CN116992194A - Rapid calculation method for temperature of flat plate wall surface containing air film and thermal barrier coating - Google Patents
Rapid calculation method for temperature of flat plate wall surface containing air film and thermal barrier coating Download PDFInfo
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Abstract
The invention belongs to the field of aeroengines and gas turbines, and relates to a method for rapidly calculating the temperature of a flat plate wall surface containing a gas film and a thermal barrier coating. Compared with the conventional three-dimensional numerical simulation method, the calculation method has higher calculation efficiency, is oriented to the design problem of the flat plate structure with the air film holes and the thermal barrier coating, can obtain a large number of wall temperatures under different structures, different materials and different working conditions in a short time, and is used for proving establishment and searching of a design scheme. In the invention, the topology of the heat transfer process of each region is converted into a solvable heat transfer model by partitioning each wall surface, so that the complex three-dimensional partial differential equation set is simplified into a series of simple one-dimensional formulas. The method can avoid a large number of repeated processes (modeling, meshing, solving and calculating, and the like) and connection and switching among a plurality of software, thereby greatly saving time cost.
Description
Technical Field
The invention belongs to the field of aeroengines and gas turbines, and relates to a method for rapidly calculating the temperature of a flat plate wall surface containing a gas film and a thermal barrier coating.
Background
With the high-speed development of aero turbine engines and gas turbines, it is more important to break through the bottleneck of high performance, and this mainly depends on the higher turbine inlet gas temperature, which also means that the temperature bearing capability of the blades is more required, and the gap between this and the material bearing temperature is difficult to be filled by a single cooling technology. At present, turbine blades often adopt a mode of cooperation of various cooling measures to further improve the temperature resistance, more commonly, the following: the air film cooling and the thermal barrier coating are combined with each other, namely, cold air flows through main flow fuel gas of the air film Kong Huiru, and the air film is formed on the fuel gas surface to cool the outer wall surface, but the cooling effect is still insufficient, so that the thermal barrier coating is required to be coated on the surface of the metal substrate, and the heating of the fuel gas is isolated by virtue of the low heat conduction characteristic of the thermal barrier coating, so that the thermal protection effect is realized. In order to seek the maximization of the cooling effect, a design of mutually spacing the air film and the thermal barrier coating can be adopted, which brings great difficulty to the design and temperature analysis of the blade.
At present, three-dimensional simulation analysis software is mainly adopted for solving the wall temperature of the part, the prior art process firstly models a metal matrix, a thermal barrier coating and a gas film hole structure by means of three-dimensional modeling software, then discrete calculation domains are obtained through a grid dividing tool, a grid model is obtained, finally, three-dimensional temperature field distribution in the metal matrix and the coating body is obtained by means of flow and heat transfer three-dimensional numerical simulation software, typical results are shown in figure 1, contours and cloud pictures show more complex temperature distribution rules on a solid wall surface, and only half of symmetrical structures are displayed for convenient observation.
In the acquisition of the temperature field distribution, the equation set formed by a plurality of partial differential equations needs to be solved, the calculation of numerical discrete and large matrix for millions of grids is involved, reliable software and powerful computer hardware are required to be relied on, the cost is high, time and labor are wasted, and the development of an engine is hindered. In addition, because the thermal barrier coating can also influence air film cooling, namely the low heat conduction characteristic of the coating not only blocks the heating of high-temperature fuel gas, but also weakens the heat dissipation of the hot wall facing the air film, a large number of wall temperature parameters under different working conditions are needed to be obtained to guide the design of two cooling measures, the two cooling measures are matched with each other, the temperature resistance of the blade is improved to the greatest extent, and the difficulty is brought to simulation analysis. In addition, for the flat model combining two cooling measures, the wall temperatures under different structures and different working conditions are compared and analyzed, which means that modeling, meshing and numerical simulation are needed to be carried out again each time, a great deal of software is involved in the repeated processes, the time cost is further increased, and the overall design efficiency is reduced.
Therefore, how to quickly and accurately obtain the wall temperature in the complex heat transfer process is a problem to be solved urgently, and has important significance for improving the development capability of the aeroengine.
Disclosure of Invention
Aiming at the defects related in the prior art, the invention provides a rapid calculation method for the temperature of the flat plate wall surface containing the air film and the thermal barrier coating.
A method for rapidly calculating the temperature of a flat plate wall surface containing a gas film and a thermal barrier coating is shown in a figure 2, and comprises the following steps:
firstly, establishing a calculation model of a typical flat plate and cylindrical air film hole structure according to input structural parameters, physical parameters and working conditions. According to the symmetry, only half of the symmetry of the calculation model is established, the length, the width and the thickness of the flat plate are respectively l, b and h, and the distance from the center point of the air film hole on the cold air side to the upstream of the flat plate is l h The diameter of the air film hole is phi D, and the included angle between the axis of the air film hole and the plate surface is beta, as shown in figure 3. Dividing the flat gas surface into a gas coverage area and a gas film coverage area by whether the gas film coverage exists, wherein the gas temperature of the gas coverage area is T g A convective heat transfer coefficient of alpha g The temperature of the effluent cold air in the air film coverage area is T c A convective heat transfer coefficient of alpha c1 The method comprises the steps of carrying out a first treatment on the surface of the The temperature of the cold air on the inner surface of the air film hole is T c A convective heat transfer coefficient of alpha c2 The method comprises the steps of carrying out a first treatment on the surface of the The cold air temperature of the flat cold air surface is T c A convective heat transfer coefficient of alpha c3 。
And secondly, carrying out partition dispersion, deformation and integration on each area of the plate surface, and extracting the size parameters of each area.
2.1, dividing the area of the flat gas surface and simplifying the shape of each area, as shown in fig. 4, specifically comprising the following steps:
2.1.1 the gas surface of the plate has a width b and a length l, and the area A of the region g Area A of gas side gh region containing flat plate gh 。
2.1.2 the gas side g1 region of the plate is reduced to a rectangle with a width of 0.5D and a length of l a The area of the region is A g1 。
2.1.3 the film covering the c1 region was reduced to a rectangle with a width of 0.5D and a length of l a The area of the region is A c1 。
2.1.4 the gas side g2a of the plate is reduced to a rectangle with a width (BR-0.2) D and a length l b The area of the region is A g2a 。
2.1.5 the gas side g2b region of the plate is reduced to L-shape with a total width of (1.6 BR-0.32) D and a total length of 1.25L b The area of the region is A g2b 。
2.1.6 the gas side g3a of the plate is reduced to a rectangle with a width b-D and a length l a +l e The area of the region is A g3a 。
2.1.7 the gas side g3b region of the plate is reduced to a rectangle with a width b- (1.6 BR-0.32) D and a length of 1.25l b The area of the region is A g3b 。
2.1.8 the gas side g3c of the plate is reduced to a rectangle with width b and length l c The area of the region is A g3c 。
2.1.9 the gas side g3d region of the plate is reduced to a rectangle with a width b and a length l d The area of the region is A g3d 。
2.1.10 the gas side gh region of the plate is reduced to a rectangle with width D and length l e Area of the regionIs A gh 。
For the convenience of calculation and solution, the flat gas side g3a region and the flat gas side g3d region are combined and topologically converted into flat gas side g3a and g3d combined regions, wherein the area is A g3ad This can be expressed as:
A g3ad ＝A g3a +A g3d (1)
combining the flat gas side g3b region and the flat gas side g3c region, and topologically converting the flat gas side g3b region and the flat gas side g3c region into a flat gas side g3b and g3c combined region with the area A g3bc This can be expressed as:
A g3bc ＝A g3b +A g3c (2)
2.2, carrying out area division on the inner surface of the air film hole along the projection of the hole axis along the direction perpendicular to the symmetry plane, as shown in fig. 5, specifically comprising the following steps:
2.2.1 the area of the c2a region on the inner surface of the air film hole is A c2a 。
2.2.2 the area of the c2b region on the inner surface of the air film hole is A c2b 。
2.3 dividing the cold air surface of the flat plate into regions and simplifying the shape of each region, as shown in fig. 6, specifically:
2.3.1 Flat Cold air surfaces have a width b and a length l, the area of this region being A c Area A of cold air side ch area of flat plate ch 。
2.3.2 reducing the Cold side c3a of the plate to a rectangular shape with a width b and a length l a +l e The area of the region is A c3a 。
2.3.3 the cold side c3b of the plate is reduced to a rectangle with a width b and a length of 1.25l b The area of the region is A c3b 。
2.3.4 the cold side c3c region of the plate is reduced to a rectangle with a width b and a length l c -l f The area of the region is A c3c 。
2.3.5 reducing the Cold side c3d region of the plate to a rectangle with a width b and a length l d The area of the region is A c3d 。
2.3.6 the cold side ch area of the flat plate is reduced to a rectangle with a width b and a lengthl f The area of the region is A ch 。
Combining the flat cold side c3a region and the flat cold side c3d region and topologically converting into a flat cold side c3a and c3d combined region with an area A c3ad This can be expressed as:
A c3ad ＝A c3a +A c3d (3)
combining the flat cold side c3b region and the flat cold side c3c region and topologically converting into a flat cold side c3b and c3c combined region having an area A c3bc This can be expressed as:
A c3bc ＝A c3b +A c3c (4)
thirdly, converting the heat transfer process topology of each region into a solvable heat transfer model, solving the heat convection coefficient of the heat barrier coating coverage region by adopting a simple calculation method, establishing a heat flow conservation equation of the heat transfer model, and solving the wall surface temperature of each region based on the heat flow conservation equation. The specific heat transfer model and the wall temperature of each region are solved as follows:
3.1, calculating the convective heat transfer coefficient of the thermal barrier coating coverage area by adopting a simple calculation method:
3.1.1 equivalent Heat convection coefficient α of gas coverage after coating g ' is:
3.1.2 equivalent Heat convection coefficient α of air film covering region c1 after coating c1 ' is:
in the formulas (5) and (6), L TBC And lambda (lambda) TBC The thickness and the heat conductivity coefficient of the thermal barrier coating respectively.
And 3.2, establishing a heat flow conservation equation of the heat transfer model, and solving the wall surface temperature of each region based on the heat flow conservation equation.
3.2.1 converting the g 1-c 1 region topology to a thickness of 0.5D, width l a A flat plate heat transfer model of length delta is shown in figure 7. Based on energy conservation, it is considered that the fuel gas is transferred into the heat Q of the g1 region of the fuel gas side of the flat plate in a form of convection heat exchange g1 Heat Q transferred in a heat-conducting manner from the gas-side g1 region of the flat plate to the gas film-covered c1 region 1 Heat Q taken away from c1 region of film cover by convection heat exchange mode of film outflow cool air c1 Equality, namely:
Q g1 ＝Q 1 ＝Q c1 (7)
solving the above equation yields:
wall temperature T of gas side g1 region of flat plate Wg1 The method comprises the following steps:
wall temperature T of gas film covered c1 region Wc1 The method comprises the following steps:
heat resistance R of convection heat exchange between gas and flat plate gas side g1 region g1 The method comprises the following steps:
if the gas coverage area is coated with a thermal barrier coating, the equivalent convective heat transfer coefficient alpha of the gas coverage area is used g ' alpha in substitution equation (11) g And (5) performing calculation.
Heat conduction resistance R between g1 area of flat gas side and c1 area covered by gas film 1 The method comprises the following steps:
in the formula (12), lambda s Is the heat conductivity of the flat plate.
Thermal resistance R of air film covered region c1 and air film outflow cool air convection heat exchange c1 The method comprises the following steps:
if the air film covers the c1 area and is coated with the thermal barrier coating, the air film covers the equivalent convective heat transfer coefficient alpha of the c1 area c1 ' replace alpha in equation (13) c1 And (5) performing calculation.
3.2.2 converting the g2 a-c 2a region topology to an axis length l b Central angle radian theta 2a The radii of the gas and cold surfaces are r g2a And r c2a Wall thickness Deltar 2a A straight round tube sector section heat transfer model of equal wall thickness as shown in figure 8. Based on energy conservation, it is considered that the fuel gas is transferred into the heat Q of the g2a region of the gas side of the flat plate in a form of convection heat exchange g2a Heat Q transferred from the region g2a of the flat gas side to the region c2a of the inner surface of the gas film hole in a heat conduction mode 2a Heat Q taken away from c2a region of inner surface of air film hole by convection heat exchange of cool air in air film hole c2a Equality, namely:
Q g2a ＝Q 2a ＝Q c2a (14)
solving the above equation yields:
wall temperature T of g2a region of flat gas side Wg2a The method comprises the following steps:
wall temperature T of c2a region of inner surface of air film hole Wc2a The method comprises the following steps:
heat resistance R of convection heat exchange between gas and flat plate gas side g2a region g2a The method comprises the following steps:
if the gas coverage area is coated with a thermal barrier coating, the equivalent convective heat transfer coefficient alpha of the gas coverage area is used g ' alpha in substitution equation (18) g And (5) performing calculation.
Thermal resistance R for heat conduction between g2a region of flat gas side and c2a region of inner surface of gas film hole 2a The method comprises the following steps:
thermal resistance R of convective heat exchange between region c2a of inner surface of air film hole and cold air in air film hole c2a The method comprises the following steps:
area A of gas side g2a of the plate g2a Area A smaller than area c2a of inner surface of air film hole c2a When the arc surface of the round pipe is calculated by adopting the formula, the bending direction of the arc surface of the round pipe is opposite to that shown in fig. 8; area A of gas side g2a of the plate g2a Area A equal to area c2a of inner surface of air film hole c2a When the heat transfer model becomes length l b Width (BR-0.2) D, thickness Δr 2a Heat conduction thermal resistance R between g2a region of flat gas side and c2a region of inner surface of gas film hole 2a The process is as follows:
the wall temperature equations (16) and (17) are calculated using equation (21).
3.2.3 willTopological conversion of g2 b-c 2b region into axial length l b Central angle radian theta 2b The radii of the gas and cold surfaces are r g2b And r c2b Wall thickness Deltar 2b A straight round tube sector section heat transfer model of equal wall thickness as shown in fig. 9. Based on energy conservation, it is considered that the fuel gas is transferred into the heat Q of the g2b region of the fuel gas side of the flat plate in a form of convection heat exchange g2b Heat Q transferred from the g2b region of the gas side of the flat plate to the c2b region of the inner surface of the gas film hole in a heat conduction mode 2b Heat Q taken away from c2b region of inner surface of air film hole by convection heat exchange of cool air in air film hole c2b Equality, namely:
Q g2b ＝Q 2b ＝Q c2b (22)
solving the above equation yields:
wall temperature T of g2b region of flat gas side Wg2b The method comprises the following steps:
wall temperature T of c2b region of inner surface of air film hole Wc2b The method comprises the following steps:
heat resistance R of convective heat exchange between gas and flat plate gas side g2b region g2b The method comprises the following steps:
if the gas coverage area is coated with a thermal barrier coating, the equivalent convective heat transfer coefficient alpha of the gas coverage area is used g Alpha in' substitution equation (26) g And (5) performing calculation.
Flat gas side g2b region and gas film hole inner surface c2b regionThermal resistance R of heat conduction between 2b The method comprises the following steps:
thermal resistance R of convective heat exchange between region c2b of inner surface of air film hole and cold air in air film hole c2b The method comprises the following steps:
area A of the gas side g2b region of the flat plate g2b Area A smaller than area c2b of inner surface of air film hole c2b When the arc surface of the round pipe is calculated by adopting the formula, the bending direction of the arc surface of the round pipe is opposite to that shown in fig. 9; area A of the gas side g2b region of the flat plate g2b Area A equal to area c2b of inner surface of air film hole c2b When the heat transfer model becomes length l b Width (BR-0.2) D, thickness Δr 2b Heat conduction thermal resistance R between g2b region of flat gas side and c2b region of inner surface of gas film hole 2b The process is as follows:
the wall temperature equations (24) and (25) are calculated using equation (29).
3.2.4 converting the topology of the combining zone of g3a and g3 d-the combining zone of c3a and c3d into the axial length b, the central angle radian theta 3ad The radii of the gas and cold surfaces are r g3ad And r c3ad Wall thickness Deltar 3ad A straight round tube sector section heat transfer model of equal wall thickness as shown in fig. 10. Based on energy conservation, the gas is considered to transfer heat Q of the combining zone of the gas sides g3a and g3d of the flat plate in a convection heat exchange mode g3ad Heat Q transferred in a thermally conductive manner from the merging zone of the gas sides g3a and g3d of the flat plate to the merging zone of the cold sides c3a and c3d of the flat plate 3ad Heat Q taken away from the merging area of the cold sides c3a and c3d of the flat cold face cold air in the form of convection heat exchange c3ad Equality, namely:
Q g3ad ＝Q 3ad ＝Q c3ad (30)
solving the above equation yields:
wall temperature T of merging area of flat plate gas side g3a and g3d Wg3ad The method comprises the following steps:
wall temperature T of merging area of flat cold air side c3b and c3c Wc3ad The method comprises the following steps:
heat resistance R of convective heat transfer of gas and flat plate gas side g3a and g3d combining area g3ad The method comprises the following steps:
if the gas coverage area is coated with a thermal barrier coating, the equivalent convective heat transfer coefficient alpha of the gas coverage area is used g Alpha in' substitution equation (34) g And (5) performing calculation.
Thermal resistance R of heat conduction between the merging region of the flat gas sides g3a and g3d and the merging region of the flat cold sides c3a and c3d 3ad The method comprises the following steps:
thermal resistance R of heat exchange between cold air convection of cold air surface and merging area of flat cold air side c3a and c3d c3ad The method comprises the following steps:
due to the area A of the merging area of the gas sides g3a and g3d of the flat plate g3ad Is necessarily smaller than the area A of the merging area of the cold sides c3a and c3d of the flat plate c3ad The heat transfer model and formula described above need not be changed.
3.2.5 topology conversion of the g3b and g3c combined region-c 3b and c3c combined region into axis length b, central angle radian theta 3bc The radii of the gas and cold surfaces are r g3bc And r c3bc Wall thickness Deltar 3bc A straight round tube sector section heat transfer model of equal wall thickness as shown in fig. 11. Based on energy conservation, it is considered that the fuel gas is transferred into the heat Q of the combining zone of the flat fuel gas sides g3b and g3c in a convection heat exchange mode g3bc Heat Q transferred in a thermally conductive manner from the merging zone of the gas sides g3b and g3c of the flat plate to the merging zone of the cold sides c3b and c3c of the flat plate 3bc Heat Q taken away by the cold air of the cold air surface of the flat plate from the merging area of the sides c3b and c3c of the flat plate in the form of convection heat exchange c3bc Equality, namely:
Q g3bc ＝Q 3bc ＝Q c3bc (37)
solving the above equation yields:
wall temperature T of merging area of flat plate gas side g3b and g3c Wg3bc The method comprises the following steps:
wall temperature T of merging area of flat cold air side c3b and c3c Wc3bc The method comprises the following steps:
heat resistance R of convective heat transfer of gas and flat plate gas side g3b and g3c combining area g3bc The method comprises the following steps:
if the gas coverage area is coated with a thermal barrier coating, the equivalent convective heat transfer coefficient alpha of the gas coverage area is used g ' alpha in substitution equation (41) g And (5) performing calculation.
Thermal resistance R of heat conduction between the merging region of the flat gas sides g3b and g3c and the merging region of the flat cold sides c3b and c3c 3bc The method comprises the following steps:
thermal resistance R of heat exchange between cold air convection of cold air surface and merging area of flat cold air side c3b and c3c c3bc The method comprises the following steps:
area A of the merging area of the gas sides g3b and g3c of the flat plate g3bc Is larger than the area A of the merging area of the cold side c3b and c3c of the flat plate c3bc When the arc surface of the round pipe is calculated by adopting the formula, the bending direction of the arc surface of the round pipe is opposite to that shown in fig. 11; area A of the merging area of the gas sides g3b and g3c of the flat plate g3bc Equal to the area A of the merging area of the cold sides c3b and c3c of the flat plate c3bc The heat transfer model became 1.25l in length b +l c -l f Width b, thickness Δr 3bc Heat conduction thermal resistance R between the combination region of the flat gas sides g3b and g3c and the combination region of the flat cold sides c3b and c3c 3bc The process is as follows:
the wall temperature equations (39) and (40) are calculated using equation (44).
And fourthly, integrating wall temperature and area values of all the subareas, and calculating to obtain the wall temperature in an area weighted average mode.
4.1 temperature T of Flat gas surface Wg The method comprises the following steps:
4.2 temperature T of inner surface of air film hole Wc2 The method comprises the following steps:
4.3 temperature T of Flat Cold air surface Wc3 The method comprises the following steps:
the invention has the beneficial effects that:
1. the calculation efficiency is high, and the temperature of each wall surface is obtained rapidly:
compared with the conventional three-dimensional numerical simulation method, the calculation method has higher calculation efficiency, is oriented to the design problem of the flat plate structure with the air film holes and the thermal barrier coating, can obtain a large number of wall temperatures under different structures, different materials and different working conditions in a short time, and is used for proving establishment and searching of a design scheme. In the invention, the topology of the heat transfer process of each region is converted into a solvable heat transfer model by partitioning each wall surface, so that the complex three-dimensional partial differential equation set is simplified into a series of simple one-dimensional formulas. And for the situation that the surface is coated with the thermal barrier coating, the equivalent conversion method of the convective heat transfer coefficient in the method can reproduce the same heat insulation effect without establishing a physical structure of the thermal barrier coating, and the weakening amplitude of the heat transfer process can be calculated by only considering two variables of the coating thickness and the heat transfer coefficient. In conclusion, the method can avoid a large number of repeated processes (modeling, meshing, solving and calculating and the like) and carrying and switching among a plurality of software, thereby greatly saving time and cost.
2. The calculation function is comprehensive, and the wall temperature of the flat plate-shaped member under various working conditions and structures can be calculated:
the method can rapidly calculate the wall surface temperature of the flat plate-shaped component with different structures, different materials and different working conditions, which contains air film cooling and thermal barrier coating protection and is optimally combined between the air film cooling and the thermal barrier coating protection, and provides guidance basis for the design of hot end components of aeroengines and gas turbines, such as combustion chambers, turbines and the like. The function of the heat exchanger is comprehensively represented by considering the influence of a plurality of factors on the heat transfer process and the wall temperature, and the factors can be classified according to three aspects of geometric structures, physical parameters of materials and working conditions.
a) Geometry: plate length l, plate width b, plate thickness h, gas film hole diameter phiD, distance l from center point of gas film hole on cold air side to upstream of plate (gas inlet end) h The included angle beta between the axis of the air film hole and the plate surface and the thickness L of the thermal barrier coating TBC 。
b) Physical parameters: coefficient of thermal conductivity lambda of flat plate s Thermal conductivity coefficient lambda of thermal barrier coating TBC 。
c) Working conditions: gas temperature T g Temperature T of cool air c Convection heat transfer coefficient alpha of blowing ratio BR and gas coverage area g Convective heat transfer coefficient α for air film coverage c1 Convection heat transfer coefficient alpha of inner surface of air film hole c2 Convection heat transfer coefficient alpha of flat cold air surface c3 。
The method can also respectively set whether the gas coverage area and the gas film coverage area are provided with the coating or not, thereby realizing the calculation and analysis of three different designs of completely non-coating, full-coating and optimized coating, adapting to different design requirements and embodying comprehensive and powerful functions.
3. The calculation result is reliable, and the temperature of each wall surface is accurately obtained:
the wall temperature obtained by calculation by the method is similar to the calculation result of three-dimensional numerical simulation strictly conforming to the flow and heat transfer equation, and the relative error (based on the calculation result of the three-dimensional numerical simulation) of the wall temperature of three calculation areas is within +/-2 percent, so that the method has higher precision.
Taking the typical calculation result shown in fig. 12 as an example for a flat gas surface, the three-dimensional value simulation result is shown in fig. 12 (b), the isotherm extends outwards around the gas film hole and the gas film coverage area, and the color of the strip gradually increases from light to dark from the two areas; taking the typical calculation result shown in fig. 13 as an example for the inner surface of the air film hole, the three-dimensional value simulation result is shown in fig. 13 (b), the isotherm trend of the three-dimensional value simulation result is approximately parallel to the axis of the air film hole, and the color of the strip gradually increases from the light to the dark from the cold side to the gas side of the hole; for the flat cold air surface, taking the typical calculation result shown in fig. 14 as an example, the three-dimensional value simulation result is shown in fig. 14 (b), the isotherm extends outwards around the air film hole, is approximately perpendicular to the length direction of the flat plate at the position far away from the air film hole at the downstream of the air film hole, and shows that the influence of cold air in the hole on the area is gradually weakened, and the influence is consistent with the trend of the strip color from shallow to deep. The method of the invention calculates each part of the same surface in a partitioning mode (the three surface partitioning modes are respectively the same as those of fig. 5, 6 and 7), the calculated wall temperatures of each partition are respectively shown as fig. 12 (a), 13 (a) and 14 (a), the temperature values are represented according to the color depths shown by the scales on the left sides of the partitions, the method is similar to that shown by the simulation results of the three-dimensional numerical values, the same trend is also shown, and the wall temperature of each region is shown to be similar to the wall temperature average value of the corresponding region in the three-dimensional simulation calculation through color comparison. The wall temperature distribution depicted by the method is not as fine as the three-dimensional simulation result, but has higher accuracy in average value.
Description of the drawings:
FIG. 1 is a cloud of wall temperature distribution of a typical flat panel under film cooling and thermal barrier coating protection;
FIG. 2 is a flow chart of a rapid calculation of plate wall temperature;
FIG. 3 is a block diagram of a flat panel;
FIG. 4 is a plot of calculated area of a flat gas panel;
FIG. 5 is a calculated area division of the inner surface of the film hole;
FIG. 6 is a computational area division of a cold face of a flat panel;
FIG. 7 is a graph of the heat transfer model after topology conversion in the g 1-c 1 region;
FIG. 8 is a graph of a heat transfer model after topological conversion in the g2 a-c 2a region;
FIG. 9 is a graph of the heat transfer model after topological conversion in the g2 b-c 2b region;
FIG. 10 is a graph of the heat transfer model after topology conversion of the g3a and g3d merge regions-c 3a and c3d merge regions;
FIG. 11 is a graph of the heat transfer model after topology conversion of the g3b and g3c merge regions-c 3b and c3c merge regions;
FIG. 12 (a) is a flat panel gas surface temperature cloud calculated by the method of the present invention;
FIG. 12 (b) is a three-dimensional simulated calculated flat panel gas surface temperature cloud;
FIG. 13 (a) is a cloud chart of the temperature of the inner surface of a gas film hole calculated by the method of the invention;
FIG. 13 (b) is a cloud chart of the temperature of the inner surface of the air film hole calculated by three-dimensional simulation;
FIG. 14 (a) is a flat cold face temperature cloud calculated by the method of the present invention;
fig. 14 (b) is a flat cold-face temperature cloud of three-dimensional simulation calculation.
The reference numerals in the figures correspond to the following: 1-a flat gas surface; 2-gas film hole inner surface, 3-flat cold air face, 4-flat gas side g1 area, 5-gas film cover c1 area, 6-flat gas side g2a area, 7-flat gas side g2b area, 8-flat gas side g3a area, 9-flat gas side g3b area, 10-flat gas side g3c area, 11-flat gas side g3d area, 12-flat gas side gh area, 13-gas film hole inner surface c2a area, 14-gas film hole inner surface c2b area, 15-flat gas side c3a area, 16-flat cold air side c3b area, 17-flat cold air side c3c area, 18-flat cold air side c3d area, 19-flat cold air side ch area, 20-flat gas side g3a and g3d merging area, 21-flat cold air side c3a and c3d merging area, 22-flat gas side g3b and g3c merging area, 23-flat cold air side c3b and c3c merging area.
Detailed Description
In order that the invention may be more readily understood, a more particular description of the invention will be rendered by reference to specific embodiments that are illustrated in the appended drawings.
Example 1:
for the case of a flat plate-shaped member with cylindrical air film holes and without a thermal barrier coating on the surface, the required geometric parameters, working conditions and physical parameters are calculated as shown in Table 1.
Table 1 example 1 calculation of the required parameters
Firstly, carrying out regional dispersion, deformation and integration on each region of the flat plate wall surface, then solving the local wall temperature based on a heat flow conservation equation, and finally solving the average wall temperature based on area weighting, namely adopting a formula (45), a formula (46) and a formula (47), and respectively calculating to obtain the wall temperature T of the flat plate gas surface Wg Wall temperature T of inner surface of air film hole Wc2 And wall temperature T of flat cold air surface Wc3 。
The method is similar to the wall temperature results of three-dimensional simulation calculation, the temperature difference of the two is within 15K, the relative error of the wall temperature (based on the three-dimensional numerical simulation calculation results) is not more than +/-1%, and the specific calculation results are shown in Table 2.
TABLE 2 wall temperature calculation results and relative errors for example 1
Example 2:
for the case of a flat plate-shaped member with cylindrical gas film holes and a flat plate gas surface fully covered with the thermal barrier coating, the parameters required for calculation are shown in Table 3, and the rest parameters are the same as those in Table 1.
Table 3 example 2 calculation of the required parameters
Firstly, carrying out regional dispersion, deformation and integration on each region of the flat plate wall surface, and then solving the local wall temperature based on a heat flow conservation equationFinally solving the average wall temperature based on area weighting, namely respectively calculating the wall temperature T of the flat gas surface by adopting a formula (45), a formula (46) and a formula (47) Wg Wall temperature T of inner surface of air film hole Wc2 And wall temperature T of flat cold air surface Wc3 。
The method is similar to the wall temperature results of three-dimensional simulation calculation, the temperature difference of the two is within 20K, the relative error (based on the three-dimensional numerical simulation calculation results) of the wall temperature is not more than +/-1.5%, and the specific calculation results are shown in Table 4.
TABLE 4 wall temperature calculation results and relative errors for example 2
Example 3:
for the flat plate-shaped member with the cylindrical air film holes, the thermal barrier coating is optimally designed, namely, the thermal barrier coating is only coated on the gas coverage area, the thermal barrier coating is not coated on the surface of the area c1 covered by the 5 air film, the calculated required parameters are shown in the table 5, and the rest parameters are the same as those in the table 1.
Table 5 example 3 calculation of the required parameters
Firstly, carrying out regional dispersion, deformation and integration on each region of the flat plate wall surface, then solving the local wall temperature based on a heat flow conservation equation, and finally solving the average wall temperature based on area weighting, namely adopting a formula (45), a formula (46) and a formula (47), and respectively calculating to obtain the wall temperature T of the flat plate gas surface Wg Wall temperature T of inner surface of air film hole Wc2 And wall temperature T of flat cold air surface Wc3 。
The method is similar to the wall temperature results of three-dimensional simulation calculation, the temperature difference of the two is within 20K, the relative error (based on the three-dimensional numerical simulation calculation results) of the wall temperature is not more than +/-1.5%, and the specific calculation results are shown in Table 6.
TABLE 6 wall temperature calculation results and relative errors for example 3
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Claims (3)
1. A method for rapidly calculating the temperature of a flat plate wall surface containing a gas film and a thermal barrier coating is characterized by comprising the following steps:
firstly, establishing a calculation model of a typical flat plate and cylindrical air film hole structure according to input structural parameters, physical parameters and working conditions; according to the symmetry, only half of the symmetry of the calculation model is established, the length, the width and the thickness of the flat plate are respectively l, b and h, and the distance from the center point of the air film hole on the cold air side to the upstream (gas inlet end) of the flat plate is l h The diameter of the air film hole is phi D, and the included angle between the axis of the air film hole and the plate surface is beta; the flat gas surface (1) is divided into a gas coverage area and a gas film coverage area by whether the gas film coverage exists, and the gas temperature of the gas coverage area is T g A convective heat transfer coefficient of alpha g The temperature of the air film covered outflow cold air is T c A convective heat transfer coefficient of alpha c1 The method comprises the steps of carrying out a first treatment on the surface of the The cold air temperature of the inner surface (2) of the air film hole is T c A convective heat transfer coefficient of alpha c2 The method comprises the steps of carrying out a first treatment on the surface of the The cold air temperature of the flat cold air surface (3) is T c A convective heat transfer coefficient of alpha c3 ；
Secondly, carrying out partition dispersion, deformation and integration on each area of the plate surface, and extracting the size parameters of each area;
2.1, carrying out area division on the flat gas surface (1) and simplifying the shape of each area, wherein the specific steps are as follows:
2.1.1 Flat gas surface (1) has a width b and a length l, and the area A of the region g Area A of the gas side gh region (12) of the plate gh ；
2.1.2 the gas side g1 zone (4) of the plate is reduced to a rectangle with a width of 0.5D and a length of l a The area of the region is A g1 ；
2.1.3 simplifying the film covering the c1 region (5) into a rectangle with a width of 0.5D and a length of l a The area of the region is A c1 ；
2.1.4 the flat gas side g2a zone (6) is reduced to a rectangle with width (BR-0.2) D and length l b The area of the region is A g2a ；
2.1.5 the flat gas side g2b zone (7) is reduced to L-shape with a total width of (1.6 BR-0.32) D and a total length of 1.25L b The area of the region is A g2b ；
2.1.6 simplifying the gas side g3a zone (8) of the plate into a rectangle with width b-D and length l a +l e The area of the region is A g3a ；
2.1.7 reducing the plate gas side g3b zone (9) to a rectangle with a width b- (1.6 BR-0.32) D and a length of 1.25l b The area of the region is A g3b ；
2.1.8 the gas side g3c region (10) of the plate is reduced to a rectangle with a width b and a length l c The area of the region is A g3c ；
2.1.9 the gas side g3d zone (11) of the plate is reduced to a rectangle with a width b and a length l d The area of the region is A g3d ；
2.1.10 reducing the gas side gh region (12) of the plate to a rectangular shape with a width D and a length l e The area of the region is A gh ；
For the purpose of calculation and solution, the flat gas side g3a region (8) and the flat gas side g3d region (11) are combined and topologically converted into a flat gas side g3a and g3d combining region (20), and the area of the flat gas side g3a and g3d combining region is A g3ad This can be expressed as:
A g3ad ＝A g3a +A g3d (1)
combining the flat gas side g3b region (9) and the flat gas side g3c region (10) and topologically converting the flat gas side g3b and g3c combined region (22) with the area of A g3bc This can be expressed as:
A g3bc ＝A g3b +A g3c (2)
2.2, carrying out regional division on the inner surface (2) of the air film hole along the projection of the hole axis along the direction perpendicular to the symmetry plane, wherein the regional division is specifically as follows: 2.2.1 the area of the region (13) of the inner surface c2a of the air film hole is A c2a ；
2.2.2 the area of the region (14) of the inner surface c2b of the air film hole is A c2b ；
2.3, dividing the cold air surface of the flat plate into areas and simplifying the shape of each area, wherein the method comprises the following steps:
2.3.1 Flat Cold air surface (3) has a width b and a length l, and the area of this region is A c Area A of cold air side ch area (19) of the plate ch ；
2.3.2 simplifying the cold side c3a region (15) of the plate into a rectangle with width b and length l a +l e The area of the region is A c3a ；
2.3.3 simplifying the cold side c3b region (16) of the plate into a rectangle with a width b and a length of 1.25l b The area of the region is A c3b ；
2.3.4 reducing the Cold side of the plate c3c region (17) to a rectangle with width b and length l c -l f The area of the region is A c3c ；
2.3.5 simplifying the cold side c3d region (18) of the plate into a rectangle with width b and length l d The area of the region is A c3d ；
2.3.6 the cold-side ch area (19) of the flat plate is reduced to a rectangle with a width b and a length l f The area of the region is A ch ；
Combining the flat cold side c3a region (15) and the flat cold side c3d region (18) and topologically converting into a flat cold side c3a and c3d combined region (21) having an area A c3ad This can be expressed as:
A c3ad ＝A c3a +A c3d (3)
combining the flat cold side c3b region (16) and the flat cold side c3c region (17) and topologically converting into a flat cold side c3b and c3c combined region (23) having an area A c3bc This can be expressed as:
A c3bc ＝A c3b +A c3c (4)
thirdly, converting the heat transfer process topology of each region into a solvable heat transfer model, solving the convective heat transfer coefficient of the heat barrier coating coverage region by adopting a simple calculation method, establishing a heat flow conservation equation of the heat transfer model, and solving the wall surface temperature of each region based on the heat flow conservation equation; the specific heat transfer model and the wall temperature of each region are solved as follows:
3.1, calculating the convective heat transfer coefficient of the thermal barrier coating coverage area by adopting a simple calculation method:
3.1.1 equivalent Heat convection coefficient α of gas coverage after coating g ' is:
3.1.2 equivalent Heat convection coefficient α of air film covering region c1 after coating c1 ' is:
in the formulas (5) and (6), L TBC And lambda (lambda) TBC The thickness and the heat conductivity coefficient of the thermal barrier coating are respectively;
and fourthly, integrating wall temperature and area values of all the subareas, and calculating to obtain the wall temperature in an area weighted average mode.
2. The method for rapidly calculating the temperature of the wall surface of the flat plate containing the air film and the thermal barrier coating according to claim 1, wherein in the step 3.2, the specific operation mode is as follows:
3.2.1 converting the g 1-c 1 region topology to a thickness of 0.5D, width l a The flat plate heat transfer model with the length delta considers that the fuel gas is transferred into the heat Q of the g1 area (4) of the flat plate fuel gas in a convection heat exchange mode according to the energy conservation g1 Heat Q transferred in a heat-conducting manner from the gas-side g1 region (4) to the gas film-covered c1 region (5) 1 Heat Q taken away from a region (5) covered by the air film in a convection heat exchange mode by air film outflow cold air c1 Equality, namely:
Q g1 ＝Q 1 ＝Q c1 (7)
solving the above equation yields:
wall temperature T of flat gas side g1 zone (4) Wg1 The method comprises the following steps:
wall temperature T of gas film covered c1 region (5) Wc1 The method comprises the following steps:
heat resistance R of convection heat exchange between fuel gas and flat plate fuel gas side g1 region (4) g1 The method comprises the following steps:
if the gas coverage area is coated with a thermal barrier coating, the equivalent convective heat transfer coefficient alpha of the gas coverage area is used g ' alpha in substitution equation (11) g Calculating;
heat conduction resistance R between flat plate gas side g1 region (4) and gas film coverage c1 region (5) 1 The method comprises the following steps:
in the formula (12), lambda s The heat conductivity coefficient of the flat plate;
thermal resistance R of convective heat exchange between air film covered region c1 (5) and air film outflow cold air c1 The method comprises the following steps:
if the film is covered withWhen the thermal barrier coating is coated on the c1 region (5), the air film is used for covering the equivalent convective heat transfer coefficient alpha of the c1 region (5) c1 ' replace alpha in equation (13) c1 Calculating;
3.2.2 converting the g2 a-c 2a region topology to an axis length l b Central angle radian theta 2a The radii of the gas and cold surfaces are r g2a And r c2a Wall thickness Deltar 2a A straight circular tube sector section heat transfer model with equal wall thickness as shown in figure 8; based on energy conservation, it is considered that the fuel gas is transferred into the heat Q of the g2a region (6) of the flat fuel gas side in a form of convection heat exchange g2a Heat Q transferred in a heat-conducting manner from the region g2a (6) of the flat gas side to the region c2a (13) of the inner surface of the gas film hole 2a Heat Q taken away from a region (13) of the inner surface c2a of the air film hole by cold air in the air film hole in a convection heat exchange mode c2a Equality, namely:
Q g2a ＝Q 2a ＝Q c2a (14)
solving the above equation yields:
wall temperature T of flat gas side g2a zone (6) Wg2a The method comprises the following steps:
wall temperature T of region (13) of inner surface c2a of air film hole Wc2a The method comprises the following steps:
heat resistance R of heat convection between fuel gas and flat plate fuel gas side g2a region (6) g2a The method comprises the following steps:
if the gas coverage area is coated with a thermal barrier coating, the equivalent convective heat transfer coefficient alpha of the gas coverage area is used g ' alpha in substitution equation (18) g Calculating;
thermal resistance R for heat conduction between flat plate gas side g2a region (6) and gas film hole inner surface c2a region (13) 2a The method comprises the following steps:
thermal resistance R of convection heat exchange between region (13) of inner surface c2a of air film hole and cold air in air film hole c2a The method comprises the following steps:
area A of the gas side g2a region (6) of the plate g2a Area A smaller than area C2a (13) of inner surface of air film hole c2a When the arc surface of the round pipe is calculated by adopting the formula, the bending direction of the arc surface of the round pipe is opposite to that shown in fig. 8; area A of the gas side g2a region (6) of the plate g2a Area A equal to area c2a (13) of inner surface of air film hole c2a When the heat transfer model becomes length l b Width (BR-0.2) D, thickness Δr 2a Heat conduction thermal resistance R between flat plate gas side g2a region (6) and gas film hole inner surface c2a region (13) 2a The process is as follows:
the wall temperature formulas (16) and (17) are calculated by adopting a formula (21);
3.2.3 converting the g2 b-c 2b region topology to an axis length l b Central angle radian theta 2b The radii of the gas and cold surfaces are r g2b And r c2b Wall thickness Deltar 2b A straight circular tube sector section heat transfer model with equal wall thickness as shown in fig. 9; based on conservation of energy, the gas is considered to exchange heat by convectionHeat Q transferred into the gas side g2b region (7) of the flat plate g2b Heat Q transferred in a heat-conducting manner from the region (7) of the gas side g2b of the flat plate to the region (14) of the inner surface c2b of the gas film hole 2b Heat Q taken away from c2b region (14) of inner surface of air film hole by convection heat exchange of cold air in air film hole c2b Equality, namely:
Q g2b ＝Q 2b ＝Q c2b (22)
solving the above equation yields:
wall temperature T of flat gas side g2b zone (7) Wg2b The method comprises the following steps:
wall temperature T of region (14) of inner surface c2b of air film hole Wc2b The method comprises the following steps:
heat resistance R of heat convection of gas and flat plate gas side g2b region (7) g2b The method comprises the following steps:
if the gas coverage area is coated with a thermal barrier coating, the equivalent convective heat transfer coefficient alpha of the gas coverage area is used g Alpha in' substitution equation (26) g Calculating;
thermal resistance R for heat conduction between flat plate gas side g2b region (7) and gas film hole inner surface c2b region (14) 2b The method comprises the following steps:
thermal resistance R of heat exchange between region c2b (14) of inner surface of air film hole and cold air convection in air film hole c2b The method comprises the following steps:
area A of the gas side g2b region (7) of the plate g2b Area A smaller than area c2b (14) of inner surface of air film hole c2b When the arc surface of the round pipe is calculated by adopting the formula, the bending direction of the arc surface of the round pipe is opposite to that shown in fig. 9; area A of the gas side g2b region (7) of the plate g2b Area A equal to region (14) of inner surface c2b of air film hole c2b When the heat transfer model becomes length l b Width (BR-0.2) D, thickness Δr 2b Heat conduction thermal resistance R between flat plate gas side g2b region (7) and gas film hole inner surface c2b region (14) 2b The process is as follows:
the wall temperature formulas (24) and (25) are calculated by a formula (29);
3.2.4 converting the topology of the combining zone of g3a and g3 d-the combining zone of c3a and c3d into the axial length b, the central angle radian theta 3ad The radii of the gas and cold surfaces are r g3ad And r c3ad Wall thickness Deltar 3ad According to the energy conservation, the fuel gas is considered to be transferred into the heat Q of the merging zone (20) of the flat plate fuel gas sides g3a and g3d in a convection heat exchange mode g3ad Heat Q transferred in a thermally conductive manner from the flat gas side g3a and g3d combining zone (20) to the flat cold gas side c3a and c3d combining zone (21) 3ad Heat Q taken away by the cold air of the cold air surface of the flat plate from the merging area (21) of the sides c3a and c3d of the flat plate in the form of convection heat exchange c3ad Equality, namely:
Q g3ad ＝Q 3ad ＝Q c3ad (30)
solving the above equation yields:
wall temperature T of the merging zone (20) of the flat gas sides g3a and g3d Wg3ad The method comprises the following steps:
wall temperature T of merging area (23) of cold side c3b and c3c of flat plate Wc3ad The method comprises the following steps:
heat resistance R of heat convection of gas and flat plate gas side g3a and g3d combining zone (20) g3ad The method comprises the following steps:
if the gas coverage area is coated with a thermal barrier coating, the equivalent convective heat transfer coefficient alpha of the gas coverage area is used g Alpha in' substitution equation (34) g Calculating;
thermal resistance R for heat conduction between the flat gas side g3a and g3d combining zone (20) and the flat cold side c3a and c3d combining zone (21) 3ad The method comprises the following steps:
thermal resistance R of convection heat exchange between cold air of flat cold air side c3a and c3d combining area (21) and cold air surface c3ad The method comprises the following steps:
3.2.5 topology conversion of the g3b and g3c combined region-c 3b and c3c combined region into axis length b, central angle radian theta 3bc The radii of the gas and cold surfaces are r g3bc And r c3bc Wall thickness Deltar 3bc According to the energy conservation, the fuel gas is considered to be transferred into the heat Q of the merging zone (22) of the g3b and g3c of the flat plate fuel gas side in a convection heat exchange mode g3bc Heat Q transferred in a thermally conductive manner from the flat gas side g3b and g3c combining zone (22) to the flat cold gas side c3b and c3c combining zone (23) 3bc Heat Q taken away by the cold air of the cold air surface of the flat plate from the merging area (23) of the sides c3b and c3c of the flat plate in the form of convection heat exchange c3bc Equality, namely:
Q g3bc ＝Q 3bc ＝Q c3bc (37)
solving the above equation yields:
wall temperature T of merging zone (22) of flat gas side g3b and g3c Wg3bc The method comprises the following steps:
wall temperature T of merging area (23) of cold side c3b and c3c of flat plate Wc3bc The method comprises the following steps:
heat resistance R of convection heat exchange of gas and flat plate gas side g3b and g3c combining area (22) g3bc The method comprises the following steps:
if the gas is coveredWhen the thermal barrier coating is coated, the equivalent convective heat transfer coefficient alpha is covered by the fuel gas g ' alpha in substitution equation (41) g Calculating;
thermal resistance R of heat conduction between the flat gas side g3b and g3c combining zone (22) and the flat cold side c3b and c3c combining zone (23) 3bc The method comprises the following steps:
thermal resistance R of convection heat exchange between cold air of flat cold air side c3b and c3c combining area (23) and cold air surface c3bc The method comprises the following steps:
area A of the merging zone (22) of the gas sides g3b and g3c of the flat plate g3bc Is larger than the area A of the merging area (23) of the cold sides c3b and c3c of the flat plate c3bc When the arc surface of the round pipe is calculated by adopting the formula, the bending direction of the arc surface of the round pipe is opposite to that shown in fig. 11; area A of the merging zone (22) of the gas sides g3b and g3c of the flat plate g3bc Is equal to the area A of the merging area (23) of the cold sides c3b and c3c of the flat plate c3bc The heat transfer model became 1.25l in length b +l c -l f Width b, thickness Δr 3bc Heat conduction resistance R between the flat gas side g3b and g3c combining zone (22) and the flat cold side c3b and c3c combining zone (23) 3bc The process is as follows:
the wall temperature equations (39) and (40) are calculated using equation (44).
3. The method for rapidly calculating the temperature of the wall surface of the flat plate containing the air film and the thermal barrier coating according to claim 1 or 2, wherein the fourth step comprises the following specific steps:
4.1 temperature T of Flat gas surface (1) Wg The method comprises the following steps:
4.2 temperature T of inner surface (2) of gas film hole Wc2 The method comprises the following steps:
4.3 temperature T of Flat Cold air surface (3) Wc3 The method comprises the following steps:
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| CN117592204B (en) * | 2024-01-19 | 2024-04-02 | 中国航发四川燃气涡轮研究院 | One-dimensional wall temperature calculation method of porous laminate |
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