Engineering calculations of the processes of changing the state of water and steam and steam cycles are carried out according to tables of thermodynamic properties of water and steam. These tables have been compiled on the basis of reliable experimental data with agreement of experimental results and calculated values at the interstate levels.
In our country, the approved standard is the tables of the thermodynamic properties of water and steam, compiled by M.P. Vukalovich, S.L. Rivkin, A.A. Aleksandrov. They include data on the thermodynamic properties of water and steam in the range of pressure changes from 0.0061 to 1000 bar and temperatures from 0 to 1000 o C.
The tables contain all the data necessary for calculating thermodynamic parameters in the area of liquid, wet steam and in the area of superheated steam. The tables do not show the values of internal energy; for its calculation, the ratio u = h - Pv is used. When calculating the internal energy, it is necessary to pay attention to the correspondence of the units of measurement of the enthalpy h, it is given in the tables in kilojoules per kilogram (kJ / kg), and the product of pv, when using pressure in kilopascals (kPa), this product will also be in kilojoules per kilogram (kJ / kg).
The tables are structured as follows. The first and second tables describe the properties of water and steam at saturation as a function of temperature (1st table) and pressure (2nd table). These two tables give the dependence of the parameters on the lines x = 0 (water in a state of saturation) and x = 1 (dry saturated steam) on temperature and pressure. All parameters are found using one value; in table. 1 - by temperature, in table. 2 - by saturation pressure. These defining parameters are in the leftmost columns of the tables. Further in the right columns are the corresponding P n and t n values: v "and v", h "and h", r = h "-h", s "and s", s "-s". Parameters with one stroke refer to saturated water, and two stroke parameters refer to dry saturated steam. The values of the parameters of wet saturated steam are determined by calculation using the degree of dryness x. To facilitate these calculations, the tables give the values for r and s "-s". For example, the determination of the specific volume, enthalpy and entropy of wet steam is carried out according to the formulas
v x = v "+ x (v" - v "); h x = h" + xr; s x = s "+ x (s" - s ").
The range of the defining parameters of these tables: from t = 0 o C to t cr = 374.12 o C and from P = 0.0061 bar to P cr = 221.15 bar, i.e. the lower limit is the triple point of water, the upper limit is the critical point of water.
It should be noted that as a defining parameter in the table. 1 and 2, you can use any of the parameters (v ", v", h ", h", s ", s"), not just the pressure and saturation temperature. Since in engineering practice, P and t are most often the determining parameters, they were placed in the left column.
The next - third - table describes the properties of water and superheated steam. Their range is from 0 to 1000 o C (maybe up to 800 o C) and from 1 kPa to 100 MPa. Two quantities are required here as the governing parameters. In 3 tables, these are pressure - the upper horizontal line - and temperature - the leftmost column. A rectangle is given below the pressure bar, which contains all the saturation state parameters corresponding to the given pressure. This allows you to quickly navigate in the phase state of water and steam and, without leafing through the table, perform the necessary calculations for various phase states of water. Each pressure and temperature in 3 tables is given v, h, s in the corresponding vertical columns.
For visual orientation, the parameters of the liquid phase and the vapor phase are separated in these columns by bold horizontal lines. Above these lines is the liquid phase of water, below - superheated steam. At pressures above the critical (22.12 MPa), these dividing lines are absent, because at supercritical parameters, there is no line of visible phase transition of liquid to vapor.
Table 3, in addition to P and t, any pair of parameters can act as determinants: P, t, v, h, s.
When orienting in the phase states of water and steam using tables, it is necessary to remember:
1) at Р = const:
t< t н – жидкая фаза воды,
t> t n - superheated steam,
T = t n - the 3rd parameter is required,
For example:
h = h "- boiling water,
h = h "- dry saturated steam,
h "< h < h" – влажный пар,
h< h" – жидкая фаза воды,
h> h "- superheated steam,
h "< h < h" – влажный пар.
2) at t = const:
R< Р н – перегретый пар,
P> P n - liquid phase of water,
P = P n - similarly t = t n at P = const with orientation to h, v, s.
Some editions of tables include 2 parts: 1st in SI, where P - in Pa, h - in kJ / kg, and 2nd in SGS, where P - in kgf / cm 2, and h - in kcal / kg.
6.8. Chart T, s for water and steam
The T, s-diagram is widely used to illustrate the processes of changing the state of water and steam and steam cycles. It provides a large amount of information that allows one to judge about the features of energy effects and about the thermal efficiency of cycles.
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In the thermal diagram T, s, lines of constant parameters of water and steam and functions of state are plotted (Fig. 6.21).
Zero entropy corresponds to the triple point of the liquid (0.01 ° C or 273.16 K and 611.2 Pa). The construction of lines of constant parameters and state functions is carried out according to the data of tables of thermodynamic properties of water and steam. Using the tabular values of the relationship between the saturation temperature T n and the entropy of the boiling liquid s "and dry saturated vapor s", it is possible to construct the lower (x = 0) and upper (x = 1) boundary curves. These boundary curves are connected at the critical point K with the coordinates T cr = 647.27 K (374.12 o C) and s cr = 4.4237 kJ / (kg · K). The line x = 0 begins at the triple point of the liquid at T = 273.16 K and s 1 "= 0. The entropy s N" = 9.1562 kJ / (kg · K) corresponds to a dry saturated vapor at the triple point (see Fig. 6.21, point N). Below the horizontal 1N there is a sublimation zone, here to the left of the line x = 1 is the region of the solid phase and vapor, and to the right of the line x = 1 is the region of superheated vapor. Above the line x = 0 is the region of the liquid phase, and above the line x = 1 is the region of superheated vapor. There is no visible zone of transition from the region of the liquid phase to the region of vapor at supercritical parameters; conventionally, this transition can be taken by the critical parameters T cr, P cr or v cr, considering the region above the critical point and to the right of P cr or v cr as the vapor region.
The isobar of subcritical pressure in the T, s-diagram is a complex curve 1234. It consists of three parts: 12 - in the liquid region, 23 - in the wet saturated vapor region, 34 - in the superheated vapor region. The configuration of the isobar can be set using the slope from the expression
¶Q p = (c p dT) p = (Tds) p,
whence the slope will be
Based on the expression for the slope (6.28), which determines the angle of inclination of the tangent to the isobar, it follows that in the region of liquid and in the region of superheated steam, when heat is supplied, the values of T / c p and s increase, the angle of inclination of the tangent increases, i.e. here the isobar is a concave curve. Moreover, in the liquid region at low pressures, c p is a value that changes little depending on temperature, and the isobar is a logarithmic curve. In the region of superheated steam, c p strongly depends on temperature and the isobar is a logarithmic curve with a variable logarithmic (the nature of the change in c p in the region of superheated steam was written earlier). In the region of wet saturated vapor, the isobar coincides with the isotherm, c p = ± ¥, and in the T, s-diagram it represents the horizontal line 23.
At low pressures (up to 100 bar), the isobars of the liquid are very close to the lower boundary curve (x = 0). Therefore, when using the T, s-diagram to illustrate the processes of water and steam, it is often assumed that the isobars of the liquid coincide with the line x = 0.
The area under isobar 12 (heating of the liquid) corresponds to the heat of the liquid q ", under isobar 23 (vaporization) - to the heat of vaporization r, under 34 (overheating of steam) - to the heat of superheat q p. The area under process 2e corresponds to the heat consumed for evaporation of the x-th share of 1 kg of saturated liquid.
For any state in the area of wet saturated steam (point e), the degree of dryness can be determined graphically as the ratio of two isobar segments between the boundary curves x = 0 and x = 1:
.
According to this principle, it is possible to construct lines of constant degrees of dryness x = const.
The critical pressure isobar at the critical point K has an inflection, here the tangent to it is a horizontal line. Supercritical pressure isobars do not fall into the wet steam region and are continuously increasing curves with inflection points, in which the tangents have a minimum slope. These points correspond to the maximum values of the isobaric heat capacity.
Isochores with v< v кр пересекают только нижнюю пограничную кривую х=0 и размещаются в области жидкости при высоких давлениях и температурах, а в области влажного насыщенного пара – при низких давлениях и температурах.
For all isochores corresponding to a specific volume greater than the specific volume of liquid at the triple point of water, with decreasing pressure and temperature of wet vapor, its degree of dryness tends to zero, but never reaches it, therefore isochores never reach the lower boundary curve (with the exception of the anomalous region in temperature range 0 - 8 о С).
Isochores with v> v cr in the area of superheated steam are concave curves (steeper than isobars), and in the area of wet steam - curves of double curvature: convex - at high degrees of dryness and concave - at low degrees of dryness. Moreover, they intersect only the right boundary curve x = 1.
In fig. 6.21 shows the lines of constant enthalpies h = const. In the region of superheated steam, the isenthalp is a smooth curve with a negative tangent of the angle of inclination to it. Isoenthalps passing from the region of wet vapor to the region of liquid have a pronounced inflection point on the line x = 0. an increase in temperature.
In fig. 6.21 at points 2 and 3 tangents to the boundary curves x = 0 and x = 1 are drawn. The subtangent c "and c" represent the heat capacities of the liquid and dry saturated vapor on the boundary curves (with a change in state along x = 0 and x = 1). It turns out that c "> 0, and c"<0. Последнее означает, что при понижении температуры для поддержания пара в состоянии сухого насыщенного к нему необходимо подводить теплоту.
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Tables of thermodynamic properties of water and steam
To determine the parameters of the state of water and water vapor, tables of thermodynamic (thermophysical) properties of water and water vapor are used. Modern tables are compiled using the International System of Units, SI. The following designations of physical quantities and their dimensions are adopted in the tables:
p- pressure, Pa: 1 MPa = 10 3 kPa = 10 6 Pa = 10 bar;
T- temperature, K;
t- temperature, о С:
v- specific volume, m 3 / kg;
h- specific enthalpy, kJ / kg;
s- specific entropy, kJ / (kg × deg).
In thermodynamic calculations, parameters (except p and t) denote for a liquid at a saturation (boiling) temperature by the "prime" index ( v", h", s"), for dry saturated steam, the suffix" two dashes "( v"", h"", s""), and for wet saturated steam the index " X" (v x, h x, s x). The tables also show the specific heat of vaporization. r = h"" – h"and the enthalpy difference in the saturation state s"" and s".
For wet saturated steam (dryness 0< x < 1) параметры пара рассчитываются по формулам:
v x = v" + x (v"" – v"); (2.74)
h x = h" + x (h"" – h") = h" +x × r; (2.75)
s x = s" + x (s"" – s"). (2.76)
Moreover, v" < v x< v""; h" < h x < h""; s" < s x < s"".
For liquid at t < t n and for superheated steam at t > t n parameters of water and steam are found in the superheated steam table
At p £ p cr = 22.115 MPa the table is divided by a horizontal line into two parts: the upper one - for the liquid area; bottom - for superheated steam. The interface between these regions passes at t = t n.
At p > p cr there is no visible phase transition of water into vapor and the substance remains homogeneous (liquid or vapor). In this case, the conditional boundary between liquid and vapor can be taken from the critical isotherm.
Internal energy for water and steam is not given in the tables, it is determined by the formula:
u = h – p× v. (2.77)
If u and h have the dimension kJ / kg, then the pressure should be expressed in kPa, and the specific volume in m 3 / kg.
Diagram h - S (enthalpy - entropy) is widely used in calculating steam processes and cycles of thermal power plants.
For practical purposes, the diagram h– s is performed not for all phase regions of water, but only for a limited region of water vapor (Fig. 2.17).
On the working diagram h– s a dense mesh of isobars, isochores, isotherms and lines of constant dryness is applied X... As already noted, in the region of wet saturated steam, the isotherm coincides with the isobar, and geometrically these are straight lines. The higher the pressure, the steeper the isobar and the closer to the ordinate axis.
In practice, four main thermodynamic processes of changing the state of water and water vapor are subject to calculation: isobaric ( p= const), isochoric ( v= const), isothermal ( T= const), adiabatic ( dq= 0). Representation of these processes in diagrams p– v and T- s is shown in fig. 2.15 and 2.16.
The state of wet saturated steam is determined in the technique by pressure R and the degree of dryness X... The point representing this state is at the intersection of the isobar and the line X= const. The state of the superheated steam is determined by the pressure R and temperature t... The point representing the state of superheated steam lies at the intersection of the corresponding isobar and isotherm.
Rice. 2.17 Working h – s steam diagram
Calculations of the main processes of water vapor can be carried out both analytically and graphically, using h– s charts. The analytical method is complicated due to the cumbersomeness of the equations of state for water vapor.
Table 2.4 shows the calculation formulas for determining the amount of heat, the work of changing the volume, and changing the internal energy for the main thermodynamic processes.
Table 2.4: Calculation formulas of the main thermodynamic processes
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Tables of thermophysical properties of water and water vapor are intended for calculating processes in water vapor and two-phase steam-water systems. They are calculated using formulas approved by the International Committee for the Equations for Water and Steam. This committee approves two systems of equations for calculating the thermodynamic properties of water and steam. One is intended for scientific calculations, and according to it, in fact, tables of the properties of water and steam are calculated. Another, less accurate, but simpler, is intended for engineering calculations on a computer.
The tables for single-phase (water or superheated steam) and two-phase (wet steam) conditions are different. The single-phase state is uniquely determined by two independent parameters; therefore, the tables of the thermodynamic properties of water and superheated steam have two arguments - pressure and temperature. Below is a part of such a table (Table 5.1).
For each given in table. 5.1 of pressure p in the range of 1 kPa - 98 MPa are given the values of the specific volume v, m3 / kg, enthalpy /, kJ / kg, and entropy s, kJ / (kgK), at temperatures from O to 800 ° C with a step of 10 ° C ... The table heading also contains the values of the saturation temperature / n, ° C, specific volumes v "and v", enthalpies V and / "and entropies s" and s "for saturated water and dry
Table 5.1
Thermodynamic properties of water and superheated steam _
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p = 0.001 MPa / n = 6.982 v "= 0.0010001; v" = 129.208 / "= 29.33; /" = 2513.8 5"= 0,1060; s " = 8,9756 |
p = 22.0 MPa / „= 373.68 v "= 0.002675; v" = 0.003757 / "= 2007.7; /" = 2192.5s "= 4.2891; s "" = 4.5748 |
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0,001002 |
s 0,000154 |
0,0009895 |
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0,0009901 |
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0,002025 |
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0,006843 |
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saturated steam, respectively, at a given pressure. Data above the bold line is for water, below for superheated steam.
The equilibrium state of a two-phase system is uniquely described by a single independent parameter; therefore, tables of thermodynamic properties of water and water vapor in a state of saturation have one argument - pressure or temperature. Typically, for ease of reference, reference books provide both possible tables: one with the argument "temperature", the other with the argument "pressure". Below is a part of such a table (Table 5.2).
Table 5.2
Thermodynamic properties of water and steam at saturation (pressure)
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s ", kJ / kg-K |
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Designations in table. 5.2 are the same as in table. 5.1, heat of phase transformationr = i "- kJ / kg.
For engineering calculations, the diagram / is often used instead of tables,s water vapor. Typically, this diagram covers the area of superheated steam, part of the upper boundary curve and the area of wet steam with a dryness x> 0.6 (Figure 5.10). The diagram shows isobars from 0.001 to 100 MPa and isotherms from 20 to 800 ° C, as well as isochores from 0.005 to 80 m 3 / kg.
To determine all parameters of water vapor from the diagram(R , t, v, /,s, x ) it is necessary to find on the diagram the point corresponding to the considered state of the vapor. For this, two independent parameters must be set. It should be remembered that in the saturation state, the pressure uniquely determines the saturation temperature and, conversely, the temperature determines the saturation pressure. Therefore, in contrast to the area of superheated steam, in the area of wet steam, all parameters can be determined if any pair of parameters is specified, except for the pressure - temperature pair.
In fig. 5.10 shows how the position of a point in the region of superheated steam is located at a given pressure and temperature (point 7). If
Rice. 5.10. Determination of steam parameters by /", s-diagram
at point 1, the process of adiabatic expansion begins to a known pressure p2, then the position of point 2 is determined by this pressure and entropy 52 = ^ 1-
To determine the temperature of wet steam from the /, s-diagram, for example, incl.2, this temperature should be determined at the same pressurep 2 and the degree of dryness x = 1 (point2"). Point temperature2" does not differ from the point temperature2, since both of them correspond to the state of saturation at the same pressure.
From the /, s-diagram, one can easily determine the external work that the steam performs during adiabatic expansion h = i (- i2, as well as the heat supplied in the isobaric process 2-4. This heat # 2-4 = C ~ h cannot be is defined as q = cp (t4 - t2), since in section 2-2 "the steam temperature does not change, and heat is spent on vaporization. As will be shown in Chapter 6, when steam is throttled, the enthalpy does not change. When steam is throttled from the state , characterized by point 7, up to pressure pb
point position 3 and steam parameters in this state can be found by pressure p 3 and enthalpy / 3 = i Y.
The examples given above show that the use of the /, t-diagram makes it easy to calculate the parameters and processes in water vapor, although with less accuracy than when using tables or special databases on a computer.
The table shows the thermophysical properties of water vapor at the saturation line depending on temperature. Steam properties are shown in the table in the temperature range from 0.01 to 370 ° C.
Each temperature corresponds to the pressure at which the water vapor is in a state of saturation. For example, at a water vapor temperature of 200 ° C, its pressure will be 1.555 MPa, or about 15.3 atm.
Specific heat capacity of steam, thermal conductivity and its increase as the temperature rises. The density of water vapor also increases. Water vapor becomes hot, heavy and viscous, with a high specific heat capacity, which positively affects the choice of steam as a heat carrier in some types of heat exchangers.
For example, according to the table, the specific heat capacity of water vapor C p at a temperature of 20 ° C it is equal to 1877 J / (kg deg), and when heated to 370 ° C, the heat capacity of steam increases to a value of 56520 J / (kg deg).
The table gives the following thermophysical properties of water vapor on the saturation line:
- steam pressure at specified temperature p · 10 -5, Pa;
- vapor density ρ″ , kg / m 3;
- specific (mass) enthalpy h ″, kJ / kg;
- r, kJ / kg;
- specific heat of steam C p, kJ / (kg deg);
- coefficient of thermal conductivity λ · 10 2, W / (m · deg);
- thermal diffusivity a · 10 6, m 2 / s;
- dynamic viscosity μ 10 6, Pa · s;
- kinematic viscosity ν 10 6, m 2 / s;
- Prandtl number Pr.
Specific heat of vaporization, enthalpy, thermal diffusivity and kinematic viscosity of water vapor decrease with increasing temperature. The dynamic viscosity and the Prandtl number of the steam increase in this case.
Be careful! Thermal conductivity in the table is indicated in the power of 10 2. Don't forget to divide by 100! For example, the thermal conductivity of steam at a temperature of 100 ° C is 0.02372 W / (m · deg).
Thermal conductivity of water vapor at various temperatures and pressures
The table shows the values of thermal conductivity of water and steam at temperatures from 0 to 700 ° C and pressures from 0.1 to 500 atm. Dimension of thermal conductivity W / (m · deg).
The line under the values in the table means the phase transition of water into steam, that is, the numbers under the line refer to steam, and above it - to water. According to the table, it can be seen that the value of the coefficient and water vapor increases with increasing pressure.
Note: the thermal conductivity in the table is indicated in the power of 10 3. Don't forget to divide by 1000!
Thermal conductivity of water vapor at high temperatures
The table shows the values of the thermal conductivity of dissociated water vapor in terms of W / (m · deg) at temperatures from 1400 to 6000 K and pressures from 0.1 to 100 atm.
According to the table, the thermal conductivity of water vapor at high temperatures noticeably increases in the range of 3000 ... 5000 K. At high pressures, the maximum thermal conductivity coefficient is achieved at higher temperatures.
Be careful! Thermal conductivity in the table is indicated in the power of 10 3. Don't forget to divide by 1000!
