CN111104719A - Method for acquiring height of smoke tower-in-one chimney of indirect air cooling unit - Google Patents
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Abstract
A method for obtaining the height of a chimney and a chimney tower of an indirect air cooling unit adopts wind tunnel physical simulation to obtain the height of the chimney: placing a cooling tower model and a chimney model in a wind tunnel, observing and recording lifting, diffusion and discharge conditions of smoke in the cooling tower by adopting a method of releasing tracing smoke under the conditions of different environmental wind speeds and chimney heights, and qualitatively determining the optimal chimney height; the method can qualitatively determine the optimal chimney height under the conditions of different environmental wind speeds, chimney heights and different working conditions, and quantitatively obtain the smoke exhaust conditions of the chimneys with different heights under different conditions.
Description
Technical Field
The invention relates to the technical field of smoke discharge of thermal power plants, in particular to a method for acquiring the height of a chimney integrated with a smoke tower of an indirect air cooling unit.
Background
The smoke tower integration technology is that a chimney in a fire-extinguishing power plant is taken, and desulfurized smoke is sent into a natural ventilation cooling tower and is discharged into the atmosphere together with airflow of the cooling tower. The flue gas tower unification technique utilizes the huge moist hot air updraft of cooling tower to form parcel and lifting to the clean flue gas after the desulfurization to promote the diffusion of pollutant in the flue gas. By adopting the technology, a reheater and a chimney of a wet flue gas desulfurization system of the thermal power plant can be omitted, the flue gas system of the thermal power plant is greatly simplified, and the equipment investment is reduced.
The smoke tower integrated technology originated in germany in the 70 th 20 th century and developed into a rather mature technology. With the wide application of flue gas desulfurization technology in China, the flue gas tower-in-one technology gradually draws wide attention. In 2006, 12 months, the first project in which the smoke-tower-integrated technology is applied is put into operation, and currently, dozens of units adopt the smoke-tower-integrated smoke discharging technology.
The clean flue gas after wet desulphurization still contains a certain amount of harmful gases such as SO2, SO3, NOx, HF, HCl and the like, and the clean flue gas containing the harmful gases is condensed on the tower wall of the cooling tower to generate strong acid corrosion on the inner wall of the cooling tower. Therefore, how to arrange the smoke exhaust chimney of the cooling tower is a problem which needs to be considered in the application of the smoke tower technology.
When two machines are combined with a smoke tower of an air cooling tower, 2 machine sets respectively use a chimney to discharge smoke. Most of the heat energy needs to be supplied to the outside due to the heating season, and only one unit may operate under the most severe working condition. At this time, the air velocity in the air cooling tower is very low, and the design according to the normal chimney height may cause the flue gas to be retained in the air cooling tower for a long time, thereby bringing about the problem of corrosion of the flue gas to the inner wall of the air cooling tower. In order to prevent this from occurring under the most adverse operating conditions and environmental conditions, a reliable method for obtaining the chimney height of the indirect air cooling unit is needed.
Based on the above, the invention designs a method for acquiring the height of a chimney integrated with a smoke tower of an indirect air cooling unit, so as to solve the above problems.
Disclosure of Invention
The invention aims to provide a method for acquiring the height of a chimney integrated with a smoke tower of an indirect air cooling unit.
In order to achieve the purpose, the invention provides the following technical scheme:
a method for obtaining the height of a chimney and a chimney tower of an indirect air cooling unit adopts wind tunnel physical simulation to obtain the height of the chimney: placing a cooling tower model and a chimney model in a wind tunnel, observing and recording lifting, diffusion and discharge conditions of smoke in the cooling tower by adopting a method of releasing tracing smoke under the conditions of different environmental wind speeds and chimney heights, and qualitatively determining the optimal chimney height; the particle image velocity field instrument is used to measure the velocity distribution of the air flow and the flue gas in the tower, and the smoke discharge conditions of chimneys with different heights under different conditions are obtained quantitatively.
The method for acquiring the height of the chimney and the tower integrated chimney of the indirect air cooling unit further determines the experimental parameters of the wind tunnel physical simulation by adopting the completely similar similarity criterion.
According to the method for acquiring the height of the chimney and the chimney combined with the smoke tower of the indirect air cooling unit, the geometric dimensions of the air cooling tower model and the chimney model are further determined according to geometric similarity.
The method for acquiring the height of the chimney integrated with the smoke tower of the indirect air cooling unit further determines the rising speed of the model smoke outlet and the rising speed of the airflow in the air cooling tower according to the rising speed of the prototype flow according to the following formula,
the method for acquiring the height of the chimney integrated with the smoke tower of the indirect air cooling unit further determines the horizontal wind speed of a simulation test according to the equal speed ratio according to the following formula,
according to the method for acquiring the height of the chimney integrated with the smoke tower of the indirect air cooling unit, the smoke flow of the simulation test is further calculated according to the smoke discharge velocity corresponding to the model.
The method for obtaining the height of the chimney integrated with the smoke tower of the indirect air cooling unit further calculates the density of the simulated smoke gas, the temperature for heating the smoke gas and the flow of the cold smoke gas according to the density ratio and the like according to the following formula,
the method for acquiring the height of the chimney and the tower integrated chimney of the indirect air cooling unit further performs a simulation experiment under four working conditions:
(1) heat supply is carried out in winter, one unit operates without mixing air;
(2) supplying heat in winter, operating one unit and mixing air;
(3) heat supply is carried out in winter, the two units operate, and air is not mixed;
(4) in winter, heat is supplied, two units operate and air is mixed.
According to the method for acquiring the height of the chimney and the tower integrated chimney of the indirect air cooling unit, the model of the cooling tower is made of transparent materials.
Compared with the prior art, the invention has the beneficial effects that: the method determines the experimental parameters of the wind tunnel physical simulation by adopting the completely similar similarity criterion through the wind tunnel physical simulation method, utilizes the wind tunnel to simulate the surrounding environment of the smoke tower, reduces the prototype through the geometric similarity distance, has small and exquisite model, is convenient for the operation of the experiment, can qualitatively determine the optimal chimney height and quantitatively obtain the smoke exhaust conditions of the chimneys with different heights under different conditions.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention.
Drawings
FIG. 1 is a schematic diagram of the invention in winter with two units operating without air blending, and a chimney with a height of 142.5m without flue gas contacting the tower wall at an ambient wind speed of 9 m/s.
FIG. 2 is a schematic diagram of the velocity distribution in the tower at a certain moment in the environment wind speed of 9m/s for heating in winter, two units operating without air mixing, and a chimney with a height of 142.5 m.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The method acquires the height of a chimney tower-in-one chimney of an indirect air cooling unit of a thermal power plant in a Qinhuang island development area, and the cogeneration comprises a domestic 2 x 350MW unit, a coal-fired unit, a supercritical unit, a single intermediate reheating unit, a suction condensing unit and an indirect air cooling unit, and a flue gas desulfurization facility and a flue gas denitration facility are synchronously built. The smoke exhaust mode adopts the combination of two machines and a smoke tower of an air cooling tower, 2 machine sets respectively exhaust smoke by using a chimney, under the condition of external heat supply, the heat exchange mode of the air cooling tower is divided into air mixing and air non-mixing, and the machine sets are divided into one machine set and two machine sets.
The following examples were conducted in a flow-through wind tunnel, the wind tunnel test section being 4m wide, 3m high and 24m long; the total length is 69m, the width is 25m, the height is 10m, and the wind speed range is 0-30 m/s; measurement of wind profiles and turbulence intensity an IFA300 intelligent flow analyzer, i.e. a hot-film anemometer, was used. The measuring probe is a glass wire with a diameter of 20 mu m and a length of 6mm coated with a platinum film, not only basically has no interference to a flow field, but also has very high response frequency which can reach more than 40kHz, is suitable for measuring the turbulent flow characteristic of flow, and is calibrated before the IFA300 is used each time so as to ensure the measuring precision; the particle image velocity field instrument (PIV) consists of a laser sheet light source, a particle release system (smoke generator), a high-speed camera system and a data acquisition and analysis system, and obtains the distribution of a velocity field by analyzing the moving track of particles in a picture obtained by high-speed shooting of a flow field; in the visualization experiment, visible smoke meeting similar criteria is released from a chimney, and the emission process of the smoke is recorded by a camera to study the smoke emission conditions under various working conditions, environmental wind speeds and different chimney heights.
Determination of wind tunnel experiment parameters:
according to the theory of plume lift and diffusion, in euler's coordinate system, the ensemble averaged plume lift height and contaminant concentration C (x, y, z) can be expressed as follows:
h(x)＝f1(x,hs,d,u,w,ρs,ρa,ν,g)
C(x,y,z)＝f2(Q,x,y,z,hs,d,u,w,ρs,ρa,ν,g)
in the formula, Q is a source discharge rate, α is the percentage of pollutants in the smoke, d is the inner diameter of a chimney outlet, hs is the height of the chimney, u is the average wind speed on the thickness of a smoke plume, w is the discharge wind speed of a smoke stream, rho a and rho s are the densities of air and the smoke stream, v is the kinematic viscosity of the smoke stream, which is assumed to be the same as the kinematic viscosity of the air, and g is gravity plus the wind speed.
After transformation, the following components are obtained:
in the dimensionless parameters at the right end of the above two formulas, except the following 4 parameters, the parameters can be realized by geometric similarity. Therefore, the key to accurately simulate plume lift and diffusion is that the following 4 dimensionless parameters are correspondingly equal to the corresponding parameters of the prototype stream. That is, the density ratio, velocity ratio and Froude number of the simulated flow and the prototype flow are all equal, which respectively correspond to the following formula:
the geometric ratio adopted is 1: 300 determine the geometry of the model. I.e. 1m in length in the model, is equal to 300m in real environment. And simulating an atmospheric boundary layer to enable the flow of the wind tunnel simulation boundary layer to become fully developed turbulent flow, wherein the wind profile of the boundary layer is in an exponential law. The power plant has been subjected to on-site meteorological tests in the environmental impact evaluation stage, and the obtained wind profile index of the B-class stability is 0.264, and the wind profile index of the D-class stability is 0.322. Considering cooling towers as high as 190m, 200m of high altitude is mostly neutral (class D) during the day even if the ground is near the convective boundary layer, especially in winter. As for nighttime, the stable boundary layer is usually about 100m and the neutral boundary layer is mostly at the top of the tower. Therefore, the class D wind profile index p of the neutral boundary layer is selected to be 0.322 during simulation. The motion similarity and power similarity criteria adopt completely similar similarity criteria.
The ambient air temperature will also be different in different seasons and the ambient wind speed will play an important role, and according to the similarity criteria, the simulated flow velocity at the top of the model cooling tower corresponding to different ambient wind speeds at 10m height (prototype wind speed) is calculated, as shown in table 1.
Table 1: wind speed at the top of a simulation experiment tower under different environmental wind speeds
| Ambient wind velocity | 5m/s | 6m/s | 9m/s |
| Simulated wind speed | 0.75m/s | 0.89m/s | 1.34m/s |
And determining simulation parameters by taking the average air temperature of each month as reference and combining the flue gas temperature and the air flow temperature in the air cooling tower. Table 2 shows the air flow rate and average temperature at the outlet of the prototype flow cooling tower in each winter month under different working conditions. Table 3 shows the calculated rates of rise of the gas flow in the tower and the volumetric flow rates for the simulation experiments based on the data of table 2 and similar criteria.
Table 2: exit velocity and average temperature of prototype flow
Table 3: tower mouth velocity and throat velocity and volume flow of model flow
To satisfy the similar criteria of equal density ratios, the gas densities at different temperatures are also calculated according to the following formula:
in the formula, the subscript m represents the simulation parameters and the subscript p represents the prototype flow. The subscript s represents the flue gas or gas in the cooling tower and the subscript a represents the ambient air. The air densities at different temperatures are shown in table 4.
Table 4: air density at various temperatures
| Ambient temperature,. degree.C | -4 | 22.5 | 23.3 | 25.7 |
| Air Density, kg/m3 | 1.31 | 1.19 | 1.19 | 1.18 |
Meanwhile, the ambient air density of the laboratory and the density of the simulated airflow in the tower under different working conditions at the ambient temperatures of different laboratories are calculated and shown in table 5,
table 5: laboratory simulation of the density of gas in a cooling tower
The following examples use heating of the cold air and flue gas in such a way that they meet the requirements of similar criteria. Table 6 shows the flow rate of the cold and hot air in the model cooling tower and the temperature to be heated.
Table 6: cold and hot air flow and heating temperature required by model cooling tower
Since most of the model smoke is ambient air, only a small amount of smoke generated by the moxa cone is mixed in the model smoke. The flue gases are transported to the vicinity of the model chimney and are in equilibrium with the ambient temperature. Therefore, the density of the model flue gas is basically equal to that of the air at the same temperature, and the calculated temperature of the model flue gas to be heated and the flow of the cold flue gas at different environmental temperatures are shown in the table 7.
Table 7: heating data of model flue gas during simulation by adopting flue gas heating method
Wind tunnel experiment: the simulation experiment selects the ambient wind speeds of 5m/s, 6m/s and 9m/s (wind profile index of 0.322) at 10m height, and selects the chimney heights of 56m, 100m and 142.5 m. The chimney height here means a height from a plane of the cooling tower, where z is 0m, to the top of the chimney. There are four conditions: heating in winter, wherein one unit operates without mixing air; (2) supplying heat in winter, operating one unit and mixing air; (3) heat supply is carried out in winter, the two units operate, and air is not mixed; (4) in winter, heat is supplied, two units operate and air is mixed.
Example 1: a chimney with a height of 56m is simulated in a backflow type wind tunnel, a transparent cooling tower model is arranged in the chimney, heat is supplied in winter, one unit operates under the working condition that air is not mixed, tests are sequentially carried out under the conditions that the wind speed is 5m/s, 6m/s and 9m/s, and other specific experimental parameters are shown in the table.
Example 2: a chimney with a height of 56m is simulated in a backflow type wind tunnel, a transparent cooling tower model is arranged in the chimney, heat is supplied in winter, one unit operates and is mixed with air, the test is sequentially carried out under the conditions that the wind speed is 5m/s, 6m/s and 9m/s, and other specific experimental parameters are shown in the table.
Example 3: a chimney with the height of 56m is simulated in a backflow type wind tunnel, a transparent cooling tower model is arranged in the chimney, heat supply is carried out in winter, two units operate under the working condition that air is not mixed, tests are carried out sequentially under the conditions that the wind speed is 5m/s, 6m/s and 9m/s, and other specific experimental parameters are shown in the table.
Example 4: a chimney with the height of 56m is simulated in a backflow type wind tunnel, a transparent cooling tower model is arranged in the chimney, the chimney is heated in winter, two units run and are mixed with air, the chimney is tested under the conditions that the wind speed is 5m/s, 6m/s and 9m/s in sequence, and other specific experimental parameters are shown in the table.
As shown in table 8, it is understood from the experimental results of examples 1 to 4 that smoke discharged from a chimney having a height of 56m causes entrainment of the smoke into the cooling tower at an ambient wind speed of 5m/s or more, the smoke is in large contact with the wall of the cooling tower, and the larger the wind speed, the larger the area of contact between the smoke and the wall of the tower, and the longer the time for which the smoke stays in the tower. (1) The height of the contact inner wall is increased along with the increase of the wind speed, and is mostly more than 130-140 m; (2) the blended air has no effect on a 56m chimney; (3) compared with the operation of one machine set, the operation of two machine sets slightly reduces the contact height of some flue gases, but the range is not large, and is about 5-10 m.
Table 8: height of chimney flue gas with height of 56m contacting inner wall of cooling tower
Example 5: a chimney with the height of 100m is simulated and placed in a backflow type wind tunnel, a transparent cooling tower model is placed in the chimney, heat is supplied in winter, one unit operates under the working condition that air is not mixed, tests are sequentially carried out under the conditions that the wind speed is 5m/s, 6m/s and 9m/s, and other specific experimental parameters are shown in the table.
Example 6: a chimney with the height of 100m is simulated and placed in a backflow type wind tunnel, a transparent cooling tower model is placed in the chimney, heat is supplied in winter, one unit operates and is mixed with air, the test is sequentially carried out under the conditions that the wind speed is 5m/s, 6m/s and 9m/s, and other specific experimental parameters are shown in the table.
Example 7: a chimney with the height of 100m is simulated and placed in a backflow type wind tunnel, a transparent cooling tower model is placed in the chimney, heat supply is carried out in winter, two units operate under the working condition that air is not mixed, tests are carried out sequentially under the conditions that the wind speed is 5m/s, 6m/s and 9m/s, and other specific experimental parameters are shown in the table.
Example 8: a chimney with the height of 100m is simulated and placed in a backflow type wind tunnel, a transparent cooling tower model is placed in the chimney, the chimney is heated in winter, two units run and are mixed with air, the chimney is tested under the conditions that the wind speed is 5m/s, 6m/s and 9m/s in sequence, and other specific experimental parameters are shown in the table.
The results of the experiments in examples 5 to 8 are shown in Table 9, and it is understood that when the chimney height is 100m, the flue gas is still entrained in the cooling tower and contacts the tower wall. At low wind speeds (5-6 m/s), the probability of entanglement is slightly lower, while at high wind speeds (9m/s), the probability of entanglement is greatly increased. The rolling height is 40-50 m, 70-80 m. The entrainment height of the flue gas can be slightly reduced (5-10 m) by mixing air; compared with the operation of one unit, the two units can reduce the rolling height by 5-10 m when operating at low wind speed, and the rolling height is larger when operating at high wind speed. If the inner wall of the cooling tower is subjected to anticorrosion treatment, 10-20 m is added on the basis, so that the cooling tower is more reliable.
Table 9: height of 100m for down-rolling smoke of chimney
Example 9: a chimney with the height of 142.5m is simulated and placed in a backflow type wind tunnel, a transparent cooling tower model is placed in the chimney, heat is supplied in winter, one unit operates under the working condition that air is not mixed, tests are sequentially carried out under the conditions that the wind speed is 5m/s, 6m/s and 9m/s, and other specific experimental parameters are shown in the table.
Example 10: a chimney with the height of 142.5m is simulated and placed in a backflow type wind tunnel, a transparent cooling tower model is placed in the chimney, heat supply is carried out in winter, one unit operates and is mixed with air, tests are carried out sequentially under the conditions that the wind speed is 5m/s, 6m/s and 9m/s, and other specific experimental parameters are shown in the table.
Example 11: a chimney with the height of 142.5m is simulated and placed in a backflow type wind tunnel, a transparent cooling tower model is placed in the chimney, heat is supplied in winter, two units operate under the working condition that air is not mixed, tests are sequentially carried out under the conditions that the wind speed is 5m/s, 6m/s and 9m/s, and other specific experimental parameters are shown in the table.
Example 12: a chimney with the height of 142.5m is simulated and placed in a backflow type wind tunnel, a transparent cooling tower model is placed in the chimney, heat supply is carried out in winter, two units operate and air mixing is carried out, tests are carried out sequentially under the conditions that the wind speed is 5m/s, 6m/s and 9m/s, and other specific experimental parameters are shown in the table.
The experimental results of examples 9 to 12 are shown in table 10, and it is found that when the chimney height is 142.5m, the flue gas can be smoothly discharged without substantially contacting the tower wall when the wind speed is not more than 9 m/s; at higher wind speed, occasionally, flue gas is involved in the cooling tower, and the height of the flue gas contacting the tower wall is 10-20 m. Table 10 shows the height of contact if the flue gas rolls down and contacts the tower wall, and if so, the tower wall for a 142.5m stack under different conditions and ambient wind speeds.
Table 10: whether the chimney smoke with the height of 142.5m rolls down or not and the height of the contact tower wall
In summary, the following steps:
(1) the mixed air has certain effect on preventing or reducing the contact of flue gas with the wall, and the height of the contact wall can be reduced by 5-10 m.
(2) The operation of the two units is better than the operation of one unit in smoke exhaust effect under certain conditions, the height of the contact wall can be reduced by 5-10 m under low wind speed (5-6 m/s), but the height of the contact wall can be increased if the chimney is lower at high wind speed (9m/s and above).
(3) The height of the flue gas contacting the cooling tower wall decreases with the increase of the chimney height and increases with the increase of the wind speed.
(4) The flue gas is basically drawn into the cooling tower by a chimney with the height of 56m and stays for a certain time, and the height of the flue gas contacting the tower wall (from the top of the tower) reaches more than 140m, so if the chimney with the height of 56m is adopted, the inner wall of the tower should be subjected to antiseptic treatment.
(5) A chimney with a height of 142.5m, and basically no smoke contact with the wall can occur below the ambient wind speed of 9 m/s. From the viewpoint of corrosion prevention, a chimney with the thickness of 142.5m is preferably adopted, and the inner wall of the chimney can be subjected to no corrosion prevention treatment or only the inner wall of the tower opening is subjected to the corrosion prevention treatment with the thickness of 10-20 m.
(6) If a chimney with a height of 100m is adopted, the inner wall of the cooling tower needs to be subjected to anticorrosion treatment, and the height of an anticorrosion layer is preferably from the throat part of the cooling tower to the top of the cooling tower.
In the description herein, references to the description of "one embodiment," "an example," "a specific example" or the like are intended to mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
The preferred embodiments of the invention disclosed above are intended to be illustrative only. The preferred embodiments are not intended to be exhaustive or to limit the invention to the precise embodiments disclosed. Obviously, many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and the practical application, to thereby enable others skilled in the art to best utilize the invention. The invention is limited only by the claims and their full scope and equivalents.
Claims (9)
1. The method for obtaining the chimney height of the indirect air cooling unit smoke tower is characterized in that the chimney height is obtained by adopting wind tunnel physical simulation: placing a cooling tower model and a chimney model in a wind tunnel, observing and recording lifting, diffusion and discharge conditions of smoke in the cooling tower by adopting a method of releasing tracing smoke under the conditions of different environmental wind speeds and chimney heights, and qualitatively determining the optimal chimney height; the particle image velocity field instrument is used to measure the velocity distribution of the air flow and the flue gas in the tower, and the smoke discharge conditions of chimneys with different heights under different conditions are obtained quantitatively.
2. The method for acquiring the height of the chimney tower-in-one chimney of the indirect air cooling unit according to claim 1, wherein the method comprises the following steps: and determining experimental parameters of the wind tunnel physical simulation by adopting completely similar similarity criteria.
3. The method for acquiring the height of the chimney tower-in-one chimney of the indirect air cooling unit according to claim 2, wherein the method comprises the following steps: and determining the geometric dimensions of the air cooling tower model and the chimney model according to the geometric similarity.
4. The method for obtaining the height of the chimney tower-in-one chimney of the indirect air cooling unit according to claim 3, wherein the method comprises the following steps: according to the following formula, determining the rising speed of the model flue gas outlet and the rising speed of the air flow in the air cooling tower according to the rising speed of the prototype flow,
5. the method for obtaining the chimney height of the indirect air cooling unit combined with the smoke tower according to claim 4, is characterized in that: according to the following formula, the horizontal wind speed of the simulation test is determined according to the speed ratio equality,
6. the method for obtaining the chimney height of the indirect air cooling unit combined with the smoke tower according to claim 5, is characterized in that: and calculating the flue gas flow of the simulation test according to the flue gas emission speed corresponding to the model.
7. The method for obtaining the chimney height of the indirect air cooling unit combined with the smoke tower according to claim 6, is characterized in that: according to the following formula, the density of the simulated flue gas, the temperature for heating the flue gas and the flow of the cold flue gas are calculated according to the equal density ratio,
8. the method for acquiring the chimney height of the indirect air cooling unit combined with the smoke tower is characterized in that a simulation experiment is carried out under four working conditions:
(1) heat supply is carried out in winter, one unit operates without mixing air;
(2) supplying heat in winter, operating one unit and mixing air;
(3) heat supply is carried out in winter, the two units operate, and air is not mixed;
(4) in winter, heat is supplied, two units operate and air is mixed.
9. The method for obtaining the chimney height of the indirect air cooling unit combined with the smoke tower according to claim 8, is characterized in that: the cooling tower model is made of transparent materials.
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