The area of the heat-transfer surface of the evaporator F, m 2, is determined by the formula:
where is the heat flow in the evaporator, W
k – heat transfer coefficient of the evaporator, W/(m 2 *K), depends on the type of evaporator;
Average logarithmic difference between the temperatures of boiling freon and the cooled medium;
–specific heat flux equal to 4700 W/m2
The coolant flow required to remove heat inflows is determined by the formula:
Where With - heat capacity of the cooled medium: for water 4.187 kJ/(kg*°C), for brine the heat capacity is taken according to special tables depending on its freezing point, which is taken 5-8°C below the boiling point of the refrigerant t 0 for open systems and 8-10°C lower t 0 for closed systems;
ρ r - density of SCR coolant, kg/m 3 ;
Δ t R - difference in temperature of the coolant at the inlet to the evaporator and at the outlet, °C.
For air conditioning conditions in the presence of nozzle irrigation chambers, water flow distribution schemes are used. According to this, Δt р will be determined as the temperature difference at the outlet of the irrigation chamber pan t w.k and at the outlet of the evaporator t X :.
8. Selection of capacitor
Calculation of a capacitor comes down to determining the area of the heat transfer surface, according to which one or more capacitors are selected with a total surface area equal to the calculated one (surface margin no more than + 15%).
1. The theoretical heat flow in the condenser is determined by the difference in specific enthalpies in the theoretical cycle with or without taking into account subcooling in the condenser:
a) the heat flow, taking into account the subcooling in the condenser, is determined by the difference in specific enthalpies in the theoretical cycle:
b) heat flow without taking into account subcooling in the condenser and in the absence of a regenerative heat exchanger
Total thermal load, taking into account the thermal equivalent of the power expended by the compressor to compress the refrigerant (actual heat flux):
2. The average logarithmic temperature difference θ cf between the condensing refrigerant and the condenser cooling medium is determined, °C:
where is the temperature difference at the beginning of the heat transfer surface (large temperature difference), 0 C:
Temperature difference at the end of the heat transfer surface (smaller temperature difference), 0 C:
3. Find the specific heat flux:
where k is the heat transfer coefficient, equal to 700 W/(m 2 *K)
4. Heat transfer surface area of the condenser:
5. Condenser cooling medium flow rate:
where is the total heat flow in the condenser from all groups of compressors, kW;
With - specific heat capacity of the condenser cooling medium (water, air), kJ/(kg*K);
ρ - density of the condenser cooling medium, kg/m 3 ;
- heating of the condenser cooling medium, °C:
1.1 - safety factor (10%), taking into account unproductive losses.
Based on water consumption and taking into account the required pressure, a circulating water supply pump of the required capacity is selected. A backup pump must be provided.
9. Selection of main refrigeration units
The selection of a refrigeration machine is carried out using one of three methods:
According to the described volume of the compressor included in the machine;
According to the machine's cooling performance graphs;
According to the tabulated values of the machine’s cooling capacity given in the technical specifications of the product.
The first method is similar to that used to calculate a single-stage compressor: the required volume described by the compressor pistons is determined, and then a machine or several machines are selected from the technical specifications tables so that the actual value of the volume described by the pistons is 20-30% greater than the obtained one by calculation.
When selecting a refrigeration machine using the third method, it is necessary to bring the refrigeration capacity of the machine, calculated for operating conditions, to the conditions under which it is given in the characteristics table, that is, to standard conditions.
After selecting the brand of the unit (according to the refrigeration capacity normalized to standard conditions), it is necessary to check whether the heat transfer surface area of the evaporator and condenser is sufficient. If the heat transfer surface area of the devices indicated in the technical specifications is equal to the calculated one or slightly larger than it, the machine has been selected correctly. If, for example, the surface area of the evaporator turns out to be less than the calculated one, it is necessary to set a new value of the temperature difference (lower boiling point), and then check whether the compressor performance is sufficient at the new value of the boiling point.
We accept a water-cooled chiller of the York YCWM brand with a cooling capacity of 75 kW.
Our own production of liquid cooling units (chillers) was organized in 2006. The first units had a cooling capacity of 60 kW and were assembled on the basis of plate heat exchangers. If necessary, they were equipped with a hydraulic module.
The hydromodule is a thermally insulated tank with a capacity of 500 liters (depending on the power, so for an installation with a cooling capacity of 50-60 kW the tank capacity should be 1.2-1.5 m3) divided by a specially shaped partition into two containers of “warm” and “cooled” water . Pump internal contour, taking water from the “warm” compartment of the tank, supplies it to a plate heat exchanger, where it, passing in countercurrent with freon, is cooled. Cooled water flows into another part of the tank. The capacity of the internal pump must be no less than the capacity of the external circuit pump. The special shape of the partition allows you to regulate the overflow volume over a wide range with a slight change in the water level.
When using water as a coolant, such installations allow it to be cooled to +5ºC ÷ +7ºC. Accordingly, when standard calculation equipment, the temperature of the incoming water (coming from the consumer) is assumed to be +10ºC ÷ +12ºС. The power of the installation is calculated based on required flow water.
Our equipment is equipped with multi-stage protection systems. Pressure switches protect the compressor from overload. The low pressure limiter does not allow boiling freon to lower its temperature below minus 2ºС, protecting the plate heat exchanger from possible freezing of water. The installed flow switch will turn off the refrigeration compressor if air lock, when pipelines are clogged, when plates freeze. The suction pressure regulator maintains the freon boiling point +1ºС ±0.2ºС.
We installed similar devices for cooling the solution of brine baths for salting cheese at cheese factories, for quickly cooling milk after pasteurization at dairies, for smoothly lowering the water temperature in pools at factories for the production (breeding and growing) of fish.
If it is necessary to lower the temperature of the coolant from +5ºC ÷ +7ºС to negative and near zero temperatures, a solution of propylene glycol is used as a coolant instead of water. It is also used if the ambient temperature drops below -5ºС, or if it is necessary to turn off the internal circuit pump from time to time (circuit: buffer tank - heat exchanger of the refrigeration unit).
When calculating equipment, we necessarily take into account changes in such properties of the coolant as heat capacity and surface heat transfer coefficient. AN INSTALLATION DESIGNED TO WORK WITH WATER WILL WORK INCORRECTLY WHEN THE COOLANT IS REPLACED WITH SOLUTIONS OF ETHYLENE GLYCOL, PROPYLENE GLYCOL OR BRINE. AND VICE VERSA .
The paraffin cooling unit, assembled according to this scheme, works in conjunction with air system coolant cooling in winter time, with automatic shutdown of the refrigeration compressor.
We have experience in designing and manufacturing chillers to solve the problem of cooling within a short period of time, but with high power cooling. For example, a milk receiving shop requires installations with an operating time of 2 hours/day to cool 20 tons of milk during this time from +25ºC ÷ +30ºС to +6ºC ÷ +8ºС. This is the so-called pulsed cooling problem.
When setting the problem of pulsed cooling of products, it is economically feasible to manufacture a chiller with a cold accumulator. As a standard, we make such settings as follows:
A) A thermally insulated tank is manufactured with a volume of 125-150% of the calculated buffer tank, filled with water by 90%;
B) An evaporator made of bent copper pipelines or metal plates with grooves milled inside is placed inside it;
By supplying freon at a temperature of -17ºC ÷ -25ºC, we ensure ice freezing required thickness. The water received from the consumer is cooled as a result of the melting of ice. Bubbling is used to increase the melting rate.
Such a system allows the use of refrigeration units with a power 5–10 times less than the value of the pulse power of the refrigeration load. It should be understood that the temperature of the water in the tank can differ significantly from 0ºC, since the rate of ice melting in water with a temperature of even +5ºC is very low. Also, the disadvantages of this system include the large weight and size of the tank with the evaporator, which is explained by the need to ensure large area heat exchange at the ice/water interface.
If it is necessary to use water with near zero temperature (0ºС÷+1ºС) as a coolant, without the possibility of using solutions of propylene glycol, ethylene glycol or brines instead (for example, the system is not tight or SANPiN requirements), we manufacture chillers using film heat exchangers.
With such a system, water coming from the consumer, passing through special system collectors and nozzles, evenly washes large metal plates cooled with freon to minus 5ºC. Flowing down, part of the water freezes on the plates, forming a thin film of ice, the rest of the water, flowing down this film, cools to desired temperature and is collected in a heat-insulated tank located under the plates, from where it is supplied to the consumer.
Such systems have strict requirements for the level of dust in the room where the tank with evaporator is installed and, for obvious reasons, require more high level ceilings. They are characterized by the largest dimensions and cost.
Our company will solve any liquid cooling problem you have. We will assemble (or select a ready-made) installation with an optimal operating principle and minimal cost, both of the installation itself and its operation.
1. Coursework assignment
According to the initial data for the course work you need:
Determine the hydraulic losses of the evaporator circulation circuit;
Determine the useful pressure in the circuit natural circulation evaporator stages;
Determine the operating circulation speed;
Determine the heat transfer coefficient.
Initial data.
Evaporator type - I -350
Number of pipes Z = 1764
Heating steam parameters: P p = 0.49 MPa, t p = 168 0 C.
Steam consumption D p = 13.5 t/h;
Dimensions:
L 1 = 2.29 m
L 2 = 2.36 m
D 1 = 2.05 m
D 2 = 2.85 m
Drop pipes
Number n op = 22
Diameter d op = 66 mm
Temperature difference per stage t = 14 o C.
2. Purpose and design of evaporators
Evaporators are designed to produce distillate that replenishes the loss of steam and condensate in the main cycle of steam turbine units of power plants, as well as to generate steam for general plant needs and external consumers.
Evaporators can be used as part of both single-stage and multi-stage evaporation plants for operation in the technological complex of thermal power plants.
Medium and low pressure steam from turbine or RDU extractions can be used as a heating medium, and in some models even water with a temperature of 150-180 °C.
Depending on the purpose and requirements for the quality of secondary steam, evaporators are manufactured with one- and two-stage steam flushing devices.
The evaporator is a vessel cylindrical and, as a rule, vertical type. Lengthwise cut The evaporator installation is shown in Figure 1. The evaporator body consists of a cylindrical shell and two elliptical bottoms welded to the shell. For fastening to the foundation, supports are welded to the body. To lift and move the evaporator, cargo fittings (trunnions) are provided.
The evaporator body is equipped with pipes and fittings for:
Heating steam supply (3);
Removal of secondary steam;
Discharge of heating steam condensate (8);
Supply feed water evaporator (5);
Water supply to the steam flushing device (4);
Continuous blowing;
Draining water from the housing and periodically purging it;
Bypass of non-condensable gases;
Installation of safety valves;
Installation of control devices and automatic regulation;
Sampling
The evaporator housing has two hatches for inspection and repair of internal devices.
Feed water flows through the collector (5) to the washing sheet (4) and through the lowering pipes to the lower part of the heating section (2). Heating steam enters through the pipe (3) into the interpipe space of the heating section. When washing the pipes of the heating section, steam condenses on the walls of the pipes. The heating steam condensate flows into the lower part of the heating section, forming an unheated zone.
Inside the pipes, first water, then the steam-water mixture rises into the steam-generating section of the heating section. The steam rises to the top, and the water flows into the annular space and falls down.
The resulting secondary steam first passes through the washing sheet, where large drops of water remain, then through the louvered separator (6), where medium and some small drops are captured. The movement of water in the lower pipes, the annular channel and the steam-water mixture in the pipes of the heating section occurs due to natural circulation: the difference in the densities of water and the steam-water mixture.
Rice. 1. Evaporation plant
1 - body; 2 - heating section; 3 - supply of heating steam; 4 - washing sheet; 5 - feed water supply; 6 - louvered separator; 7 - down pipes; 8 - drainage of heating steam condensate.
3. Determination of parameters of secondary steam of the evaporation plant
Fig.2. Evaporation plant diagram.
The secondary steam pressure in the evaporator is determined by the temperature pressure of the stage and the flow parameters in the heating circuit.
At P p = 0.49 MPa, t p = 168 o C, h p = 2785 KJ/kg
Parameters at saturation pressure P n = 0.49 MPa,
t n = 151 o C, h" p = 636.8 KJ/kg; h" p = 2747.6 KJ/kg;
The secondary steam pressure is determined by the saturation temperature.
T n1 = t n ∆t = 151 14 = 137 o C
where ∆t = 14 o C.
At saturation temperature t n1 = 137 o C secondary steam pressure
P 1 = 0.33 MPa;
Enthalpies of steam at P 1 = 0.33 MPa h" 1 = 576.2 KJ/kg; h" 1 = 2730 KJ/kg;
4. Determination of the productivity of the evaporation plant.
The performance of the evaporation plant is determined by the flow of secondary steam from the evaporator
D iу = D i
The amount of secondary steam from the evaporator is determined from the heat balance equation
D ni ∙(h ni -h΄ ni )∙η = D i ∙h i ˝+ α∙D i ∙h i ΄ - (1+α)∙D i ∙h pv ;
Hence the consumption of secondary steam from the evaporator:
D = D n ∙(h n - h΄ n )η/((h˝ 1 + αh 1 ΄ - (1 + α)∙h pv )) =
13.5∙(2785 636.8)0.98/((2730+0.05∙576.2 -(1+0.05)∙293.3)) = 11.5 4 t/h.
where is the enthalpy of heating steam and its condensate
H n = 2785 KJ/kg, h΄ n = 636.8 KJ/kg;
Enthalpies of secondary steam, its condensate and feed water:
H˝ 1 =2730 KJ/kg; h΄ 1 = 576.2 KJ/kg;
Enthalpy of feedwater at t pv = 70 o C: h pv = 293.3 KJ/kg;
Blowing α = 0.05; those. 5 %. Evaporator efficiency, η = 0.98.
Evaporator performance:
D иу = D = 11.5 4 t/h;
5. Thermal calculation of the evaporator
The calculation is performed using the successive approximation method.
Heat flow
Q = (D /3.6)∙ =
= (11,5 4 /3,6)∙ = 78 56.4 kW;
Heat transfer coefficient
k = Q/ΔtF = 7856.4/14∙350 = 1.61 kW/m 2 ˚С = 1610 W/m 2 ˚С,
where Δt=14˚C; F= 350 m2;
Specific heat flux
q =Q/F = 78 56.4/350 = 22.4 kW/m2;
Reynolds number
Re = q∙H/r∙ρ"∙ν = 22, 4 ∙0,5725/(21 10 , 8 ∙9 1 5∙2,03∙10 -6 ) = 32 , 7 8;
Where is the height of the heat exchange surface
H = L 1 /4 = 2.29 /4 = 0.5725 m;
Heat of vaporization r = 2110.8 kJ/kg;
Liquid density ρ" = 915 kg/m 3 ;
Kinematic viscosity coefficient at P n = 0.49 MPa,
ν =2.03∙10 -6 m/s;
Heat transfer coefficient from condensing steam to the wall
at Re = 3 2, 7 8< 100
α 1н =1.01∙λ∙(g/ν 2 ) 1/3 Re -1/3 =
1.01∙0.684∙(9.81/((0.2 0 3∙10 -6 ) 2 )) 1/3 ∙3 2 , 7 8 -1/3 = 133 78 .1 W/m 2 ˚С ;
where at P p = 0.49 MPa, λ = 0.684 W/m∙˚С;
Heat transfer coefficient taking into account the oxidation of pipe walls
α 1 =0.75∙α 1n =0.75∙133 78.1 = 10 0 3 3.6 W/m 2 ˚С;
6. Determination of circulation speed.
The calculation is carried out using the graphic-analytical method.
Given three values of the circulation rate W 0 = 0.5; 0.7; 0.9 m/s we calculate the resistance in the supply lines ∆Р sub and useful pressure ∆Р floor . Based on the calculation data, we construct a graph ΔР sub .=f(W) and ΔР floor .=f(W). At these speeds, the dependence of the resistance in the supply lines ∆Р sub and useful pressure ∆Р floor do not intersect. Therefore, we re-set three values of the circulation rate W 0 = 0.8; 1.0; 1.2 m/s; We calculate the resistance in the supply lines and the useful pressure again. The intersection point of these curves corresponds to the operating value of the circulation speed. Hydraulic losses in the supply part consist of losses in the annular space and losses in the inlet sections of the pipes.
Annular area
F k =0.785∙[(D 2 2 -D 1 2 )-d 2 op ∙n op ]=0.785[(2.85 2 2.05 2 ) 0.066 2 ∙22] = 3.002 m 2 ;
Equivalent diameter
D eq =4∙F k /(D 1 +D 2 +n∙d op ) π =4*3.002/(2.05+2.85+ 22∙0.066)3.14= 0.602 m;
Water speed in the annular channel
W to =W 0 ∙(0.785∙d 2 in ∙Z/F to ) =0.5∙(0.785∙0.027 2 ∙1764 /3.002) = 0.2598 m/s;
Where inner diameter heating section pipes
D in = d n 2∙δ = 32 - 2∙2.5 = 27 mm = 0.027 m;
Number of heating section pipes Z = 1764 pcs.
We carry out the calculation in tabular form, table 1
Calculation of circulation speed. Table 1.
|
p/p |
Name, definition formula, unit of measurement. |
Speed, W 0 , m/s |
||
|
Water speed in the ring channel: W to =W 0 *((0.785*d int 2 z)/F to), m/s |
0,2598 |
0,3638 |
0,4677 |
|
|
Reynolds number: Re =W to ∙D eq / ν |
770578,44 |
1078809,8 |
1387041,2 |
|
|
Friction coefficient in the annular channel λ tr = 0.3164/Re 0.25 |
0,0106790 |
0,0098174 |
0,0092196 |
|
|
Pressure loss when moving in the annular channel, Pa: ΔР k =λ tr *(L 2 /D eq)*(ρ΄W k 2 /2); |
1,29 |
2,33 |
3,62 |
|
|
Pressure loss at the inlet from the annular channel, Pa; ΔР in =(ξ in +ξ out )*((ρ"∙W to 2 )/2), Where ξin =0.5;ξout =1.0. |
46,32 |
90,80 |
150,09 |
|
|
Pressure loss at the inlet to the pipes of the heating section, Pa; ΔР inlet .=ξ inlet .*(ρ"∙W to 2 )/2, Where ξ inlet = 0.5 |
15,44 |
30,27 |
50,03 |
|
|
Pressure loss when water moves in a straight section, Pa; ΔР tr =λ gr *(ℓ but /d in )*(ρ΄W to 2 /2), where ℓ but -height of the lower unheated area, m. ℓ but = ℓ +(L 2 -L 1 )/2=0.25 +(3.65-3.59)/2=0.28 m,ℓ =0.25-condensate level |
3,48 |
6,27 |
9,74 |
|
|
Losses in downpipes, Pa; ΔР op = ΔР in +ΔР to |
47,62 |
93,13 |
153,71 |
|
|
Losses in an unheated area, Pa; ΔР but =ΔР in.tr.+ΔР tr. |
18,92 |
36,54 |
59,77 |
|
|
Heat flow, kW/m 2 ; G in =kΔt= 1.08∙10= 10.8 |
22,4 |
22,4 |
22,4 |
|
|
The total amount of heat supplied in the annular space, kW; Q k =πД 1 L 1 kΔt=3.14∙2.5∙3.59∙2.75∙10= 691.8 |
330,88 |
330,88 |
330,88 |
|
|
Increase in enthalpy of water in the annular channel, KJ/kg; Δh k =Q k /(0.785∙d int 2 Z∙W∙ρ") |
0,8922 |
0,6373 |
0,4957 |
|
|
Height of economizer section, m;ℓ eq =((-Δh to - -(ΔР op +ΔР but )∙(dh/dр)+gρ"∙(L 1 - ℓ but )∙(dh/dр))/ ((4g in /ρ"∙W∙d in )+g∙ρ"∙(dh/dр)), where (dh/dр)= =Δh/Δр=1500/(0.412*10 5 )=0.36 |
1,454 |
2,029 |
2,596 |
|
|
Losses in the economizer section, Pa; ΔР eq =λ∙ ℓ eq ∙(ρ"∙W 2 )/2 |
1,7758 |
4,4640 |
8,8683 |
|
|
15 15 |
Total resistance in supply lines, Pa; ΔР sub =ΔР op +ΔР but +ΔР ek |
68,32 |
134,13 |
222,35 |
|
Amount of steam in one pipe, kg/s D" 1 =Q/z∙r |
0,00137 |
0,00137 |
0,00137 |
|
|
Reduced speed at the outlet of the pipes, m/s, W" ok =D" 1 /(0.785∙ρ"∙d int 2) = 0.0043/(0.785∙1.0∙0.033 2 ) =1.677 m/s; |
0,83 |
0,83 |
0,83 |
|
|
Average given speed, W˝ pr =W˝ ok /2= =1.677/2=0.838 m/s |
0,42 |
0,42 |
0,42 |
|
|
Consumable steam content, β ok =W˝ pr /(W˝ pr +W) |
0,454 |
0,373 |
0,316 |
|
|
Ascent speed of a single bubble in a stationary liquid, m/s W belly =1.5 4 √gG(ρ΄-ρ˝/(ρ΄)) 2 |
0,2375 |
0,2375 |
0,2375 |
|
|
Interaction factor Ψ in =1.4(ρ΄/ρ˝) 0.2 (1-(ρ˝/ρ΄)) 5 |
4,366 |
4,366 |
4,366 |
|
|
Group speed of bubble ascent, m/s W* =W belly Ψ up |
1,037 |
1,037 |
1,037 |
|
|
Mixing speed, m/s W cm.r =W pr "+W |
0,92 |
1,12 |
1,32 |
|
|
Volumetric vapor content φ ok =β ok /(1+W*/W cm.r) |
0,213 |
0,193 |
0,177 |
|
|
Driving pressure, Pa ΔР dv =g(ρ-ρ˝)φ ok L steam, where L steam =L 1 -ℓ but -ℓ eq =3.59-0.28-ℓ eq; |
1049,8 |
40,7 |
934,5 |
|
|
Friction losses in the steam-water line ΔР tr.steam = =λ tr ((L steam /d in))(ρ΄W 2 /2)) |
20,45 |
1,57 |
61,27 |
|
|
Losses at the outlet of the pipe ΔР out =ξ out (ρ΄W 2 /2)[(1+(W pr ˝/W)(1-(ρ˝/ρ΄)] |
342,38 |
543,37 |
780,96 |
|
|
Flow acceleration losses ΔР ус =(ρ΄W) 2 (y 2 -y 1), where y 1 =1/ρ΄=1/941.2=0.00106 at x=0; φ=0 y 2 =((x 2 k /(ρ˝φ k ))+((1-x k ) 2 /(ρ΄(1-φ k ) |
23 , 8 51 0,00106 0,001 51 |
38 , 36 0,00106 0,001 44 |
5 4,0 6 0,00106 0,001 39 |
|
|
W cm =W˝ ok +W β to =W˝ ok /(1+(W˝ok/W cm)) φ k =β k /(1+(W˝ ok /W cm )) x k =(ρ˝W˝ ok)/(ρ΄W) |
1 , 33 0, 62 0, 28 0 0,000 6 8 |
1 , 53 0, 54 0, 242 0,0005 92 |
1 , 7 3 0,4 8 0,2 13 0,000 523 |
|
|
Useful head, Pa; ΔР floor =ΔР in -ΔР tr -ΔР out -ΔР ac |
663 ,4 |
620 , 8 |
1708 , 2 |
|
The dependency is built:
ΔР lower=f(W) and ΔР floor .=f(W) , fig. 3 and find W p = 0.58 m/s;
Reynolds number:
Re = (W р d in )/ν = (0.5 8∙0.027)/(0.20 3∙10 -6) = 7 7 1 4 2.9;
Nusselt number:
N and = 0.023∙Re 0.8 ∙Pr 0.37 = 0.023∙77142.9 0.8 ∙1.17 0.37 = 2 3 02, 1;
where the number Pr = 1.17;
Heat transfer coefficient from the wall to boiling water
α 2 = Nuλ/d ext = (2302.1∙0.684)/0.027 = 239257.2 W/m 2 ∙˚С
Heat transfer coefficient from the wall to boiling water taking into account the oxide film
α΄ 2 =1/(1/α 2 )+0.000065=1/(1/ 239257.2 )+0.000065= 1,983 W/m 2 ∙˚С;
Heat transfer coefficient
K=1/(1/α 1 )+(d in /2λ st )*ℓn*(d n /d in )+(1/α΄ 2 )*(d in /d n ) =
1/(1/ 1983 )+(0.027/2∙60)∙ℓn(0.032/0.027)+(1/1320)∙(0.027/0.032)=
17 41 W/m 2 ∙˚С;
where for Art. 20 we have λst= 60 W/m∙OWITH.
Deviation from earlier accepted value
δ = (k-k0 )/k0 ∙100%=[(1 741 1603 )/1 741 ]*100 % = 7 , 9 % < 10%;
Literature
1. Ryzhkin V.Ya. Thermal power plants. M. 1987.
2. Kutepov A.M. and others. Hydrodynamics and heat transfer during vaporization. M. 1987.
3. Ogai V.D. implementation technological process at the thermal power plant. Guidelines to implementation course work. Almaty. 2008.
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Change |
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Document№ |
Subp |
date |
KR-5V071700 PZ |
Sheet |
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Completed |
Poletaev P. |
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Supervisor |
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When calculating the designed evaporator, its heat transfer surface and the volume of circulating brine or water are determined.
The heat transfer surface of the evaporator is found using the formula:
where F is the heat transfer surface of the evaporator, m2;
Q 0 – cooling capacity of the machine, W;
Dt m – for shell-and-tube evaporators this is the average logarithmic difference between the coolant and boiling temperatures refrigerant, and for panel evaporators - the arithmetic difference between the temperatures of the outlet brine and the boiling point of the refrigerant, 0 C;
– heat flux density, W/m2.
For approximate calculations of evaporators, use the values of heat transfer coefficients obtained experimentally in W/(m 2 ×K):
for ammonia evaporators:
shell-and-tube 450 – 550
panel 550 – 650
for freon shell-and-tube evaporators with rolling fins 250 – 350.
The average logarithmic difference between the temperatures of the coolant and the boiling point of the refrigerant in the evaporator is calculated using the formula:
(5.2)
where t P1 and t P2 are the coolant temperatures at the inlet and outlet of the evaporator, 0 C;
t 0 – boiling point of the refrigerant, 0 C.
For panel evaporators, due to the large tank volume and intensive coolant circulation, it average temperature can be taken equal to the temperature at the outlet of the tank t P2. Therefore for these evaporators 
The volume of circulating coolant is determined by the formula:
(5.3)
where V P is the volume of circulating coolant, m 3 /s;
с Р – specific heat capacity of brine, J/(kg × 0 C);
r P – brine density, kg/m3;
t P2 and t P1 – temperature of the coolant, respectively, at the entrance to the cooled room and exit from it, 0 C;
Q 0 – cooling capacity of the machine.
The values of c P and r P are found from reference data for the corresponding coolant depending on its temperature and concentration.
The temperature of the coolant as it passes through the evaporator drops by 2 - 3 0 C.
Calculation of evaporators for air cooling in refrigeration chambers
To distribute the evaporators included in the refrigeration machine, determine the required heat transfer surface using the formula:
where SQ is the total heat flow to the chamber;
K – heat transfer coefficient of chamber equipment, W/(m 2 ×K);
Dt – calculated temperature difference between the air in the chamber and the average temperature of the coolant during brine cooling, 0 C.
The heat transfer coefficient for the battery is 1.5–2.5 W/(m 2 K), for air coolers – 12–14 W/(m 2 K).
The estimated temperature difference for batteries is 14–16 0 C, for air coolers - 9–11 0 C.
The number of cooling devices for each chamber is determined by the formula:
where n is the required number of cooling devices, pcs.;
f – heat transfer surface of one battery or air cooler (taken based on technical specifications cars).
Capacitors
There are two main types of capacitors: water-cooled and air-cooled. In high-capacity refrigeration units, water-air-cooled condensers, called evaporative condensers, are also used.
In refrigeration units for commercial refrigeration equipment Air-cooled condensers are most often used. Compared to a water-cooled condenser, they are economical to operate and easier to install and operate. Refrigeration units that include water-cooled condensers are more compact than units with air-cooled condensers. In addition, they make less noise during operation.
Water-cooled condensers are distinguished by the nature of water movement: flow type and irrigation type, and by design - shell-and-coil, two-pipe and shell-and-tube.
The main type is horizontal shell-and-tube condensers (Fig. 5.3). Depending on the type of refrigerant, there are some differences in the design of ammonia and freon condensers. In terms of the size of the heat transfer surface, ammonia condensers cover a range from approximately 30 to 1250 m2, and freon condensers - from 5 to 500 m2. In addition, ammonia vertical shell-and-tube condensers are produced with a heat transfer surface area from 50 to 250 m 2.
Shell-and-tube condensers are used in medium and high-capacity machines. Hot refrigerant vapors enter through pipe 3 (Fig. 5.3) into the interpipe space and condense on the outer surface of the horizontal pipe bundle.
Cooling water circulates inside the pipes under the pressure of the pump. The pipes are flared in tube sheets, closed from the outside with water caps with partitions creating several horizontal passages (2-4-6). Water enters through pipe 8 from below and exits through pipe 7. On the same water cover there is a valve 6 for releasing air from the water space and a valve 9 for draining water during inspection or repair of the condenser.
Fig.5.3 - Horizontal shell-and-tube condensers
On top of the device there is safety valve 1, connecting the inter-tube space of the ammonia condenser with a pipeline led outside, above the ridge of the roof itself tall building within a radius of 50 m. An equalizing line is connected through pipe 2, connecting the condenser to the receiver, where liquid refrigerant is discharged through pipe 10 from the bottom of the device. An oil sump with pipe 11 for draining oil is welded to the bottom of the body. The liquid refrigerant level at the bottom of the casing is monitored using level indicator 12. During normal operation, all liquid refrigerant should drain into the receiver.
On top of the casing there is a valve 5 for releasing air, as well as a pipe for connecting a pressure gauge 4.
Vertical shell-and-tube condensers are used in high-capacity ammonia refrigeration machines; they are designed for heat loads from 225 to 1150 kW and are installed outside the machine room, without occupying its usable area.
IN Lately plate-type capacitors appeared. The high intensity of heat transfer in plate condensers, compared to shell-and-tube condensers, makes it possible, with the same thermal load, to approximately halve the metal consumption of the device and increase its compactness by 3–4 times.
Air capacitors are used mainly in machines of low and medium productivity. Based on the nature of air movement, they are divided into two types:
With free air movement; such capacitors are used in machines with very low performance (up to approximately 500 W), used in household refrigerators;
With forced air movement, that is, with blowing of the heat transfer surface using axial fans. This type of capacitor is most applicable in small and medium-capacity machines, but recently, due to water shortages, they are increasingly used in high-capacity machines.
Air-type condensers are used in refrigeration units with sealed, sealless and hermetic compressors. The capacitor designs are the same. The capacitor consists of two or more sections connected in series by coils or in parallel by collectors. The sections are straight or U-shaped tubes assembled into a coil using rolls. Pipes – steel, copper; ribs - steel or aluminum.
Forced air condensers are used in commercial refrigeration units.
Calculation of capacitors
When designing a condenser, the calculation comes down to determining its heat transfer surface and (if it is water-cooled) the amount of water consumed. First of all, calculate the actual thermal load on the capacitor
where Q к is the actual thermal load on the capacitor, W;
Q 0 – compressor cooling capacity, W;
N i – indicator power of the compressor, W;
N e – effective compressor power, W;
h m – mechanical efficiency of the compressor.
In units with hermetic or sealless compressors, the thermal load on the condenser should be determined using the formula:
(5.7)
where N e – electric power at the compressor motor terminals, W;
h e – efficiency of the electric motor.
The heat transfer surface of the capacitor is determined by the formula:
(5.8)
where F is the area of the heat transfer surface, m2;
k – heat transfer coefficient of the condenser, W/(m 2 ×K);
Dt m – average logarithmic difference between the condensation temperatures of the refrigerant and cooling water or air, 0 C;
q F – heat flux density, W/m2.
The average logarithmic difference is determined by the formula:
(5.9)
where t in1 is the temperature of water or air at the inlet to the condenser, 0 C;
tb2 – temperature of water or air at the outlet of the condenser, 0 C;
tk – condensation temperature of the refrigeration unit, 0 C.
Heat transfer coefficients various types capacitors are given in table. 5.1.
Table 5.1 - Heat transfer coefficients of capacitors
Irrigation for ammoniaEvaporative for ammonia
Air-cooled (with forced air circulation) for refrigerants
Values To defined for a ribbed surface.
One of the most important elements for a vapor compression machine is . It performs the main process of the refrigeration cycle - selection from the cooled environment. Other elements of the refrigeration circuit, such as the condenser, expansion device, compressor, etc., only provide reliable operation evaporator, therefore it is the choice of the latter that must be given due attention.
It follows from this that when selecting equipment for a refrigeration unit, it is necessary to start with the evaporator. Many novice repairmen often make the mistake typical mistake and start completing the installation with a compressor.
In Fig. Figure 1 shows a diagram of the most common vapor compression refrigeration machine. Its cycle, specified in coordinates: pressure R And i. In Fig. 1b points 1-7 of the refrigeration cycle is an indicator of the state of the refrigerant (pressure, temperature, specific volume) and coincides with the same in Fig. 1a (functions of state parameters).
Rice. 1 – Diagram and in coordinates of a conventional vapor compression machine: RU expansion device, Pk– condensation pressure, Ro– boiling pressure.
Graphic representation fig. 1b shows the state and functions of the refrigerant, which vary depending on pressure and enthalpy. Line segment AB on the curve in Fig. 1b characterizes the refrigerant in the state saturated steam. Its temperature corresponds to the starting point of boiling. The refrigerant vapor fraction is 100%, and superheat is close to zero. To the right of the curve AB the refrigerant has a state (the temperature of the refrigerant is greater than the boiling point).
Dot IN is critical for a given refrigerant, since it corresponds to the temperature at which the substance cannot go into a liquid state, no matter how high the pressure is. On the segment BC, the refrigerant has the state of a saturated liquid, and on the left side - a supercooled liquid (refrigerant temperature less temperature boiling).
Inside the Curve ABC the refrigerant is in the state of a vapor-liquid mixture (the proportion of vapor per unit volume is variable). The process occurring in the evaporator (Fig. 1b) corresponds to the segment 6-1 . The refrigerant enters the evaporator (point 6) in the state of a boiling vapor-liquid mixture. In this case, the share of steam depends on the specific refrigeration cycle and is 10-30%.
At the exit from the evaporator, the boiling process may not be completed, period 1 may not coincide with the point 7 . If the temperature of the refrigerant at the outlet of the evaporator is higher than the boiling point, then we get an overheated evaporator. Its size ΔToverheat represents the difference between the temperature of the refrigerant at the outlet of the evaporator (point 1) and its temperature at the saturation line AB (point 7):
ΔToverheat=T1 – T7
If points 1 and 7 coincide, then the refrigerant temperature is equal to the boiling point, and the superheat ΔToverheat will be equal to zero. Thus, we get a flooded evaporator. Therefore, when choosing an evaporator, you first need to make a choice between a flooded evaporator and an overheated evaporator.
Note that when equal conditions a flooded evaporator is more advantageous in terms of the intensity of the heat extraction process than with overheating. But it should be taken into account that at the outlet of the flooded evaporator the refrigerant is in a state of saturated vapor, and it is impossible to supply a humid environment to the compressor. Otherwise, there is a high probability of water hammer occurring, which will be accompanied by mechanical destruction of compressor parts. It turns out that if you choose a flooded evaporator, then it is necessary to provide additional protection compressor from saturated steam entering it.
If you give preference to an evaporator with overheating, then you do not need to worry about protecting the compressor and getting saturated steam into it. The likelihood of water hammer occurring will only occur if the superheat value deviates from the required value. IN normal conditions operation of the refrigeration unit, superheat value ΔToverheat should be within 4-7 K.
When the superheat indicator decreases ΔToverheat, the intensity of heat extraction from the environment increases. But at extremely low values ΔToverheat(less than 3K) there is a possibility of wet steam entering the compressor, which can cause water hammer and, consequently, damage to the mechanical components of the compressor.
Otherwise, with a high reading ΔToverheat(more than 10 K), this indicates that insufficient refrigerant is entering the evaporator. The intensity of heat extraction from the cooled medium sharply decreases and the thermal conditions of the compressor worsen.
When choosing an evaporator, another question arises related to the boiling point of the refrigerant in the evaporator. To solve it, it is first necessary to determine what temperature of the cooled medium should be provided for normal operation refrigeration unit. If air is used as the cooled medium, then in addition to the temperature at the outlet of the evaporator, it is also necessary to take into account the humidity at the outlet of the evaporator. Now let us consider the behavior of the temperatures of the cooled medium around the evaporator during operation of a conventional refrigeration unit (Fig. 1a).
In order not to go deep into this topic We will neglect the pressure losses on the evaporator. We will also assume that the heat exchange occurring between the refrigerant and environment carried out according to a direct-flow scheme.
In practice, such a scheme is not often used, since in terms of heat transfer efficiency it is inferior to a counterflow scheme. But if one of the coolants has a constant temperature, and the overheating readings are small, then forward flow and counter flow will be equivalent. It is known that the average temperature difference does not depend on the flow pattern. Consideration of the direct-flow circuit will provide us with a more clear idea of the heat exchange that occurs between the refrigerant and the cooled medium.
First, let's introduce the virtual quantity L, equal to the length of the heat exchange device (condenser or evaporator). Its value can be determined from the following expression: L=W/S, Where W– corresponds to the internal volume of the heat exchange device in which the refrigerant circulates, m3; S– heat exchange surface area m2.
If we are talking about a refrigeration machine, then the equivalent length of the evaporator is almost equal to the length of the tube in which the process takes place 6-1 . Therefore her outside surface washed by a cooled environment.
First, let's pay attention to the evaporator, which acts as an air cooler. In it, the process of removing heat from the air occurs as a result of natural convection or with the help of forced blowing of the evaporator. Note that in modern refrigeration units the first method is practically not used, since air cooling by natural convection is ineffective.
Thus, we will assume that the air cooler is equipped with a fan, which provides forced air flow to the evaporator and is a tubular-fin heat exchanger (Fig. 2). Its schematic representation is shown in Fig. 2b. Let's consider the main quantities that characterize the blowing process.
Temperature difference
The temperature difference across the evaporator is calculated as follows:ΔT=Ta1-Ta2,
Where ΔTa is in the range from 2 to 8 K (for tubular-fin evaporators with forced air flow).
In other words, during normal operation of the refrigeration unit, the air passing through the evaporator must be cooled not lower than 2 K and not higher than 8 K.
Rice. 2 – Scheme and temperature parameters of air cooling on the air cooler:
Ta1 And Ta2– air temperature at the inlet and outlet of the air cooler;
- FF– refrigerant temperature;
- L– equivalent length of the evaporator;
- That– boiling point of the refrigerant in the evaporator.
Maximum temperature difference
The maximum temperature pressure of air at the evaporator inlet is determined as follows:DTmax=Ta1 – To
This indicator is used when selecting air coolers, since foreign manufacturers refrigeration equipment provides evaporator cooling capacity values Qsp depending on size DTmax. Let's consider the method for selecting an air cooler for a refrigeration unit and determine the calculated values DTmax. To do this, let us give as an example generally accepted recommendations for selecting the value DTmax:
- For freezers DTmax is within 4-6 K;
- for storage rooms for unpackaged products – 7-9 K;
- for storage rooms for hermetically packaged products – 10-14 K;
- for air conditioning units – 18-22 K.
Degree of steam superheat at the evaporator outlet
To determine the degree of steam superheat at the outlet of the evaporator, use the following form:F=ΔToverload/DTmax=(T1-T0)/(Ta1-T0),
Where T1– temperature of the refrigerant vapor at the outlet of the evaporator.
This indicator is practically not used in our country, but foreign catalogs stipulate that the readings of the cooling capacity of air coolers Qsp corresponds to the value F=0.65.
During operation the value F It is customary to take from 0 to 1. Let us assume that F=0, Then ΔТoverload=0, and the refrigerant leaving the evaporator will be in the state of saturated vapor. For this air cooler model, the actual cooling capacity will be 10-15% greater than the figure given in the catalog.
If F>0.65, then the cooling performance indicator for this air cooler model should be less than value given in the catalogue. Let's assume that F>0.8, then the actual performance for this model will be 25-30% greater than the value given in the catalog.
If F->1, then the evaporator cooling capacity Quse->0(Fig. 3).
Fig. 3 – dependence of the evaporator cooling capacity Qsp from overheating F
The process depicted in Fig. 2b is also characterized by other parameters:
- arithmetic mean temperature difference DTsr=Tasr-T0;
- average temperature of the air that passes through the evaporator Tasp=(Ta1+Ta2)/2;
- minimum temperature difference DTmin=Ta2-To.
Rice. 4 – Diagram and temperature parameters showing the process on the evaporator:
Where Te1 And Te2 water temperature at the evaporator inlets and outlets;
- FF – coolant temperature;
- L – equivalent length of the evaporator;
- T is the boiling point of the refrigerant in the evaporator.
If the temperature difference across the water ΔTe=Te1-Te2, then for shell-and-tube evaporators ΔTe should be maintained in the range of 5±1 K, and for plate evaporators the indicator ΔTe will be within 5±1.5 K.
Unlike air coolers, in liquid coolers it is necessary to maintain not a maximum, but a minimum temperature pressure DTmin=Te2-To– the difference between the temperature of the cooled medium at the outlet of the evaporator and the boiling point of the refrigerant in the evaporator.
For shell-and-tube evaporators, the minimum temperature difference is DTmin=Te2-To should be maintained within 4-6 K, and for plate evaporators - 3-5 K.
The specified range (the difference between the temperature of the cooled medium at the outlet of the evaporator and the boiling point of the refrigerant in the evaporator) must be maintained for the following reasons: as the difference increases, the cooling intensity begins to decrease, and as it decreases, the risk of freezing of the cooled liquid in the evaporator increases, which can cause its mechanical failure. destruction.
Evaporator design solutions
Regardless of the method of using various refrigerants, the heat exchange processes occurring in the evaporator are subject to the main technological cycle of refrigeration consuming production, according to which refrigeration units and heat exchangers are created. Thus, in order to solve the problem of optimizing the heat exchange process, it is necessary to take into account the conditions for the rational organization of the technological cycle of refrigeration-consuming production.As is known, cooling of a certain environment is possible using a heat exchanger. Its design solution should be selected according to the technological requirements that apply to these devices. Especially important point is the compliance of the device with the technological process heat treatment environment, which is possible under the following conditions:
- maintaining a given temperature of the working process and control (regulation) over temperature conditions;
- selection of device material, according to chemical properties environment;
- control over the length of time the medium remains in the device;
- correspondence of operating speeds and pressure.
- ensuring the necessary speed of working media to implement turbulent conditions;
- creating the most suitable conditions for removing condensate, scale, frost, etc.;
- Creation favorable conditions for the movement of working media;
- preventing possible contamination of the device.
The ease of use and reliability of the device are influenced by factors such as strength and tightness. detachable connections, compensation for temperature deformations, ease of maintenance and repair of the device. These requirements form the basis for the design and selection of a heat exchange unit. The main role in this is to ensure the required technological process in refrigeration-consuming production.
In order to choose the right design solution for the evaporator, you must be guided by the following rules. 1) cooling of liquids is best done using a rigid tubular heat exchanger or a compact plate heat exchanger; 2) the use of tubular-fin devices is due to the following conditions: The heat transfer between the working media and the wall on both sides of the heating surface differs significantly. In this case, the fins must be installed on the side with the lowest heat transfer coefficient.
To increase the intensity of heat exchange in heat exchangers, it is necessary to adhere to the following rules:
- security proper conditions for condensate removal in air coolers;
- reducing the thickness of the hydrodynamic boundary layer by increasing the speed of movement of the working fluids (installation of inter-tube partitions and dividing the tube bundle into passages);
- improving the flow of working fluids around the heat exchange surface (the entire surface should actively participate in the heat exchange process);
- compliance with basic temperature indicators, thermal resistances, etc.
Improving heat exchange processes is one of the main processes for improving the heat exchange equipment of refrigeration machines. In this regard, research is being carried out in the fields of energy and chemical engineering. This is the study of the regime characteristics of the flow, turbulization of the flow by creating artificial roughness. In addition, new heat exchange surfaces are being developed, which will make heat exchangers more compact.
Choosing a rational approach for calculating the evaporator
When designing an evaporator, structural, hydraulic, strength, thermal and technical and economic calculations should be carried out. They are performed in several versions, the choice of which depends on performance indicators: technical and economic indicators, efficiency, etc.To perform a thermal calculation of a surface heat exchanger, it is necessary to solve the heat transfer and heat balance equation, taking into account certain conditions device operation ( design dimensions heat transfer surfaces, temperature change limits and patterns regarding the movement of the cooling and cooled medium). To find a solution to this problem, you need to apply rules that will allow you to obtain results from the original data. But due to numerous factors, find common decision not possible for different heat exchangers. At the same time, there are many methods for approximate calculations that are easy to perform manually or by machine.
Modern technologies allow you to select an evaporator using special programs. They are mainly provided by manufacturers of heat exchange equipment and allow you to quickly select the required model. When using such programs, it is necessary to take into account that they assume the operation of the evaporator under standard conditions. If actual conditions differ from standard conditions, the evaporator performance will be different. Thus, it is advisable to always carry out verification calculations of the evaporator design you have chosen, relative to its actual operating conditions.