OLGA 7
Methods and assumptions Thermal calculations for the wall rest on the assumption that radial heat conduction through the concentric walls is the dominating phenomenon. The heat flux may be calculated in two ways: The heat flux through the pipe wall layers is calculated by the code with user-defined thermal conductivities, specific heat capacities and densities for each wall layer. The heat flux is determined by a user-defined overall heat transfer coefficient. The former is recommended since the heat storage capacity in the wall is often significant. It is preferred to include a dynamic calculation of the temperatures of individual wall layers in a transient simulation. The latter option will save some CPU time, but should be used with care and preferably in steady state situations only.
Figure A: Illustration of a buried pipe Buried pipelines may be modelled with the soil as the outermost wall layer. The first method of calculating the heat flux (where heat flux is a function of wall properties) should then always be used due to the large thermal mass of the soil. The thickness of the composite soil layer is based on an equivalent heat transfer coefficient for the soil for a pipeline burial of a particular depth. Theoretically, the equivalent heat transfer coefficient from the outer surface of a buried pipeline to the top of the soil can be calculated to be:
(a) where: D H
= outer diameter diameter of buried pipe = distance from centre of pipe to top of soil lsoil = soil heat conductivity hsoil = overall heat heat transfer coefficient for soil
The term cosh-1 (x) can be expressed mathematically as follows: cosh-1 (x) = ln ( x + ( x2 - 1 ) 0.5 )
for x ³ 1
The thickness of the composite soil layer can be determined using the expression below for a known value of the soil thermal conductivity:
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(b) where: Rsi
= inner radius of soil layer (=outer radius of pipe wall)
Rso = outer radius of soil layer ksoil = input value of soil conductivity The specific heat capacity of the soil may be adjusted as follows in order to predict the transient heat transfer accurately:
(c) where: Cp input = input value of soil thermal capacity Cp soil = soil thermal capacity Heat transfer at steady state conditions depends only on the outer soil layer radius R so and on ksoil. However, for dynamic situations, a good soil discretization is important in order to obtain a reliable temperature profile across the wall layer. Alternatively, the Solid Bundle module may be used in such a situation. Phase changing materials The model for simulating phase changing materials accounts for latent heat of fusion and the difference in thermal properties for unfrozen and frozen materials. Thermal conductivity and heat capacity are given for three ranges, above the melting point, below the melting point and in the transition phase. For heat capacity, the value specified in HEATTRANSFER is used for all temperatures above the melting point. A multiplier ( HCAPMULT) is used below the melting point. If the FUISIONMULT key is different from 0, a step wise function is used for heat capacity having the value equal to FUSIONMULT in the phase changing region. If the FUSIONMULT key is 0, linear interpolation is performed between 1 and HCAPMULT. The FUSIONMULT key takes the latent heat of fusion (additional energy added or withdrawn for a phase change) into consideration. The exmple below describes how the latent heat of fusion is caluated. The phase changing region is from 0 to -1 C. Then, one multiplier is used between 0 and -1 C, while another multiplier is used below -1 C. The multiplier between 0 and -1 C also takes into consideration the latent heat of fusion. As an example soil with dry density 1900 kg/m3. With 10% water weight/dry soil weight the moist unfrozen heat capacity is 1067 J/(kgC) (0.255 btu/(lbF) and the frozen heat capacity is 876 J/(kgC) (0.209 btu/(lbF). The latent heat of fusion is (190 kg/m3*333 kJ/kg)/(2090 kg/m3) = 30.27 kJ/kg. This gives a multiplier of 29.4 in the range from 0 and -1 C. Thermal conductivity given in HEATTRANSFER is used directly for temperatures above the melting point. A conductivity multiplier (CONDMULT) is used for temperatures below the melting point. Linear interpolation is used in between.
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Limitations Wall Layer Thickness
The numerical solution for the temperatures in the wall layer depends on the discretisation of the layer. It is sufficient to undiscretize the wall layer for steady-state calculations. A finer discretisation of the wall layers may be necessary for transient calculations, when the heat storage in the pipe walls can be important (cool down or warm up), A wall layer should, as a rule of thumb, not be thicker than approximately 30% of the outer radius of the layer. The change in thickness, δ, between two neighbouring layers should be 0.2 ≤ δ(i)/δ(i-1) ≤ 5 to obtain a good accuracy. If ELECTRICHEAT is defined in the WALL definition, it is preferable to have at least three layers and define the electric heating in the middle layer. Very thin layers, such as paint etc., should be included in a neighbouring layer by adjusting the thickness and conductivity of that layer. Only the thickness needs to be adjusted if the thermal conductivity of the thin layer is fairly close to the conductivity of one of it's neighbours.
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SOLIDBUNDLE Description ( See also: Keys) This network component stores all information that is required to configure a solid bundle. This may be done by either editing the keywords and keys directly, or through the Bundle Editor in the GUI. Associated keywords: COMPONENT AMBIENTDATA TRENDDATA PROFILEDATA
Example - Buried pipeline In the following example, a (partially) buried pipeline is modelled. The pipe is assumed to have a centre line, yc, located 25 cm below the soil surface. The air temperature is measured to be 25 ° C and the soil temperature 1 m under the ground is 20 ° C. The soil temperature reading is assumed to be uninfluenced by the presence of the pipe.
1.
Start by adding a COMPONENT and associate the flowpath to this. A natural choice for the soil surface is y = 0, so the pipe must be moved down 25 cm. This is done by setting YOFFSET = -25 cm for this COMPONENT. 2. The soil is modelled by using a rectangular SHAPE with an associated soil MATERIAL. We assume that the effect of the pipe on the soil temperature is negligible at a distance of approximately 1.5 m to each side and 2 m down. The parameters for the shape then becomes: X_LOWER_LEFT = -1.5 m, Y_LOWER_LEFT = -2 m, X_UPPER_RIGHT = 1.5 m, Y_UPPER_RIGHT = 0 m. 3. Finally, the ambient conditions must be specified. In this case we can use a single AMBIENTDATA with TYPE = SIMPLEBURIED. Above ground we have air at 25 ° C, thus HOUTEROPTION = AIR and TAMBIENT = 25 C. We have positioned the soil surface at y = 0 m, so SOILSURFACELEVEL = 0 m. The soil temperature is set by specifying SOILTEMPERATURE = 20 C and SOILTEMPLEVEL = -1 m. COMMENTS: In this example, the OLGA WALL is in contact with both air and the solid SHAPE. Due to the 596 / 769
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potentially large temperature difference between the top and botom of the pipe, it may be advisable to remove some of the outer wall layers from the OLGA WALL and use one or more SHAPES to model the wall layers. This is done by simply creating a circular SHAPE with the outer radius of the wall layer. Please note that the order of the SHAPE COMPONENTS are important and that the wall layer COMPONENT must be defined after the rectangular soil COMPONENT. Otherwise, the wall layer COMPONENT will be hidden by the soil COMPONENT. The vertical boundaries of the soil above SOILTEMPLEVEL was modelled using the default NOFLUX option for SOILVERTBOUND. This option assumes that there naturally is no heat flux across these boundaries. However, if the boundaries are too close to the pipe, the temperature in the soil may be overestimated. A better choice may then be to use the FIXEDTEMP option. This will force the temperature to be equal to the SOILTEMPERATURE on these boundaries
SOLIDBUNDLE Keys ( See also: Description ) Key
Type
Parameter set
Unit:( )
Default:[ ]
Description
DELTAT
Real (s)
Time-step in thermal calculations.
DTPLOT
Real (s)
Time-step for saving thermal data.
LABEL
String
[SOLIDBUNDLE_tag]
Network component label (if nothing is given the NC tag is used).
MESHFINENESS
Integer
[32]
The number of nodes on the largest SHAPE in the SOLIDBUNDLE. The higher the number the finer the mesh. Minimum value is 32 and it will always be rounded down to nearest multiple of 32.
PLOTTING
Symbol
OFF | [ON]
Key for turning ON/OFF detailed plot of Finite Element results in .osi file
Link to: SOLIDBUNDLE Description Keys
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