Calculation of the heat exchanger currently takes no more than five minutes. Any organization that manufactures and sells such equipment, as a rule, provides everyone with their own selection program. It can be downloaded for free from the company's website, or their technician will come to your office and install it for free. However, how correct is the result of such calculations, can it be trusted and is the manufacturer not being cunning when fighting in a tender with his competitors? Checking an electronic calculator requires knowledge or at least an understanding of the methodology for calculating modern heat exchangers. Let's try to understand the details.
What is a heat exchanger
Before performing the calculation of the heat exchanger, let's remember what kind of device this is? A heat and mass transfer apparatus (aka a heat exchanger, aka a heat exchanger, or TOA) isa device for transferring heat from one coolant to another. In the process of changing the temperatures of heat carriers, their densities and, accordingly, the mass indicators of substances also change. That is why such processes are called heat and mass transfer.
Types of heat transfer
Now let's talk about the types of heat transfer - there are only three of them. Radiative - heat transfer due to radiation. As an example, consider sunbathing on the beach on a warm summer day. And such heat exchangers can even be found on the market (tube air heaters). However, most often for heating residential premises, rooms in an apartment, we buy oil or electric radiators. This is an example of another type of heat transfer - convection. Convection can be natural, forced (hood, and there is a heat exchanger in the box) or mechanically driven (with a fan, for example). The latter type is much more efficient.
However, the most efficient way to transfer heat is conduction, or, as it is also called, conduction (from the English. Conduction - "conduction"). Any engineer who is going to conduct a thermal calculation of a heat exchanger, first of all, thinks about how to select efficient equipment in minimum dimensions. And it is possible to achieve this precisely due to thermal conductivity. An example of this is the most efficient TOA today - plate heat exchangers. A plate heat exchanger, according to the definition, is a heat exchanger that transfers heat from one coolant to another through a wall separating them. Maximumthe possible contact area between the two media, together with correctly selected materials, plate profile and thickness, allows minimizing the size of the selected equipment while maintaining the original technical characteristics required in the technological process.
Types of heat exchangers
Before calculating the heat exchanger, it is determined with its type. All TOA can be divided into two large groups: recuperative and regenerative heat exchangers. The main difference between them is as follows: in regenerative TOAs, heat exchange occurs through a wall separating two coolants, while in regenerative ones, two media have direct contact with each other, often mixing and requiring subsequent separation in special separators. Regenerative heat exchangers are divided into mixing and heat exchangers with packing (stationary, falling or intermediate). Roughly speaking, a bucket of hot water, exposed to frost, or a glass of hot tea, set to cool in the refrigerator (never do this!) - this is an example of such a mixing TOA. And pouring tea into a saucer and cooling it in this way, we get an example of a regenerative heat exchanger with a nozzle (the saucer in this example plays the role of a nozzle), which first contacts the surrounding air and takes its temperature, and then takes away part of the heat from the hot tea poured into it, seeking to bring both media into thermal equilibrium. However, as we have already found out earlier, it is more efficient to use thermal conductivity to transfer heat from one medium to another, thereforeThe more heat transfer useful (and widely used) TOAs of today are, of course, regenerative ones.
Thermal and structural design
Any calculation of a recuperative heat exchanger can be carried out based on the results of thermal, hydraulic and strength calculations. They are fundamental, obligatory when designing new equipment and form the basis of the methodology for calculating subsequent models of a line of similar devices. The main task of the thermal calculation of TOA is to determine the required area of the heat exchange surface for the stable operation of the heat exchanger and maintaining the required parameters of the media at the outlet. Quite often, in such calculations, engineers are given arbitrary values of the weight and size characteristics of the future equipment (material, pipe diameter, plate dimensions, bundle geometry, type and material of fins, etc.), therefore, after the thermal calculation, they usually carry out a constructive calculation of the heat exchanger. Indeed, if at the first stage the engineer calculated the required surface area for a given pipe diameter, for example, 60 mm, and the length of the heat exchanger turned out to be about sixty meters, then it would be more logical to assume a transition to a multi-pass heat exchanger, or to a shell-and-tube type, or to increase the diameter of the tubes.
Hydraulic calculation
Hydraulic or hydromechanical, as well as aerodynamic calculations are carried out in order to determine and optimize hydraulic(aerodynamic) pressure losses in the heat exchanger, as well as calculate the energy costs to overcome them. The calculation of any path, channel or pipe for the passage of the coolant poses a primary task for a person - to intensify the heat transfer process in this area. That is, one medium must transfer, and the other receive as much heat as possible in the minimum period of its flow. For this, an additional heat exchange surface is often used, in the form of a developed surface ribbing (to separate the boundary laminar sublayer and enhance flow turbulence). The optimal balance ratio of hydraulic losses, heat exchange surface area, weight and size characteristics and removed thermal power is the result of a combination of thermal, hydraulic and structural calculation of TOA.
Check calculation
The verification calculation of the heat exchanger is carried out in the case when it is necessary to lay a margin in terms of power or in terms of the area of the heat exchange surface. The surface is reserved for various reasons and in different situations: if it is required by the terms of reference, if the manufacturer decides to make an additional margin in order to be sure that such a heat exchanger will reach the regime and minimize errors made in the calculations. In some cases, redundancy is required to round off the results of constructive dimensions, while in others (evaporators, economizers), a surface margin is specially introduced into the calculation of the heat exchanger power, for contamination by compressor oil present in the refrigeration circuit. And poor water qualitymust be taken into account. After some time of uninterrupted operation of heat exchangers, especially at high temperatures, scale settles on the heat exchange surface of the apparatus, reducing the heat transfer coefficient and inevitably leading to a parasitic decrease in heat removal. Therefore, a competent engineer, when calculating a water-to-water heat exchanger, pays special attention to additional redundancy of the heat exchange surface. A verification calculation is also carried out in order to see how the selected equipment will work in other, secondary modes. For example, in central air conditioners (supply units), the first and second heating heaters, which are used in the cold season, are often used in the summer to cool the incoming air, supplying cold water to the air heat exchanger tubes. How they will function and what parameters will give out, allows you to evaluate the verification calculation.
Exploratory calculations
Research calculations of TOA are carried out on the basis of the obtained results of thermal and verification calculations. They are necessary, as a rule, to make the last amendments to the design of the designed apparatus. They are also carried out in order to correct any equations that are incorporated in the implemented calculation model of TOA, obtained empirically (according to experimental data). Performing research calculations involves tens and sometimes hundreds of calculations according to a special plan developed and implemented in production in accordance withmathematical theory of planning experiments. Based on the results, the influence of various conditions and physical quantities on the TOA efficiency indicators is revealed.
Other calculations
When calculating the heat exchanger area, do not forget about the resistance of materials. TOA strength calculations include checking the designed unit for stress, for torsion, for applying the maximum allowable working moments to the parts and assemblies of the future heat exchanger. With minimum dimensions, the product must be strong, stable and guarantee safe operation in various, even the most demanding operating conditions.
Dynamic calculation is carried out in order to determine the various characteristics of the heat exchanger in variable operating modes.
Heat exchanger design types
Recuperative TOA by design can be divided into a fairly large number of groups. The most famous and widely used are plate heat exchangers, air (tubular finned), shell-and-tube, tube-in-pipe heat exchangers, shell-and-plate and others. There are also more exotic and highly specialized types, such as spiral (coil heat exchanger) or scraped type, which work with viscous or non-Newtonian fluids, as well as many other types.
Pipe-in-pipe heat exchangers
Let's consider the simplest calculation of the "pipe in pipe" heat exchanger. Structurally, this type of TOA is maximally simplified. As a rule, they let into the inner tube of the apparatushot coolant, to minimize losses, and a cooling coolant is launched into the casing, or into the outer pipe. The engineer's task in this case is reduced to determining the length of such a heat exchanger based on the calculated area of the heat exchange surface and the given diameters.
Here it is worth adding that in thermodynamics the concept of an ideal heat exchanger is introduced, that is, an apparatus of infinite length, where the heat carriers work in countercurrent, and the temperature difference is completely worked out between them. The pipe-in-pipe design is the closest to meeting these requirements. And if you run the coolants in countercurrent, then it will be the so-called "real counterflow" (and not cross, as in plate TOAs). The temperature head is most effectively worked out with such an organization of movement. However, when calculating the “pipe in pipe” heat exchanger, one should be realistic and not forget about the logistics component, as well as ease of installation. The length of the eurotruck is 13.5 meters, and not all technical premises are adapted to the skidding and installation of equipment of this length.
Shell and tube heat exchangers
Therefore, very often the calculation of such an apparatus smoothly flows into the calculation of a shell-and-tube heat exchanger. This is an apparatus in which a bundle of pipes is located in a single housing (casing), washed by various coolants, depending on the purpose of the equipment. In condensers, for example, the refrigerant is run into the shell, and the water is run into the tubes. With this method of media movement, it is more convenient and more efficient to controloperation of the device. In evaporators, on the contrary, the refrigerant boils in the tubes, while they are washed by the cooled liquid (water, brines, glycols, etc.). Therefore, the calculation of a shell-and-tube heat exchanger is reduced to minimizing the dimensions of the equipment. Playing with the shell diameter, the diameter and number of internal pipes and the length of the apparatus, the engineer reaches the calculated value of the heat exchange surface area.
Air heat exchangers
One of the most common heat exchangers today is tubular finned heat exchangers. They are also called snakes. Where they are not only installed, starting from fan coil units (from the English fan + coil, i.e. "fan" + "coil") in the indoor units of split systems and ending with giant flue gas recuperators (heat extraction from hot flue gas and transmission for heating needs) in boiler plants at CHP. That is why the calculation of a coil heat exchanger depends on the application where this heat exchanger will go into operation. Industrial air coolers (HOPs) installed in meat blast freezing chambers, low-temperature freezers and other food refrigeration facilities require certain design features in their design. The spacing between the lamellas (fins) should be as large as possible in order to increase the time of continuous operation between defrost cycles. Evaporators for data centers (data processing centers), on the contrary, are made as compact as possible by clamping the interlamellarminimum distance. Such heat exchangers operate in “clean zones”, surrounded by fine filters (up to HEPA class), therefore, such a calculation of a tubular heat exchanger is carried out with an emphasis on minimizing dimensions.
Plate heat exchangers
Currently, plate heat exchangers are in stable demand. According to their design, they are completely collapsible and semi-welded, copper-soldered and nickel-soldered, welded and soldered by diffusion (without solder). The thermal calculation of a plate heat exchanger is quite flexible and does not present any particular difficulty for an engineer. In the selection process, you can play with the type of plates, the depth of forging channels, the type of fins, the thickness of steel, different materials, and most importantly, numerous standard-size models of devices of different sizes. Such heat exchangers are low and wide (for steam heating of water) or high and narrow (separating heat exchangers for air conditioning systems). They are also often used for phase change media, i.e. as condensers, evaporators, desuperheaters, precondensers, etc. The thermal calculation of a two-phase heat exchanger is slightly more difficult than a liquid-liquid heat exchanger, however, for experienced engineer, this task is solvable and does not present any particular difficulty. To facilitate such calculations, modern designers use engineering computer databases, where you can find a lot of necessary information, including state diagrams of any refrigerant in any sweep, for example, a programCoolPack.
Example of heat exchanger calculation
The main purpose of the calculation is to calculate the required area of the heat exchange surface. Thermal (refrigeration) power is usually specified in the terms of reference, however, in our example, we will calculate it, so to speak, to check the terms of reference itself. Sometimes it also happens that an error can creep into the source data. One of the tasks of a competent engineer is to find and correct this error. As an example, let's calculate a plate heat exchanger of the "liquid-liquid" type. Let this be a pressure breaker in a tall building. In order to unload equipment by pressure, this approach is very often used in the construction of skyscrapers. On one side of the heat exchanger, we have water with an inlet temperature Tin1=14 ᵒС and an outlet temperature Тout1=9 ᵒС, and with a flow rate G1=14,500 kg / h, and on the other - also water, but only with the following parameters: Тin2=8 ᵒС, Тout2=12 ᵒС, G2=18 125 kg/h.
We calculate the required power (Q0) using the heat balance formula (see the figure above, formula 7.1), where Ср is the specific heat capacity (table value). For simplicity of calculations, we take the reduced value of the heat capacity Срв=4.187 [kJ/kgᵒС]. Counting:
Q1=14,500(14 - 9)4, 187=303557. 5 [kJ/h]=84321, 53 W=84. 3 kW - on the first side and
Q2=18 125(12 - 8)4, 187=303557. 5 [kJ/h]=84321, 53 W=84. 3 kW - on the second side.
Note that, according to formula (7.1), Q0=Q1=Q2, regardless ofon which side the calculation was made.
Further, using the main heat transfer equation (7.2), we find the required surface area (7.2.1), where k is the heat transfer coefficient (taken equal to 6350 [W/m2]), and ΔТav.log. - average logarithmic temperature difference, calculated according to the formula (7.3):
ΔT average log.=(2 - 1) / ln (2 / 1)=1 / ln2=1 / 0, 6931=1, 4428;
F then=84321 / 63501, 4428=9.2 m2.
When the heat transfer coefficient is unknown, the calculation of the plate heat exchanger is a bit more complicated. According to formula (7.4), we calculate the Reynolds criterion, where ρ is the density, [kg/m3], η is the dynamic viscosity, [Ns/m2], v – medium velocity in the channel, [m/s], d cm – wetted channel diameter [m].
According to the table, we look for the value of the Prandtl criterion [Pr] we need and, using formula (7.5), we obtain the Nusselt criterion, where n=0.4 - under conditions of liquid heating, and n=0.3 - under conditions of liquid cooling.
Next, using formula (7.6), we calculate the heat transfer coefficient from each coolant to the wall, and using formula (7.7), we calculate the heat transfer coefficient, which we substitute into formula (7.2.1) to calculate the area of the heat exchange surface.
In the indicated formulas, λ is the thermal conductivity coefficient, ϭ is the channel wall thickness, α1 and α2 are the heat transfer coefficients from each of the heat carriers to the wall.
