The external heat transfer of dams during construction is complex because such transfer is location specific and time varying. An external thermal model is developed in this paper. Five types of external heat flux are considered in the mathematical model: air-side convection, electromagnetic radiation, absorbed solar input, water-side convection, and surface insulation effect. A method for extracting and classifying the external surfaces of dams on the basis of Boolean operations is proposed. Heat transfer conditions can be automatically set up for each step according to the proposed method, and the method can be used as a preprocessing facility for finite element analysis. A 285 m high arch dam in Southwest China is examined as a study case. The model is implemented and found to correctly identify different types of external surfaces. Simulation result agrees well with the monitored temperatures.
Concrete is the most widely used building material in the world. Rough statistics [
A dam comprises an extremely large amount of concrete and is referred to as a typical case of massive concrete. To complete this colossal project, the structure must be divided into numerous blocks cast at different times. The entire construction usually requires a number of years to complete, which means that the climate condition changes with seasonal variation during the construction phase. A good example would be the construction of the famous Three Gorges Dam, which took a total of 14 years to complete 27.2 million cubic meters of concrete [
The boundary conditions should be consistent with the practical situation to ensure the accuracy of simulating the heat transfer problem. However, the setup work poses difficulty in simulating large and complex structures such as concrete dams. On one hand, the dam is bounded by a group of surfaces, which are subjected to various external thermal conditions. On the other hand, the dam constantly grows with the gradually changing boundary surfaces. Therefore, external thermal conditions are location specific and time varying, which makes the selection and setup of the boundary conditions complex. The surfaces of different steps are manually chosen in conventional thermal simulations, which is a tedious and time-consuming task that does not guarantee absolute accuracy.
A number of experimental and numerical studies on the external heat transfer problem of concrete were conducted. For instance, Demir [
Much effort was given to study the external heat transfer of dams. Léger and Seydou [
The finite element (FE) method is widely used to simulate the thermal problem of dams during the construction phase. Numerous relevant studies address the FE method [
The numerical thermal simulation of dams had been studied, but the setup problem of the external boundary conditions at each step was not technically discussed. Limited studies focus on the preliminary procedure of external surfaces for the external heat transfer of dams. Therefore, this study presents a method for the automatic setup of external heat transfer boundaries during the analysis of the entire construction phase. The external heat transfer of dams is classified, and the basic mathematical model is established. Boolean-based algorithms are proposed to extract different types of external surfaces and to set appropriate heat transfer conditions. A super-high arch dam is examined as a study case by using the developed program to test the automatic method in practical engineering applications.
The governing equation of 3D unsteady heat transfer can be derived from the energy conservation principle and the Fourier law of heat conduction, which is written as follows:
Massive concrete has complex boundary conditions during the construction phase. The external heat transfer of the boundary surfaces can generally be expressed as
Heat convection occurs upon exposed concrete surfaces because of the bulk motion of air fluids that carry and disperse the heat [
Air temperature always varies and hardly remains constant even throughout a single day. In this work, the
Ambient temperature sinusoid curve for one day (or one year).
Unfortunately, recording or accessing detailed local weather data in some engineering projects is difficult and cannot be guaranteed even though only one temperature measurement per day is taken. That implies that daily temperatures cannot be determined from (
Electromagnetic energy is constantly emitted by concrete through exposed surfaces and can be calculated by using the Stefan-Boltzmann law:
Solar radiation was not considered in numerous thermal studies on dams [
The revolution orbit and rotation circle of the earth are not on the same plane because the equatorial plane tilts at an angle of 23.45° to the orbital plane. Solar declination
Positions of the Sun and the Earth (this figure shows a winter time for the north because the Earth–Sun line crosses the Southern Hemisphere).
Figures
Solar angles involved for a structure surface.
We can obtain the exact values of
When the sun’s position and solar angles are determined as described, we can calculate the total solar energy input that strikes the structure surface. This energy input can be measured by using three components:
The extraterrestrial solar radiant flux
The relative air mass
The ground reflectance
The parameters that represent the optical depths
In terms of reaching solar energy
Solar radiation input occurs only during daytime with a clear sky.
Several dams begin to fill the reservoir during the construction phase to improve the performance of power production, which results in the concrete exchanging heat with the reservoir through the water-side surface below the reservoir level. This phenomenon is considered a convection boundary with liquid fluid, which can also be described in Newton’s law of cooling:
In engineering applications,
The concrete surface may be covered with insulation protections during construction to prevent thermal cracks induced by atmospheric temperature shock. Materials with high thermal resistances, such as cotton quilts, polystyrene foam plastic (PFP) [
Surface protection and its equivalent model.
Solving (
The 3D space
Given the boundary conditions mentioned in (
Equation (
The external heat transfer conditions during the construction phase of a large dam are complex. For a proper FE analysis of a dam under construction, the casting of a new lift means activating the lift elements, which changes the external surface regions. In some large projects, the dam is composed of thousands of lifts, which makes the manual selection of different types of surfaces at each step impractical. Therefore, an automatic surface extracting and taxonomy method based on Boolean operations is presented in this study.
Boolean operations are a group of symbolic computation rules used to operate polygons. Three basic operations are always conducted as illustrated in Figure Intersection: it is denoted as Union: it is denoted as Difference: it is denoted as
Surface Boolean operations.
Four simple preliminary surface groups should be identified to obtain precisely different types of external surfaces in the simulation. Figure Model-side surfaces: the in-rock boundary surfaces of the model should be identified and noted as Dam-top surfaces: the top surfaces of the dam body should be identified and noted as Upstream surfaces: the upstream surfaces of the dam should be identified and noted as Downstream surfaces: the downstream surfaces of the dam should be identified and noted as
Preliminary defined surface groups.
Death/rebirth technology is used to simulate the construction process in FE analysis. The entire analysis is divided into numerous steps on the basis of the casting-time plan. The lift elements are activated at the beginning of each step. A
Predefined variables.
Variables | Dependence | Note |
---|---|---|
|
Element dependent | The label of the casting sequence and |
|
Lift dependent | The variable represents the monolith to which the lift belongs, and |
|
Monolith dependent | The variable represents the highest elevation of each monolith during construction, where all variables are initially set as 0. |
We are now ready to present the surface extraction and taxonomy procedures based on Boolean operations. First we set a nomenclature rule of the surface group identification.
Various types of external heat transfer occur on different surfaces during construction. More than one type of heat transfer may co-exist on one surface. The surfaces stored in Algorithm
External surface taxonomies for boundary conditions setup.
Surface region | Combination of boundary conditions | |
---|---|---|
In-rock boundary surfaces |
|
|
Rock-exposed surfaces |
|
|
Upstream surfaces |
|
|
Downstream surfaces |
|
|
Joint surfaces |
|
|
Top surfaces |
|
|
Outlet hole surfaces |
|
|
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22)
A few remarks should be made on the setup rule in Table The in-rock vertical surfaces generated by the model-side cutting are adiabatic because the horizontal heat transfer in the infinite rock is symmetrical to these surfaces. The ground temperature beneath the upper 6 m of the surface of the Earth maintains a nearly constant temperature between 10°C and 16°C [ A protection scheme should be established based on the design plan when a prediction is conducted or based on the actual condition when simulating the past.
Algorithm
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Example of recognizing the inside faces. The red bold number is the minimum node number of the face.
The detection algorithm of
(1) (2) (3) (4) (5) Recognize all external surfaces of elements with
also be included. (6)
A remark should be noticed that the algorithms can also be applied as a preprocessing facility for a third-party FEM software package. An improvement which should be made on the origin Algorithm
In this study, a user-friendly interface for data input is developed based on the EXCEL software. The embedded VBA programming language can be utilized to provide a convenient user interface and to handle the data automatically. Several forms are generated for users to collect the information required in the simulation, including climate condition, construction procedure, material properties, and predefined surfaces. The form style is concise, explicit, and easy-to-use.
A C-language-based program is compiled to process the data input from the spreadsheet and the FE meshes. Algorithm
Several commercial or free source FEM packages exist. Our developed program can be exported as requested provided that the input format is known. In this study, MSC.Marc [
Common users found the postprocessing module of MSC.Marc to be inconvenient and awkward. A program is developed to decode the .t16 result output file for fast, automatic, and easy-to-use postprocessing. A customized form, which can be found in the EXCEL interface, offers two options: desired nodes and desired contour time. The developed program can then extract and plot the data, including the time-temperature curves and temperature contours.
Figure
Flowchart of the software development.
The site of the Xiluodu hydropower project is located in the lower reach of the Jinsha River, Yunnan Province in Southwest China. The geographic coordinate is 28°
The dam started casting concrete in March 2009. The dam comprises about 2100 lifts within an approximately five-year construction period because of considerations for proper concrete casting and to avoid thermal cracks. A total of 1961 lifts were completed by June 2013. The detailed casting-time sequence was recorded.
The upstream cofferdam was demolished in March 2012, and the reservoir was impounded. The upstream water level was measured and recorded (see Figure
Water level process during construction.
The site is located in a V-shaped canyon of the Jinsha River and is subjected to a subtropical climate. A nearby hydrologic station records the weather data daily. The ambient temperatures and wind speeds from January 2009 to May 2013 are shown in Figure
Weather curve (air temperatures and wind speeds).
A meteorological station is located near the dam site in Zhaotong, and the fundamental solar measurement data were used as the reference for the simulation. Table
Calculation of solar irradiation.
Xiluodu Dam | Latitude: 28° |
Longitude: 103° |
| ||
Zhaotong Station | Latitude: 27°19′ |
Longitude: 103°45′ |
Jan 21st | Feb 21st | Mar 21st | Apr 21st | May 21st | Jun 21st | |
---|---|---|---|---|---|---|
|
21 | 52 | 80 | 111 | 141 | 172 |
|
0.362 | 0.369 | 0.448 | 0.479 | 0.525 | 0.504 |
|
2.080 | 2.084 | 1.835 | 1.791 | 1.707 | 1.820 |
|
674.24 | 719.12 | 750.84 | 764.69 | 762.99 | 758.19 |
|
189.32 | 204.92 | 217.25 | 223.84 | 224.33 | 223.10 |
|
|
|
|
|
|
|
|
466.16 | 504.89 | 541.53 | 551.07 | 547.52 | 546.35 |
|
132.36 | 143.80 | 154.89 | 158.71 | 158.28 | 157.89 |
|
401.51 | 360.70 | 280.32 | 162.93 | 91.00 | 71.70 |
|
378.29 | 448.80 | 521.64 | 561.99 | 568.09 | 568.47 |
| ||||||
Jul 21st | Aug 21st | Sep 21st | Oct 21st | Nov 21st | Dec 21st | |
| ||||||
|
202 | 233 | 264 | 294 | 325 | 355 |
|
0.512 | 0.546 | 0.487 | 0.448 | 0.391 | 0.365 |
|
1.820 | 1.708 | 1.833 | 1.883 | 2.025 | 2.076 |
|
751.02 | 754.78 | 740.12 | 707.95 | 667.55 | 650.57 |
|
222.60 | 220.96 | 214.20 | 201.56 | 187.34 | 181.68 |
|
|
|
|
|
|
|
|
547.62 | 539.21 | 526.69 | 498.23 | 463.08 | 446.57 |
|
158.32 | 155.75 | 150.59 | 142.10 | 131.67 | 129.80 |
|
89.61 | 157.91 | 270.12 | 360.71 | 401.60 | 407.44 |
|
568.91 | 550.41 | 507.16 | 441.23 | 375.37 | 348.70 |
Table
A number of digital thermometers are embedded 0.10 m under the dam surfaces to monitor the concrete surface temperature distribution. Pairs of thermometers are arranged at the same elevation in the same concrete lift: one at the upstream surface and the other at the downstream surface. Monoliths number 6, number 9, number 16, number 22, and number 27 are selected as monitoring sections. Figure
Instruments setup (viewed from upstream to downstream).
A double exponent hydration model [
Material properties of concrete.
Material property | Type I | Type II | Type III | |
---|---|---|---|---|
Basic heat transfer |
|
943.0 | 934.0 | 860.0 |
|
2663 | 2663 | 2663 | |
|
2.14 | 2.14 | 2.14 | |
| ||||
Hydration model |
|
26.3 | 25.5 | 24.7 |
|
0.252 | 0.252 | 0.252 | |
|
0.025 | 0.025 | 0.025 | |
|
0.6 | 0.6 | 0.6 | |
| ||||
Radiation |
|
0.88 | 0.88 | 0.88 |
| ||||
Air-side convection |
|
0.99 | 0.99 | 0.99 |
|
0.21 | 0.21 | 0.21 | |
|
1.0 | 1.0 | 1.0 | |
| ||||
Solar input |
|
0.50 | 0.50 | 0.50 |
|
0.07 | 0.07 | 0.07 | |
|
0.20 | 0.20 | 0.20 | |
| ||||
Protection |
|
0.045 | 0.045 | 0.045 |
|
0.036 | 0.036 | 0.036 |
The 3D dam-foundation system is discretized into hexahedral meshes. A total of 154,008 elements represent the dam body, and 28,026 elements represent the foundation. The total number of nodes is 216,837. The FE mesh layout of the dam body is shown in Figure
Finite element meshes of the dam body.
The surface procedure mentioned in this study is implemented as a preprocessing facility. The surface groups classified at each step are stored. Figure
Sketch of surface taxonomy map.
Time when 500th lift cast
Time when 1000th lift cast
The calculation temperature history of nodes that are near the positions of the embedded thermometers is extracted by the program and compared with the monitored data. It is found that they have a good agreement, which verifies the correctness of the external heat transfer analysis method present in this study. Three thermometers are picked out as shown in Figure
Simulation results.
The simulation result is automatically transported into Tecplot to draw the temperature contour, as mentioned in Section External thermal flux has great impact on the area underneath the boundary surfaces, for the temperature varies following the seasonal change. The arch dam seals the joint layer by layer and starts cooling the sealed regions before the sealing time. We can see that the weather-affected border is obviously narrow in some lifts because of the strong internal cooling source, like (d)~(f) in the figure. The after-sealed internal concrete, located a particular height below the top elevation, is not sensitive to the external weather. The temperature does not change much throughout a whole year. The surface temperature gradient is more obvious in summer than in winter, for the dam’s sealing temperature is 13°C, much lower than the average summer air temperature and closer to the average winter air temperature. The new-cast lift can reach a relatively high temperature peak due to the hydration reaction and induce a temperature gradient with the old concrete and the external surfaces. The ground temperature has impact on the footing region where the temperature is higher than the sealing temperature. The upstream face regions which contact with water are mainly affected by the water temperature after March 2012, when the reservoir starts impounding, like (j)~(i) in the figure. The blank area is the outlet hole, like (h)~(i) in the figure. The hollow hole makes the hole wall contact with the air, which generates a temperature gradient near the surface.
Temperature contour of the section in monolith 15 throughout a year from June 2011 to May 2012.
June 2011
July 2011
August 2011
September 2011
October 2011
November 2011
December 2011
January 2012
February 2012
March 2012
April 2012
May 2012
The external heat transfer of dams during the construction phase is complex because such transfer is location specific and time varying. A sound model for the external heat transfer of dams during construction is developed in this study. First, a mathematical model of five external thermal flux factors, namely, air-side convection, electromagnetic radiation, absorbed solar input, water-side convection, and surface insulation effect, is proposed. A surface procedure for FE analysis is also established based on Boolean operations. The proposed procedure can extract external surfaces and can create a taxonomy of surfaces for proper boundary conditions. An arch dam that is under construction in China with a height of 285 m is used to test the proposed method. The method can precisely extract the external surface and can correctly classify these surfaces in each step. The numerical result is compared with the monitoring temperatures. The result shows good agreement, thereby verifying the validity of the proposed method.
Hour angle
Then the apparent solar time (AST) can be expressed in the following equation:
Finally the hour angle
A remark is notable that when
Temperature (°C)
Specific heat (J/kg·°C)
External heat flux (W/m2)
Air-side convection heat exchange rate (W/m2)
Absorbed solar irradiation heat flux (W/m2)
Heat exchange rate through the protection (W/m2)
Radiative electromagnetic heat flux (W/m2)
Water-side convection heat flux (W/m2)
Air-side convection coefficient (W/m2°C)
Normal direction
Emissivity of surface
Ambient temperature (°C)
Wind speed (m/s)
The normal direction to the surface
Internal heat source per unit volume (W/m3)
Empirical parameter in (
Empirical parameter in (
Empirical parameter in (
Measured air temperature 1 (°C)
Measured air temperature 2 (°C)
Measured time 1 (h)
Measured time 2 (h)
The middle hour of day between the temperature peak and valley (h)
Maximum temperature of a year (°C)
Minimum temperature of a year (°C)
The middle day between
Mean temperature throughout a year (°C)
Heat capacity matrix
Thermal conductivity matrix
Heat flux vector
3D domain space of FEM
Symbol for degree Kelvin
Symbol for degree Celsius
Hour angle (°)
Latitude angle (°)
The width of each protection (m)
The total solar energy input reaching the structure surface (W/m2)
Beam (direct) component of solar radiation (W/m2)
Diffuse component of solar radiation (W/m2)
Ground reflector component of solar radiation (W/m2)
Irradiation coefficient of the beam component
Irradiation coefficient of the diffuse component
Extraterrestrial solar radiant flux (W/m2)
The relative air mass
Ground reflectance factor of foreground
Solar constant (W/m2)
Water-side convection coefficient (W/m2°C)
Water temperature (°C)
Sunrise hour (h)
Sunset hour (h).
Density (kg/m3)
Thermal conductivity (W/m·°C)
Time (s)
Parameter representing optical depths
Absorptivity of the exposed surface
The conduction coefficient of each protection (W/m·°C)
Surface azimuth (°)
Stefan-Boltzmann constant (W m−2 K−4)
Inclination angle of the structure surface (°)
The surface-solar azimuth angle (°)
Solar altitude angle (°)
Solar azimuth angle (°)
Angle of incidence (°).
This work is supported by the National “973” Researching Project of China (no. 2013CB035902), Research Project of State Key Laboratory of Hydroscience and Engineering of Tsinghua University (no. 2012-KY-4), and the National Nature Science Foundation of China (no. 51279087).