is performed using the relationship of A _f). A plurality of fins arranged side by side at predetermined intervals and a tube joined so as to be in contact with the plurality of fins are provided, and air is circulated between the plurality of fins and the tube to allow air to flow between the plurality of fins and the medium in the tube. A performance evaluation device for an air-conditioning heat exchanger core that exchanges heat between the fins and the fins.
It is assumed that the first calculation means for obtaining the pressure loss and the average heat transfer coefficient when air flows along the fins of the heat exchanger core for air conditioning and the temperature distribution of the fins have a uniform average temperature. , A second calculation means for obtaining the temperature distribution of the fin from the fin efficiency, the fin root temperature, and the outside air temperature.
Assuming that the heat transfer between the medium and the tube has a turbulent heat transfer coefficient relationship,
A third calculation means for dividing the fin into a plurality of parts along the air flow direction and obtaining the temperature of the air by a difference method for each divided region of the air.
A fourth calculation means for obtaining the temperature of the medium for each of the divided regions of the tube by dividing the tube into the same number as the divided regions of the air, assuming that the tube is a straight pipe.
Assuming that the relational expression of air wind velocity x total fin area x inlet / outlet air temperature difference x specific heat = medium amount x specific heat x inlet / water temperature difference holds, the amount of the medium is obtained by solving this relational expression, and the air outlet is further obtained. A performance evaluation device for an air conditioner heat exchanger core, which comprises a fifth calculation means for obtaining a temperature and a water outlet temperature. Assuming that the relational expression of air velocity x total fin area x inlet / outlet air temperature difference x specific heat = amount of medium x specific heat x inlet / output medium temperature difference holds, when solving this relational expression, a coefficient is added to the heat transfer coefficient of the medium. The performance evaluation device for the heat exchanger core for air conditioning according to claim 8, further comprising a function of multiplying by and matching the calculation result on the left side and the calculation result on the right side of the relational expression. As a pressure loss calculation model when air is circulated through the air conditioning heat exchanger core, the pressure loss Pc of the air conditioning heat exchanger core is expressed by the following equations (1), (2), and (3). The performance evaluation device for an air conditioning heat exchanger core according to claim 8 or 9, wherein the relationship represented is provided.
However, in (1), (2), Pc: pressure loss in the heat exchanger core for air conditioning, _{C D:} flow loss coefficient, [rho: density _{^{(kg / m 3), U}} c: air conditioning heat exchanger core the wind passing through the air (heat exchanger passes wind _{speed: m / sec), D ec} :( typical dimension: wetted perimeter: m), _{L t:} air conditioning heat exchanger core of the air flow direction length (m), Re: Reynolds number, in equation (3), _Ac : free passage area (total area where fins and tubes do not exist when the air conditioning heat exchanger core is viewed along the air flow direction), A _o : Total heat transfer area.

Regarding the temperature calculation model, the average heat transfer of the heat exchanger core for air conditioning is obtained in relation to the Nusselt number Nu represented by the following equation (4), and the Nusselt number is related to the heat transfer coefficient h. The performance evaluation device for the heat exchanger core for air conditioning according to any one of claims 8 to 10, which has a relationship represented by the following equation (5).
However, in equation (4), Re: Reynolds number, Pr: Prandle number, _Ipt : Fin spacing (m), Nusselt number: Nu (dimensionless number) = hL / λ, and (5). ), H is the heat transfer coefficient, λ: the thermal conductivity of the fin material (W / mK), and L is the representative length or the _Dec.

The fin temperature has a relationship expressed by the following equations (6) and (7), and the temperature of the passing air and the temperature of the fin are required to obtain the heat conduction amount from the heat transfer rate. In the above equation (7), the temperature distribution of the fin has a uniform average temperature θm, and θm can be obtained from the fin efficiency ηf, the fin root temperature θ ₀ , and the outside air temperature t _0. The performance evaluation device for a heat exchanger core for air conditioning according to any one of claims 8 to 11, further comprising a function.
However, in the equation (7), df is the tube height pitch, dc is the tube depth pitch (in the case of one tube, the depth dimension (m), and F ₁ is the fin thickness (m).

The heat exchange for air conditioning according to any one of claims 8 to 12, wherein the heat transfer between the medium and the tube has a turbulent heat transfer coefficient relationship shown in the following equation (8). Instrument core performance evaluation device.

Relates to the aforementioned heat exchanger passing wind velocity _{U c,} relative face velocity _{U 0} to the heat exchanger core the air conditioner, by multiplying the ratio of the free passage area _{A c} the frontal projected area _{A f, U c = (A} c / The performance evaluation device for an air conditioning heat exchanger core according to any one of claims 8 to 13, characterized in that it has a function of calculating using the relationship of A _f). A plurality of fins arranged side by side at predetermined intervals and a tube joined so as to be in contact with the plurality of fins are provided, and air is circulated between the plurality of fins and the tube to allow air to flow between the plurality of fins and a medium in the tube. This is a performance evaluation program for the heat exchanger core for air conditioning that exchanges heat between the fins and the fins.
A first calculation means for obtaining a pressure loss and an average heat transfer coefficient when air flows along the fins of the heat exchanger core for air conditioning.
Assuming that the temperature distribution of the fins has a uniform average temperature, a second calculation means for obtaining the temperature distribution of the fins from the fin efficiency, the fin root temperature, and the outside air temperature,
Assuming that the heat transfer between the medium and the tube has a turbulent heat transfer coefficient relationship,
A third calculation means for dividing the fin into a plurality of parts along the air flow direction and obtaining the temperature of the air by a difference method for each divided region of the air.
A fourth calculation means for obtaining the temperature of the medium for each of the divided regions of the tube by dividing the tube into the same number as the divided regions of the air, assuming that the tube is a straight pipe.
Assuming that the relational expression of air wind velocity x total fin area x inlet / outlet air temperature difference x specific heat = medium amount x specific heat x inlet / water temperature difference holds, the amount of the medium is obtained by solving this relational expression, and the air outlet is further obtained. A performance evaluation program for an air conditioner core, which is characterized by functioning as a fifth calculation means for determining the temperature and the water outlet temperature. Assuming that the relational expression of air velocity x total fin area x inlet / outlet air temperature difference x specific heat = amount of medium x specific heat x inlet / output medium temperature difference holds, when solving this relational expression, a coefficient is added to the heat transfer coefficient of the medium. The performance evaluation program for the heat exchanger core for air conditioning according to claim 15, further comprising a function of multiplying by and matching the calculation result on the left side and the calculation result on the right side of the relational expression. As a pressure loss calculation model when air is circulated through the air conditioning heat exchanger core, the pressure loss Pc of the air conditioning heat exchanger core is expressed by the following equations (1), (2), and (3). The performance evaluation program for an air conditioning heat exchanger core according to claim 15 or 16, characterized in that the relationships represented are provided.
However, in (1), (2), Pc: pressure loss in the heat exchanger core for air conditioning, _{C D:} flow loss coefficient, [rho: density _{^{(kg / m 3), U}} c: air conditioning heat exchanger core the wind passing through the air (heat exchanger passes wind _{speed: m / sec), D ec} :( typical dimension: wetted perimeter: m), _{L t:} air conditioning heat exchanger core of the air flow direction length (m), Re: Reynolds number, in equation (3), _Ac : free passage area (total area where fins and tubes do not exist when the air conditioning heat exchanger core is viewed along the air flow direction), A _o : Total heat transfer area.

As a temperature calculation model, the average heat transfer of the heat exchanger core for air conditioning is obtained in relation to the Nusselt number Nu represented by the following equation (4), and the Nusselt number is related to the heat transfer coefficient h. The performance evaluation program for the heat exchanger core for air conditioning according to any one of claims 15 to 17, which has a relationship represented by the following equation (5).
However, in Eq. (4), Pr: Prandle number, _Ipt : Fin spacing (m), Nusselt number: Nu (non-dimensional number) = hL / λ, and h in Eq. (5) Heat transfer coefficient, λ: Thermal conductivity of fin material (W / mK), L is a representative length or the _Dec.

The temperature of the fin has a relationship represented by the following equations (6) and (7), and the temperature of the passing air and the temperature of the fin are required in order to obtain the heat conduction amount from the heat transfer rate. Assuming that there is, in the above equation (7), the temperature distribution of the fin has a uniform average temperature θm, and θm is a function that can be obtained from _{the fin efficiency ηf, the fin root temperature θ 0} , and the outside air temperature t _0. The performance evaluation program for the heat exchanger core for air conditioning according to any one of claims 15 to 18, wherein the heat exchanger core is provided.
However, in the equation (7), df is the tube height pitch, dc is the tube depth pitch (in the case of one tube, the depth dimension (m), and F ₁ is the fin thickness (m).

The heat exchange for air conditioning according to any one of claims 15 to 19, wherein the heat transfer between the medium and the tube has a turbulent heat transfer coefficient relationship shown in the following equation (8). Instrument core performance evaluation program.

Relates to the aforementioned heat exchanger passing wind velocity _{U c,} relative face velocity _{U 0} to the heat exchanger core the air conditioner, by multiplying the ratio of the free passage area _{A c} the frontal projected area _{A f, U c = (A} c / The performance evaluation program for an air conditioning heat exchanger core according to any one of claims 15 to 20, wherein it has a function of calculating using the relationship of A _f).

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