Calculation of the heat exchanger: an example. Calculation of the area, power of the heat exchanger

Calculation of the heat exchanger currently takes no more than five minutes. Any organization that produces and sells such equipment, as a rule, provides everyone with its own selection program. It can be downloaded for free from the company's website, or their technical specialist will come to your office and install it for free. However, how well is the result of such calculations, is it possible to trust him and do not fool the producer, battling in a tender with his competitors? Checking the 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 calculating the heat exchanger, let's remember, but what kind of device is this? Heat and mass transfer equipment (a heat exchanger, a heat exchanger, or TOA) is a device for transferring heat from one coolant to another. In the process of changing the temperatures of the heat carriers, their densities and, accordingly, the mass indexes of the substances also change. That is why such processes are called heat and mass exchange.

Types of heat transfer

Now let's talk about the types of heat exchange - there are only three. Radiation - the transfer of heat due to radiation. As an example, you can remember taking sun baths on the beach on a warm summer day. And such heat exchangers can even be found on the market (lamp air heaters). However, most often for heating of living rooms, rooms in the apartment, we buy oil or electric radiators. This is an example of another type of heat exchange - convection. Convection is natural, forced (exhaust, and in the box is recuperator) or with a mechanical impulse (with a fan, for example). The latter type is much more effective.

However, the most effective way of transferring heat is heat conduction, or, as it is also called, conduction (from English conduction - "conductivity"). Any engineer who intends to conduct heat calculation of a heat exchanger first of all thinks about choosing efficient equipment in minimum dimensions. And to achieve this, it is due to heat conduction. An example of this is the most effective to date TOA - plate heat exchangers. Plate TOA, according to the definition, is a heat exchanger transferring heat from one coolant to another through the wall that separates them. The maximum possible contact area between two media in combination with properly selected materials, the plate profile and their thickness makes it possible to minimize the size of the selected equipment while preserving the initial 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 the following: in recuperative TOA, heat exchange occurs through the wall separating the two heat-transfer media, and in the regenerative two environments they 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 a nozzle (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 so!) - this is an example of such a mixing TOA. And by pouring tea in 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 some of the heat from the hot tea poured into it , Seeking to bring both environments into a thermal equilibrium regime. However, as we have already explained, it is more efficient to use thermal conductivity to transfer heat from one environment to another, so more useful in terms of heat transfer (and widely used) TOA today - of course, recuperative.

Thermal and constructive calculation

Any calculation of a recuperative heat exchanger can be carried out based on the results of thermal, hydraulic and strength calculations. They are fundamental, mandatory for the design of new equipment and form the basis for calculating the subsequent models of the line of the same type of apparatus. The main task of thermal calculation of TOA is to determine the necessary area of the heat exchange surface for the stable operation of the heat exchanger and to maintain the necessary parameters of the media at the outlet. Quite often, in such calculations, engineers are assigned arbitrary values of the mass-dimensional characteristics of the future equipment (material, pipe diameter, plate dimensions, beam geometry, fin type and material, etc.), so after a thermal analysis, a structural calculation of the heat exchanger is usually carried out. After all, if in the first stage the engineer has calculated the necessary surface area for a given pipe diameter, for example, 60 mm, and the length of the heat exchanger has turned out to be about sixty meters, it is more logical to assume a transition to a multi-pass heat exchanger, either 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 to determine and optimize the hydraulic (aerodynamic) pressure losses in the heat exchanger, and also to calculate the energy costs for overcoming them. Calculation of any tract, channel or pipe for the passage of the coolant sets the primary task for man to intensify the process of heat exchange in this area. That is, one medium must transmit, and the other must receive as much heat as possible at the minimum interval of its flow. To do this, an additional heat exchange surface is often used, in the form of a developed surface finning (for detaching the boundary laminar sublayer and intensifying the flow turbulence). The optimal balance ratio of hydraulic losses, the areas of the heat exchange surface, mass-dimension characteristics and the removed heat output is the result of a combination of thermal, hydraulic and structural calculations of the TOA.

Verification calculation

Verification calculation of the heat exchanger is carried out in the case when it is necessary to lay a reserve for capacity or for the area of the heat exchange surface. The surface is reserved for various reasons and in different situations: if so required by the specification, if the manufacturer decides to make an additional stock in order to be certain that such a heat exchanger will enter the mode, and to minimize errors in the calculations. In some cases, redundancy is required to round off the results of structural dimensions, while in others (evaporators, economizers), the calculation of the heat exchanger's power specifically introduces a margin over the surface, to contamination with compressor oil present in the refrigeration circuit. Yes, and the poor quality of water must be taken into account. After some time of uninterrupted operation of the heat exchangers, especially at high temperatures, the scum settles on the heat exchange surface of the apparatus, reducing the heat transfer coefficient and inevitably leading to a parasitic reduction in the heat dissipation. Therefore, a competent engineer, when calculating the water-to-water heat exchanger, pays special attention to the additional reservation of the heat exchange surface. The verification calculation is also carried out in order to see how the selected equipment will operate in other, secondary modes. For example, in central air-conditioners (air-handling units), the first and second heating calorifiers used during the cold period of the year are often used in summer to cool the incoming air by supplying cold water to the tubes of the air heat exchanger. How they will function and what parameters will produce, allows you to evaluate the verification calculation.

Research calculations

The TOA research calculations are based on the results of the thermal and verification calculations. They are necessary, as a rule, to make the latest amendments to the design of the projected apparatus. They are also carried out with the aim of correcting any equations that are laid down in the feasible TOA model, obtained empirically (according to experimental data). The implementation of research calculations involves carrying out tens, and sometimes hundreds of calculations according to a special plan, developed and implemented in the production according to the mathematical theory of experimental planning. Based on the results, the influence of various conditions and physical quantities on the TOA efficiency indicators is revealed.

Other calculations

When calculating the area of the heat exchanger, do not forget about the resistance of materials. Strength calculations of the TOA include checking the designed unit for stress, torsion, applying the maximum permissible operating moments to the parts and assemblies of the future heat exchanger. With the minimum dimensions, the product should be strong, stable and guarantee safe operation in various, even the most stressful operating conditions.

Dynamic calculation is carried out with the purpose of definition of various characteristics of the heat exchanger in variable modes of its operation.

Types of heat exchangers

Recuperative TOA by design can be divided into a sufficiently large number of groups. The most famous and widely used are plate heat exchangers, air (tubular finned), shell-and-tube heat exchangers, "tube-in-pipe" heat exchangers, shell-plate heat exchangers and others. There are also more exotic and narrowly specialized types, for example, spiral (heat exchanger-snail) or scraper, which work with viscous or non-Newtonian fluids, as well as many other types.

Pipe-to-pipe heat exchangers

Let us consider the simplest calculation of the "tube-in-pipe" heat exchanger. Structurally this type of TOA is simplified as much as possible. As a rule, a hot heat carrier is allowed to flow into the inner tube of the apparatus, in order to minimize losses, a coolant is started in the casing or in the outer tube. The task of the engineer in this case is to determine the length of such a heat exchanger based on the calculated area of the heat exchange surface and the specified 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 transfer media work in countercurrent, and a temperature head is fully activated between them. The pipe-in-pipe design closest to these requirements. And if you start the coolant in a countercurrent, it will be the so-called "real countercurrent" (and not cross, as in the plate TOA). The temperature head achieves maximum efficiency with such a traffic organization. However, when performing the calculation of the "pipe-in-pipe" heat exchanger, one should be realistic and not forget about the logistics component, as well as the convenience of installation. The length of the eurofury is 13.5 meters, and not all technical rooms are adapted to skidding and assembling equipment of this length.

Shell and tube heat exchangers

Therefore, very often the calculation of such a device smoothly flows into the calculation of the shell-and-tube heat exchanger. This device, in which the bundle of pipes is in a single shell (casing), washed by various heat carriers, depending on the purpose of the equipment. In condensers, for example, the coolant is launched into the casing, and the water into the tubes. With this method of medium motion, it is more convenient and more efficient to control the operation of the apparatus. In evaporators, on the contrary, the refrigerant boils in the tubes, while they are washed with a cooled liquid (water, brines, glycols, etc.). Therefore, the calculation of the shell-and-tube heat exchanger reduces to minimizing the dimensions of the equipment. While playing with the diameter of the casing, the diameter and number of internal pipes and the length of the apparatus, the engineer enters the calculated value of the area of the heat exchange surface.

Air heat exchangers

One of the most common heat exchangers for today is the tubular finned heat exchangers. They are also called coils. Where they are not installed, starting from fan coils (from fan + coil, ie "fan + coil") in the indoor units of split systems and ending with giant flue gas recuperators (heat removal from hot flue gas and transmission For heating purposes) in boiler plants at the CHPP. That is why the calculation of the coil heat exchanger depends on the application to which this heat exchanger will go into operation. Industrial air coolers (VOPs), installed in the chambers of shock freezing of meat, in freezing chambers of low temperatures and at other objects of food cold supply, require certain design features in their performance. The distance between the lamellae (finning) should be maximum, to increase the time of continuous work between the defrost cycles. Evaporators for data centers (data centers), on the contrary, make it as compact as possible, clamping the interlam distance to a minimum. Such heat exchangers operate in "clean zones", surrounded by fine filters (up to class HEPA), so this calculation of the tubular heat exchanger is carried out with an emphasis on minimizing the size.

Plate Heat Exchangers

At present, plate heat exchangers are in stable demand. By their design, they are completely collapsible and semi-welded, copper-soldered and nickel-plated, welded and welded by the diffusion method (without solder). The thermal calculation of the plate heat exchanger is sufficiently flexible and does not present a particular difficulty for the engineer. In the process of selection you can play the type of plates, the depth of punching channels, the type of fins, the thickness of steel, different materials, and most importantly - numerous standard models of devices of different sizes. Such heat exchangers are low and wide (for steam water heating) or high and narrow (separation heat exchangers for air conditioning systems). They are often used for mediums with a phase transition, that is, as condensers, evaporators, desuperheaters, precondensors, etc. Performing a heat calculation of a heat exchanger operating in a two-phase circuit is a little more complicated than a liquid-liquid heat exchanger; An experienced engineer, this problem is solvable and does not represent a particular complexity. To facilitate such calculations, modern designers use engineering computer databases, where you can find a lot of necessary information, including diagrams of any refrigerant in any scan, for example, the program CoolPack.

Example of heat exchanger calculation

The main purpose of the calculation is to calculate the required area of the heat exchange surface. Thermal (refrigerating) power is usually specified in the technical design, but in our example we will calculate it for, say, checking the technical specification itself. Sometimes it happens and so that the original data can sneak an error. One of the tasks of a competent engineer is to find and correct this mistake. As an example, we can calculate the plate-type heat exchanger of the liquid-liquid type. Let it be a pressure breaker in a high-rise building. In order to relieve pressure equipment, this approach is often used in the construction of skyscrapers. On the one side of the heat exchanger we have water with an inlet temperature of Твх1 = 14 ᵒС and an outlet Тvy1 = 9 ᵒС, and with a flow rate G1 = 14,500 kg / h, and on the other - also water, but only with such parameters: Твх2 = 8 ᵒС, Тvy2 = 12 ᵒС, G2 = 18,125 kg / h.

We calculate the required power (Q0) by the heat balance formula (see the figure above, formula 7.1), where Cp is the specific heat (tabular value). For the sake of simplicity of calculations, let us take the reduced heat capacity Cp = 4.187 [kJ / kg * ᵒC]. We consider:

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 the formula (7.1), Q0 = Q1 = Q2, regardless of which side of the calculation.

Then, using the basic heat transfer equation (7.2), we find the required surface area (7.2.1), where k is the heat transfer coefficient (assumed equal to 6350 [W / m ² ]), and ΔTp.log. - the average logarithmic temperature head, calculated according to the formula (7.3):

ΔT avglog. = (2 - 1) / ln (2/1) = 1 / ln2 = 1 / 0.69131 = 1.4428;

F = 84321/6350 * 1.4428 = 9.2 m ² .

In the case where the heat transfer coefficient is unknown, the calculation of the plate heat exchanger is slightly more complicated. According to formula (7.4), we assume the Reynolds criterion, where ρ is the density, [kg / m ³ ], η is the dynamic viscosity, [H * s / m ² ], v is the velocity of the medium in the channel, [m / s], d cm - wetted channel diameter [m].

From the table we find the necessary value of the Prandtl criterion [Pr] and by the formula (7.5) we obtain the Nusselt criterion, where n = 0.4 - under fluid heating conditions, and n = 0.3 - under fluid cooling conditions.

Then, according to formula (7.6), the heat transfer coefficient from each coolant to the wall is calculated, and by formula (7.7) we consider the heat transfer coefficient, which we substitute into formula (7.2.1) for calculating the area of the heat exchange surface.

In these formulas, λ is the coefficient of thermal conductivity, ϭ is the thickness of the channel wall, α1 and α2 are the heat transfer coefficients from each of the heat carriers to the wall.