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Liquid properties (TL)#

block

Block appearance in REPEAT VISION#

 The Liquid Properties (TL) block provides physical liquid properties for the thermal liquid network.

Important

These properties are global: they do not apply to one component, but to all that make up the network.

Important

Each thermal liquid network in the model shall be connected to exactly one instance of that block

 The parameters defined in this block are:

  • Thermal-dynamic properties — density, specific internal energy and specific heat capacity;

  • Derived properties — volume modulus of elasticity and thermal expansion coefficient;

  • Transport properties — kinematic viscosity and thermal conductivity.

1.  Parameterization#

 The block provides several parameterization options for independent state, density and specific internal energy variables.

Note

The parameterization selected determines which data to retrieve and which state variables to set.

2.  Density and its derivatives#

 The block provides three types of parameterization for density and two derived parameters, on which the calculation of density often depends - isothermal volume module and isobaric coefficient of thermal expansion:

  • Tables of density, volumetric modulus and thermal expansion coefficient — require tabular data on temperature and pressure;

  • Density table/vector — sets the density depending on the temperature (and pressure in the 2D case). The block calculates the isothermal volumetric modulus and isobaric coefficient of thermal expansion using the finite difference method (1), (2) :

(1)#\[B_p=\rho\cdot (\frac{∂p}{∂\rho})_T\]
(2)#\[\alpha=\frac{1}{\rho}\cdot (\frac{∂p}{∂T})_p\]

  • Reference density — specifies density, volumetric modulus and coefficient of thermal expansion at known temperature and pressure (3) :

(3)#\[ln(\frac{\rho}{\rho_R})=-\alpha \cdot(T-T_R)+\frac{p-p_R}{B_R}\]

3.  Specific internal energy#

 As with density, the block provides three types of specific internal energy parameterization:

  • Tables of specific internal energy and specific heat capacity — require tabular data on temperature and pressure;

  • Specific internal energy table/vector — calculates the specific heat capacity (4) :

(4)#\[c_p(T, p)=(\frac{∂U}{∂T})_p+\frac{p\cdot \alpha}{\rho}\]

  • Specific heat capacity table/vector — calculates specific internal energy {eq} ‘ThermalLiquidPropertiesBlock5’:

(5)#\[u(T, p)=\int^T_{T_{R}}(c_p(T, p)-\frac{p\cdot \alpha(T, p)}{\rho (T, p)})dT+u_R\]

4.  Specific heat capacity at constant volume#

 Specific heat capacity at constant volume should be greater than zero. It is calculated using the formula (6) :

(6)#\[c_v=c_p-\frac{T\cdot \alpha^2}{B\cdot \rho}\]

where:

 \(c_p\) — specific heat capacity at constant pressure, [J/(kg\(\cdot\)K)];

 T — temperature, [K];

 \(\alpha\) — coefficient of thermal expansion, [К\(^{-1}\)];

 B — volumetric modulus of elasticity, [Pa];

 \( ho\) — density, [kg/m\(^3\)].”

5.  Properties#

Property

Default Value

Description

Units of measurement

Related block

-

You need to select the thermohydraulics block that has already been added to the canvas

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Parameter

-

You must select the parameter of the selected linked block

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Table dimensions:
2D;
1D;
0D

2D

-

-

Temperature vector, available when selecting Table dimensions - 2D or 1D

273.15;283.15;293.15;303.15;313.15;323.15;333.15;343.15;353.15;363.15;373.15

-

К

Pressure vector, available when selecting Table dimensions -2D

10000.0;100000.0;5000000.0;1.0E7;1.5E7;2.0E7;2.5E7;3.0E7;3.5E7;4.0E7;4.5E7;5.0E7

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Pa

Atmospheric pressure

101325.0

-

Pa

Density parameterization:
Reference density;
Density vector - \( ho(T)\), available when selecting Table dimensions -1D

Reference density

-

-

Density parameterization:
Density, bulk modulus and thermal expantion tables - \( ho\)(T,p), \(\alpha\)(T,p), \(\beta\)(T,p);
Density table - \( ho\)(T,p);
Reference density, available when selecting Table dimensions - 2D or 1D

Density, bulk modulus and thermal expantion tables - \( ho\)(T,p), \(\alpha\)(T,p), \(\beta\)(T,p)

-

-

Density, available when selecting Density parameterization - Reference density, Table dimensions - 1D or Density parameterization - Reference density, Table dimensions - 2D or 0D

998.21

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kg/m\(^3\)

Density table - \( ho\)(T,p), available when selecting Table dimensions - 2D, Density parameterization - Density, bulk modulus and thermal expantion tables - $ ho$(T,p), $\alpha$(T,p), $\beta$(T,p) or Density table - $ ho$(T,p)

\u003C999.7973;999.6579;998.1632;995.6057;992.1724;988.02;983.18;977.75;971.77;965.26;958.62\u003E_\u003C999.8431;999.7009;998.2045;995.6458;992.2119;988.0299;983.1901;977.7583;971.7836;965.3023;958.6315\u003E_\u003C1002.3216;1002.0303;1000.4375;997.8186;994.3513;990.1568;985.3217;979.9094;973.9673;967.5311;960.627\u003E_\u003C1004.8218;1004.382;1002.6924;1000.0128;996.5113;992.3035;987.4721;982.0783;976.1678;969.7753;962.9267\u003E_\u003C1007.293;1006.7084;1004.9239;1002.1841;998.6484;994.4268;989.5983;984.2216;978.3409;971.9901;965.1944\u003E_\u003C1009.7358;1009.0101;1007.1324;1004.3332;1000.7633;996.5273;991.7008;986.34;980.4876;974.1764;967.4314\u003E_\u003C1012.1506;1011.2874;1009.3183;1006.4603;1002.8563;998.6056;993.7803;988.4343;982.6087;976.3354;969.6387\u003E_\u003C1014.5379;1013.5407;1011.4819;1008.566;1004.928;1000.6622;995.8374;990.505;984.7049;978.4676;971.8173\u003E_\u003C1016.8979;1015.7703;1013.6236;1010.6505;1006.9788;1002.6976;997.8726;992.5529;986.7768;980.5741;973.9681\u003E_\u003C1019.2311;1017.9766;1015.7438;1012.7144;1009.009;1004.7123;999.8864;994.5786;988.8254;982.6556;976.0921\u003E_\u003C1021.538;1020.1599;1017.8428;1014.758;1011.0192;1006.7067;1001.8795;996.5825;990.8511;984.7129;978.19\u003E_\u003C1023.8188;1022.3206;1019.921;1016.7815;1013.0097;1008.6813;1003.8522;998.5654;992.8545;986.7465;980.2628\u003E

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kg/m\(^3\)

Density vector - \( ho\)(T), available when selecting Table dimensions - 1D, Density parameterization - Density vector - $ ho(T)$

999.84; 999.7; 998.2; 995.65; 992.21; 988.03; 983.19; 977.76; 971.78; 965.3; 958.8;

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kg/m\(^3\)

Reference temperature, available when selecting Density parameterization - Reference density, Table dimensions - 1D or Density parameterization - Reference density, Table dimensions - 2D or 0D

293.16

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К

Reference pressure, available when selecting Density parameterization - Reference density or Density vector - $ ho(T)$, Table dimensions - 1D or Density parameterization - Reference density, Table dimensions - 2D or 0D

101325.0

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Pa

Constant isothermal bulk modulus, available when selecting Density parameterization - Reference density or Density vector - $ ho(T)$, Table dimensions - 1D or Density parameterization - Reference density, Table dimensions - 2D or 0D

2.1791E9

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Pa

Isothermal bulk modulus table - \(\beta\)(T,p), available when selecting Table dimensions - 2D, Density parameterization - Density, bulk modulus and thermal expantion tables - $ ho$(T,p), $\alpha$(T,p), $\beta$(T,p)

\u003C1.9649E9;2.0913E9;2.1786E9;2.2332E9;2.26E9;2.2638E9;2.2472E9;2.214E9;2.1668E9;2.1081E9;2.0494E9\u003E_\u003C1.9654E9;2.0918E9;2.1791E9;2.2337E9;2.2605E9;2.2638E9;2.2472E9;2.214E9;2.1668E9;2.1081E9;2.0494E9\u003E_\u003C1.9929E9;2.1191E9;2.2067E9;2.2619E9;2.2895E9;2.2936E9;2.2779E9;2.2455E9;2.1992E9;2.1413E9;2.0739E9\u003E_\u003C2.0213E9;2.1471E9;2.235E9;2.2908E9;2.3191E9;2.324E9;2.3092E9;2.2776E9;2.2321E9;2.175E9;2.1084E9\u003E_\u003C2.0499E9;2.1752E9;2.2634E9;2.3197E9;2.3487E9;2.3544E9;2.3403E9;2.3096E9;2.2649E9;2.2086E9;2.1428E9\u003E_\u003C2.0787E9;2.2036E9;2.2919E9;2.3487E9;2.3784E9;2.3848E9;2.3715E9;2.3415E9;2.2976E9;2.2421E9;2.177E9\u003E_\u003C2.1078E9;2.2322E9;2.3206E9;2.3778E9;2.4081E9;2.4151E9;2.4025E9;2.3733E9;2.3301E9;2.2754E9;2.211E9\u003E_\u003C2.1372E9;2.261E9;2.3494E9;2.407E9;2.4378E9;2.4455E9;2.4336E9;2.405E9;2.3626E9;2.3085E9;2.2449E9\u003E_\u003C2.1668E9;2.2899E9;2.3784E9;2.4363E9;2.4675E9;2.4758E9;2.4646E9;2.4367E9;2.3949E9;2.3415E9;2.2786E9\u003E_\u003C2.1966E9;2.3191E9;2.4075E9;2.4657E9;2.4973E9;2.5062E9;2.4955E9;2.4683E9;2.4272E9;2.3744E9;2.3121E9\u003E_\u003C2.2268E9;2.3485E9;2.4367E9;2.4951E9;2.5272E9;2.5365E9;2.5264E9;2.4998E9;2.4593E9;2.4072E9;2.3455E9\u003E_\u003C2.2572E9;2.3781E9;2.4661E9;2.5246E9;2.5571E9;2.5669E9;2.5573E9;2.5313E9;2.4914E9;2.4399E9;2.3788E9\u003E

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Pa

Constant isobaric thermal expantion coefficient, available when selecting Density parameterization - Reference density, Table dimensions - 1D or Density parameterization - Reference density, Table dimensions - 2D or 0D

2.0691E-4

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1/К

Isobaric thermal expantion coefficient table - \(\alpha\)(T,p), available when selecting Table dimensions - 2D, Density parameterization - ``Density, bulk modulus and thermal expantion tables - \( ho\)(T,p), \(\alpha\)(T,p), \(\beta\)(T,p)`

\u003C-6.79E-5;8.78E-5;2.068E-4;3.034E-4;3.855E-4;4.578E-4;5.233E-4;5.84E-4;6.414E-4;6.967E-4;7.519E-4\u003E_\u003C-6.76E-5;8.81E-5;2.069E-4;3.035E-4;3.856E-4;4.578E-4;5.233E-4;5.84E-4;6.414E-4;6.967E-4;7.519E-4\u003E_\u003C-4.9E-5;9.98E-5;2.141E-4;3.074E-4;3.87E-4;4.572E-4;5.209E-4;5.801E-4;6.36E-4;6.898E-4;7.423E-4\u003E_\u003C-3.07E-5;1.114E-4;2.213E-4;3.113E-4;3.884E-4;4.566E-4;5.186E-4;5.762E-4;6.307E-4;6.831E-4;7.342E-4\u003E_\u003C-1.3E-5;1.227E-4;2.283E-4;3.152E-4;3.899E-4;4.562E-4;5.165E-4;5.725E-4;6.256E-4;6.766E-4;7.264E-4\u003E_\u003C4.1E-6;1.337E-4;2.352E-4;3.191E-4;3.914E-4;4.558E-4;5.144E-4;5.691E-4;6.208E-4;6.705E-4;7.189E-4\u003E_\u003C2.06E-5;1.445E-4;2.42E-4;3.229E-4;3.93E-4;4.555E-4;5.125E-4;5.657E-4;6.161E-4;6.646E-4;7.118E-4\u003E_\u003C3.65E-5;1.549E-4;2.486E-4;3.267E-4;3.946E-4;4.552E-4;5.107E-4;5.625E-4;6.117E-4;6.589E-4;7.049E-4\u003E_\u003C5.19E-5;1.651E-4;2.551E-4;3.305E-4;3.961E-4;4.55E-4;5.09E-4;5.595E-4;6.074E-4;6.535E-4;6.983E-4\u003E_\u003C6.68E-5;1.75E-4;2.614E-4;3.341E-4;3.977E-4;4.549E-4;5.074E-4;5.566E-4;6.033E-4;6.482E-4;6.92E-4\u003E_\u003C8.11E-5;1.846E-4;2.676E-4;3.377E-4;3.993E-4;4.548E-4;5.059E-4;5.538E-4;5.994E-4;6.432E-4;6.859E-4\u003E_\u003C9.49E-5;1.939E-4;2.736E-4;3.413E-4;4.009E-4;4.547E-4;5.045E-4;5.512E-4;5.956E-4;6.384E-4;6.8E-4\u003E

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1/К

Internal energy parametrization:
Specific internal energy vector - U(T);
Specific heat vector - Cp(T), available when selecting Table dimensions - 1D

Specific internal energy vector - U(T)

-

-

Internal energy parametrization:
Specific internal energy and specific heat tables - U(T,p), Cp(T,p);
Specific internal energy table - U(T,p);
Specific heat table - Cp(T,p), available when selecting Table dimensions - 2D

Specific internal energy and specific heat tables - U(T,p), Cp(T,p)

-

-

Specific internal energy vector - U(T), available when selecting Table dimensions - 1D, Internal energy parametrization - Specific internal energy vector - U(T)

1.8;42060.0;83948.0;125760.0;167560.0;209360.0;251190.0;293060.0;334990.0;377000.0;418010.0;

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J/kg

Specific internal energy table - U(T,p), available when selecting Table dimensions - 2D, Internal energy parametrization - Specific internal energy and specific heat tables - U(T,p), Cp(T,p) or Specific internal energy table - U(T,p)

\u003C0.2;42062.0;83953.0;125770.0;167570.0;209360.0;251190.0;293060.0;334990.0;377000.0;419010.0\u003E_\u003C1.8;42060.0;83948.0;125760.0;167560.0;209360.0;251190.0;293060.0;334990.0;377000.0;419010.0\u003E_\u003C86.0;41935.0;83651.0;125310.0;166960.0;208630.0;250330.0;292070.0;333860.0;375730.0;417690.0\u003E_\u003C158.8;41804.0;83349.0;124860.0;166370.0;207900.0;249470.0;291070.0;332730.0;374460.0;416270.0\u003E_\u003C219.0;41668.0;83049.0;124410.0;165790.0;207190.0;248620.0;290100.0;331630.0;373220.0;414890.0\u003E_\u003C267.0;41527.0;82749.0;123970.0;165210.0;206480.0;247790.0;289140.0;330540.0;372000.0;413540.0\u003E_\u003C303.4;41382.0;82451.0;123530.0;164650.0;205790.0;246980.0;288200.0;329480.0;370810.0;412210.0\u003E_\u003C328.8;41233.0;82153.0;123100.0;164090.0;205110.0;246180.0;287280.0;328440.0;369640.0;410910.0\u003E_\u003C343.6;41081.0;81856.0;122680.0;163540.0;204450.0;245390.0;286380.0;327410.0;368500.0;409640.0\u003E_\u003C348.3;40924.0;81560.0;122250.0;163000.0;203790.0;244620.0;285490.0;326410.0;367380.0;408400.0\u003E_\u003C343.5;40763.0;81265.0;121840.0;162460.0;203140.0;243860.0;284620.0;325430.0;366270.0;407170.0\u003E_\u003C329.4;40599.0;80971.0;121420.0;161940.0;202500.0;243120.0;283770.0;324460.0;365190.0;405980.0\u003E

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J/kg

Specific heat table - Cp(T,p), available when selecting Table dimensions - 2D, Internal energy parametrization - Specific internal energy and specific heat tables - U(T,p), Cp(T,p) or Specific internal energy table - U(T,p)

\u003C4219.9;4195.5;4184.3;4180.1;4179.6;4181.3;4185.0;4190.1;4196.8;4205.2;4213.6\u003E_\u003C4219.4;4195.1;4184.0;4179.8;4179.4;4181.3;4185.0;4190.1;4196.8;4205.2;4213.6\u003E_\u003C4195.7;4176.9;4169.0;4166.7;4167.5;4170.2;4174.2;4179.5;4186.2;4194.4;4204.5\u003E_\u003C4172.6;4159.2;4154.3;4153.8;4155.8;4159.2;4163.6;4169.0;4175.7;4183.7;4193.5\u003E_\u003C4150.8;4142.2;4140.1;4141.3;4144.4;4148.4;4153.2;4158.8;4165.5;4173.3;4182.8\u003E_\u003C4130.0;4125.9;4126.4;4129.3;4133.4;4138.0;4143.2;4148.9;4155.5;4163.2;4172.4\u003E_\u003C4110.3;4110.3;4113.3;4117.7;4122.7;4127.9;4133.4;4139.3;4145.8;4153.4;4162.3\u003E_\u003C4091.6;4095.4;4100.7;4106.4;4112.3;4118.1;4123.9;4129.9;4136.4;4143.8;4152.4\u003E_\u003C4073.8;4081.2;4088.5;4095.6;4102.3;4108.6;4114.6;4120.7;4127.3;4134.5;4142.9\u003E_\u003C4056.9;4067.6;4076.8;4085.1;4092.6;4099.3;4105.6;4111.8;4118.3;4125.5;4133.5\u003E_\u003C4040.8;4054.5;4065.6;4075.0;4083.2;4090.3;4096.9;4103.2;4109.6;4116.6;4124.5\u003E_\u003C4025.4;4042.1;4054.8;4065.3;4074.1;4081.6;4088.4;4094.7;4101.2;4108.0;4115.7\u003E

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J/(kg\(\cdot\)K)

Specific heat, available when selecting Table dimensions - 0D

4184.3

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J/(kg\(\cdot\)K)

Kinematic viscosity, available when selecting Table dimensions - 0D

1.0034E-6

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m\(^2\)/s

Kinematic viscosity vector - Nu(T), available when selecting Table dimensions - 1D

1.0034E-6;1.0034E-6;1.0034E-6;1.0034E-6;1.0034E-6;1.0034E-6;1.0034E-6;1.0034E-6;1.0034E-6;1.0034E-6;1.0034E-6;

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m\(^2\)/s

Kinematic viscosity table - Nu(T,p), available when selecting Table dimensions - 0D

\u003C1.7917E-6;1.3061E-6;1.0032E-6;8.006E-7;6.577E-7;5.53E-7;4.739E-7;4.127E-7;3.643E-7;3.254E-7;2.866E-7\u003E_\u003C1.7914E-6;1.3059E-6;1.0032E-6;8.005E-7;6.577E-7;5.53E-7;4.739E-7;4.127E-7;3.643E-7;3.254E-7;2.866E-7\u003E_\u003C1.7763E-6;1.2986E-6;9.995E-7;7.987E-7;6.57E-7;5.529E-7;4.741E-7;4.131E-7;3.648E-7;3.261E-7;2.945E-7\u003E_\u003C1.7615E-6;1.2914E-6;9.959E-7;7.97E-7;6.562E-7;5.527E-7;4.743E-7;4.135E-7;3.654E-7;3.267E-7;2.952E-7\u003E_\u003C1.7473E-6;1.2845E-6;9.924E-7;7.953E-7;6.555E-7;5.526E-7;4.745E-7;4.139E-7;3.659E-7;3.273E-7;2.959E-7\u003E_\u003C1.7338E-6;1.2779E-6;9.891E-7;7.937E-7;6.548E-7;5.525E-7;4.747E-7;4.143E-7;3.665E-7;3.28E-7;2.965E-7\u003E_\u003C1.7208E-6;1.2716E-6;9.859E-7;7.922E-7;6.543E-7;5.524E-7;4.75E-7;4.148E-7;3.67E-7;3.286E-7;2.972E-7\u003E_\u003C1.7085E-6;1.2656E-6;9.829E-7;7.908E-7;6.537E-7;5.524E-7;4.753E-7;4.152E-7;3.676E-7;3.293E-7;2.979E-7\u003E_\u003C1.6967E-6;1.2598E-6;9.801E-7;7.894E-7;6.532E-7;5.524E-7;4.755E-7;4.157E-7;3.682E-7;3.299E-7;2.986E-7\u003E_\u003C1.6854E-6;1.2543E-6;9.774E-7;7.881E-7;6.528E-7;5.524E-7;4.758E-7;4.162E-7;3.688E-7;3.306E-7;2.993E-7\u003E_\u003C1.6747E-6;1.2491E-6;9.748E-7;7.87E-7;6.523E-7;5.524E-7;4.762E-7;4.167E-7;3.694E-7;3.312E-7;3.0E-7\u003E_\u003C1.6645E-6;1.2441E-6;9.724E-7;7.859E-7;6.52E-7;5.525E-7;4.765E-7;4.172E-7;3.7E-7;3.319E-7;3.007E-7\u003E

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m\(^2\)/s

Thermal conductivity, available when selecting Table dimensions - 0D

0.59844

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W/(m\(\cdot\)K)

Thermal conductivity vector - K(T), available when selecting Table dimensions - 1D

0.59844;0.59844;0.59844;0.59844;0.59844;0.59844;0.59844;0.59844;0.59844;0.59844;0.59844;

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W/(m\(\cdot\)K)

Thermal conductivity table - K(T,p), available when selecting Table dimensions - 2D

\u003C0.56104;0.58002;0.59844;0.61548;0.6306;0.64361;0.65439;0.66313;0.67002;0.67527;0.68052\u003E_\u003C0.56109;0.58007;0.59848;0.61552;0.63064;0.64361;0.65439;0.66313;0.67002;0.67527;0.68052\u003E_\u003C0.5638;0.58245;0.60073;0.61773;0.63287;0.64588;0.65673;0.66554;0.67251;0.67785;0.68177\u003E_\u003C0.56656;0.58488;0.60303;0.62;0.63515;0.64821;0.65912;0.668;0.67505;0.68048;0.6845\u003E_\u003C0.56932;0.58732;0.60533;0.62226;0.63744;0.65053;0.6615;0.67046;0.67759;0.68311;0.68722\u003E_\u003C0.57208;0.58975;0.60764;0.62454;0.63972;0.65286;0.66389;0.67291;0.68012;0.68573;0.68994\u003E_\u003C0.57482;0.59218;0.60994;0.62681;0.64201;0.65518;0.66627;0.67536;0.68264;0.68834;0.69264\u003E_\u003C0.57754;0.59461;0.61224;0.62907;0.64429;0.65751;0.66865;0.6778;0.68516;0.69094;0.69534\u003E_\u003C0.58024;0.59702;0.61454;0.63134;0.64657;0.65982;0.67102;0.68024;0.68767;0.69353;0.69802\u003E_\u003C0.58292;0.59942;0.61682;0.6336;0.64884;0.66214;0.67338;0.68267;0.69017;0.69611;0.70069\u003E_\u003C0.58557;0.6018;0.6191;0.63585;0.65111;0.66444;0.67574;0.68509;0.69266;0.69868;0.70335\u003E_\u003C0.58818;0.60416;0.62136;0.63809;0.65336;0.66674;0.67809;0.6875;0.69514;0.70124;0.706\u003E

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W/(m\(\cdot\)K)

6.  Inputs and outputs#

No

7.  Примеры использования#

 С примерами использования данного блока можно ознакомиться в следующих разделах:

Практическое руководство

Раздел

Название руководства

Энергетика

Development of a model of the industrial circuit system of oil coolers of NPP with WCWR
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