JP5055851B2 - Local heat transfer coefficient determination program and local heat transfer coefficient determination device - Google Patents

Description

  The present invention relates to a local heat transfer determination program and a local heat transfer coefficient determination device for determining a local heat transfer coefficient of a surface of a material to be treated that is gas-cooled in a heat treatment furnace.

  In the quenching process by gas cooling, it is necessary to optimize the cooling conditions such as the supply gas flow rate and the supply gas temperature in order to improve the dimensional accuracy and quenchability after quenching of the metal product as the material to be processed.

  In order to obtain an appropriate value for such a cooling condition, a strain prediction simulation for predicting a strain of a material to be treated after quenching by a numerical analysis method such as a finite element method, a finite volume method, or a difference method is recently used. . By using strain prediction simulation, the time required to develop a new heat treatment process can be shortened and development costs can be reduced.

  The strain prediction simulation uses a local heat transfer coefficient on the surface of the material to be processed as a boundary condition. Therefore, in order to improve the accuracy of the distortion prediction simulation, it is necessary to obtain a highly accurate local heat transfer coefficient.

  As a conventional method for determining a high-accuracy local heat transfer coefficient, a method using a heat conduction inverse analysis (hereinafter referred to as a first conventional technique) and a method using an unsteady heat flow analysis (hereinafter referred to as a second technique). (Referred to as prior art).

The first prior art includes Patent Document 1 (Japanese Patent Laid-Open No. 7-188734), Patent Document 2 (Japanese Patent Laid-Open No. 2003-42984) and Non-Patent Document 1 ("Heat Treatment Deformation Simulation and Cooling", Michiharu Narazaki, Heat Treatment No. 42, No. 5, 2002, pp. 333-340). In the prior art 1, the local heat transfer coefficient is determined by the following procedure. First, the temperature change of the material to be treated is expressed by the energy conservation equation (unsteady heat conduction equation) shown in Equation (2).

Here, ρ _s is the density of the treated material (kg / m ³ ), C _{m, s} is the average specific heat (J / kg / K) of the treated material, and λ _s is the thermal conductivity (W / W) of the treated material. m / K), T _s is the temperature (K) of the material to be treated. The subscript s in each symbol indicates that it is a solid. In Expression (2), “·” indicates an inner product, and “∇” is a differential operator defined by ∇≡ (∂ / ∂x, ∂ / ∂y, ∂ / ∂z). Moreover, t in Formula (2) shows time (s).

Average specific heat Cm _{, s} in Formula (2) is defined by Formula (3) using true specific heat Cs.

In this prior art, a numerical analysis method is used to obtain the temperature distribution inside and on the surface of the workpiece. Specifically, first, the material to be analyzed is divided into minute regions such as elements and lattices. Next, Formula (2) is discretized in each region, and the temperature in each region is calculated. In such a numerical analysis method, a local heat transfer coefficient on the surface of the material to be processed is required as a boundary condition. The local heat transfer coefficient h (x) (W / m ² / K) is defined by equation (4).

h (x) ≡q (x) / (T _f −T _{t, s} ) (4)

Here, q (x) is a heat flux (W / m ² ) at a predetermined surface position x of the material to be processed. T _f is the temperature (K) of the atmospheric fluid, and in the case of gas cooling, a gas supply temperature (hereinafter referred to as supply gas temperature) is used as the temperature of the atmospheric fluid. T _{t, s} is the surface temperature of the workpiece at time t.

Since the heat transfer coefficient is not a physical property value such as heat conductivity, the heat transfer coefficient varies depending on the predetermined surface position x of the material to be processed and the cooling conditions. Therefore, in the first conventional technique, the local heat transfer coefficient h (x) is determined by the following procedure.
(1) An experiment is performed under predetermined cooling conditions, and temperature transition data (cooling curve) at one or more predetermined positions of the material to be processed is collected. That is, temperature data is acquired by experiment.
(2) Temporarily set a local heat transfer coefficient h (x) on the surface of the workpiece. Formula (2) is discretized using the temporarily set local heat transfer coefficient h (x), and the temperature at the predetermined position is calculated. That is, temperature data is calculated by simulation.
(3) Compare the experimental temperature data and simulation temperature data at a predetermined position at the same time, and change the temporary set value of local heat transfer coefficient h (x) repeatedly until the temperature difference between the two is within the allowable range. Perform a simulation. When the temperature difference between the two is within the allowable range, the temporarily set local heat transfer coefficient h (x) is determined as the local heat transfer coefficient used for the strain prediction simulation.

  As described above, in the first prior art, temperature data is measured in advance by experiment, and compared with temperature data obtained by simulation based on a numerical analysis method, the local heat transfer coefficient h (x) is determined. .

  However, in the first prior art, experimental data must be collected in order to set the local heat transfer coefficient h (x). The determined local heat transfer coefficient h (x) is a value based on experimental data, and is an optimal value under cooling conditions during the experiment. Therefore, in the case of cooling conditions different from the collected experimental data, new experimental data must be collected under different cooling conditions, and the local heat transfer coefficient h (x) must be determined again based on the collected experimental data. . That is, in the first conventional technique, a new experiment must be performed every time the cooling condition is changed.

  The second conventional technique (determination method based on unsteady heat flow analysis) calculates the heat flux on the surface of the material to be processed while progressing time by a numerical analysis method, and calculates the local heat transfer coefficient based on the calculated heat flux. To decide. The second conventional technique can determine the local heat transfer coefficient h (x) only by simulation, and does not require experimental data as in the first conventional technique.

In this method, the energy conservation equation (2) is used to calculate the temperature distribution of the material to be processed, and the mass conservation equation (5) shown below is used to calculate the temperature distribution of the gas flow field surrounding the material to be processed. ), Momentum conservation equation (Navier-Stokes equation) (6), and energy conservation equation (7). In addition to these equations (2) and (5) to (7), in order to increase the accuracy of the relationship between gas density and pressure and the relationship between gas density and temperature, the gas equation of state is used. May be.

Here, ρ _g is the gas density (kg / m ³ ), U _g is the gas flow rate (m / s), _pg is the gas pressure (Pa), T _g is the gas temperature (K), and μ _g is the gas viscosity. The coefficient (Pa · s), C _{m, g} is the average specific heat (J / kg / K) of the gas, λ _g is the thermal conductivity (W / m / K) of the gas, and g in each symbol is the gas ( Gas). The average specific heat C _{m, g} of the gas is defined by equation (8) using the true specific heat C _g .

Hereinafter, a method for determining the local heat transfer coefficient h (x) according to the second prior art will be described with reference to FIG. In this method, first, supply gas temperature T _{g, in} and supply gas mass flow rate G _in (and supply gas composition) are set as cooling conditions (S101). At this time, the calculation end time t _max of the unsteady heat flow analysis is also set. The calculation end time t _max is, for example, the same time as the time from the start to the end of gas cooling.

Subsequently, the time step n = 0, sets the gas flow velocity U _g ^n, the gas pressure p _g ^n, the gas temperature T _g ^n, and the treated material temperature T _s ⁿ at time step n (= 0) (S102 ). In other words, the initial value of the ^{_{U g n, p g n,}} T g n, and T _s ⁿ at an initial time step (n = 0).

After setting, the gas flow rate U _g ⁿ , gas pressure p _g ⁿ , gas temperature T _g ⁿ , material temperature T _{sn to} be processed ^, and local heat transfer coefficient h (x) at a predetermined surface position x of the material to be processed Time history response analysis (unsteady heat flow analysis) is performed (S103 to S107). Specifically, simulation is performed based on a numerical analysis method using time t = t + Δt (S103) and using equations (2) and (5) to (7). As a result, the distribution of the gas flow rate U _g ^{n + 1} , the gas pressure p _g ^{n + 1} and the gas temperature T _g ^{n + 1} in the gas flow field at the time step n + 1 when Δt has elapsed from the time step n, and the material temperature to be processed The distribution of T _s ^{n + 1} is calculated (S104). Thereby, the temperature distribution in the material to be processed at time step n + 1 and the temperature distribution in the boundary layer near the surface of the material to be processed are obtained.

  Based on the temperature distribution obtained in step S104, the local heat transfer coefficient h (x) at time step n + 1 is calculated (S105).

The heat flux q (x) at the predetermined surface position x satisfies Expression (9).

Here, n (x) is a normal vector at the predetermined surface position x. The heat flux q (x) is calculated from Equation (9) using the temperature distribution data of T _s or T _g obtained in step S104. The calculated heat flux q (x) is substituted into equation (4) to determine the local heat transfer coefficient h (x) at the predetermined surface position x.

After the calculation, when the time t set in step S103 has not reached the calculation end time _tmax (NO in S106), n is incremented to n = n + 1. At this time, U _g ⁿ = U _g ^{n + 1} , p _g ⁿ = p _g ^{n + 1} , T _g ⁿ = T _g ^{n + 1} , and T _s ⁿ = T _s ^{n + 1} are set (S107). After setting, the process returns to step S103. In short, the simulation is repeated until the time t reaches the calculation end time _tmax .

  Thus, the second prior art does not use experimental data. Therefore, it is not necessary to collect experimental data every time the cooling condition is changed. Furthermore, even if the surface shape of the material to be processed is complicated, a highly accurate local heat transfer coefficient h (x) can be obtained.

However, since the second prior art performs time history response analysis, it takes a lot of time to obtain a calculation result under one cooling condition. Furthermore, when determining the local heat transfer coefficient h (x) under another cooling condition different from the previously set cooling condition (YES in S108 in FIG. 1), the process returns to step S101 and the time history response analysis is performed again. Must be implemented from the beginning. Therefore, every time cooling conditions are changed, unsteady heat flow calculation must be performed over a long time.
JP-A-7-188734 JP 2003-42984 A Heat Treatment Deformation Simulation and Cooling, Michiharu Narazaki, Heat Treatment No. 42, No. 5, 2002, 333-340

  An object of the present invention is to provide a local heat transfer coefficient determination program and a local heat transfer coefficient determination device that do not require experimental data and can determine the local heat transfer coefficient in a short time even if the cooling conditions are changed. is there.

Means for Solving the Problems and Effects of the Invention

The local heat transfer coefficient determination program according to the present invention causes a computer to determine the local heat transfer coefficient on the surface of a material to be processed in gas cooling in which gas is supplied into a heat treatment furnace to cool the material to be processed. The local heat transfer program includes a step of setting a gas flow field region in a predetermined range surrounding the material to be processed in the space in the heat treatment furnace as a calculation region, a supply gas temperature, a supply gas mass flow rate, a surface of the material to be processed A step of setting a reference cooling condition including the temperature, a step of performing a steady heat flow analysis of the calculation region by a numerical analysis method based on the reference cooling condition, and a step in the reference cooling condition based on the result of the steady heat flow analysis. A step of _obtaining a reference local heat transfer coefficient h _ref (x) at a predetermined surface position x of the workpiece, and at least one of a supply gas temperature, a supply gas mass flow rate, and a workpiece surface temperature is different from the reference cooling condition. setting a target cooling condition, after obtaining the reference local heat transfer coefficient h _ref (x), and the reference average heat transfer coefficient hm _ref determined by the reference cooling conditions, pair is determined by the target cooling conditions And average heat transfer coefficient hm, the reference local heat transfer coefficient h _ref (x), a target local heat transfer coefficient h (x) at a predetermined surface position x in the target cooling conditions, so as to satisfy the equation (1), And determining a target local heat transfer coefficient h (x).

h (x) / hm = h _ref (x) / hm _ref (1)

Preferably, the local heat transfer coefficient determination program according to the present invention further registers a plurality of gas property values including a gas viscosity coefficient, a specific heat of the gas, and a heat conductivity of the gas in a property value database in association with a plurality of temperatures. Comprising steps. The step of determining the target local heat transfer coefficient h (x) is formed on the predetermined surface position x under the target cooling condition and the reference film temperature of the turbulent boundary layer formed on the predetermined surface position x under the reference cooling condition. Determining a target film temperature of the turbulent boundary layer, obtaining a reference gas property value corresponding to the reference film temperature, and a target gas property value corresponding to the target film temperature from a property value database. The step of determining the target local heat transfer coefficient h (x) is determined based on the reference average heat transfer coefficient hm _ref determined based on the acquired reference gas physical property value and the acquired target gas physical property value. The target local heat transfer coefficient h (x) is determined so that the target average heat transfer coefficient hm satisfies the formula (1).

In gas cooling, the gas flow field becomes a fully developed turbulent flow. Therefore, even if the cooling conditions such as the gas flow rate and the gas temperature are slightly changed, the macro flow field shape is always similar. As a result, the distribution shape of the local heat transfer coefficient at the predetermined surface position of the material to be processed is also substantially constant without depending on the cooling condition. The local heat transfer coefficient determination program according to the present invention uses the point that the distribution shape of the local heat transfer coefficient is similar without depending on the cooling condition. Specifically, in gas cooling, equation (1) is established based on the similarity law. Therefore, if the reference local heat transfer coefficient h _ref (x) at the reference cooling condition is obtained by steady heat flow analysis, even if the cooling condition is changed, the target local heat transfer coefficient h (x ) Can be determined in a short time based on equation (1). That is, it is not necessary to acquire experimental data or perform a time-consuming heat flow analysis every time the cooling conditions are changed as in the prior art.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. In the drawings, the same or corresponding parts are denoted by the same reference numerals and description thereof will not be repeated.

  [Method for determining local heat transfer coefficient according to the present invention]

  First, the outline of the method for determining the local heat transfer coefficient according to the present invention will be described.

  Since the gas flow during gas cooling is high-speed, the gas flow field is considered to be a fully developed turbulent flow. In fully developed turbulence, it is known that the macro flow field shape is similar even if the gas flow rate and gas temperature are slightly changed.

  In this way, in the flow field where the macro flow field shape is similar, the distribution of the local heat transfer coefficient on the surface of the material to be processed is almost similar without depending on the change in cooling conditions such as gas flow rate, gas temperature, and surface temperature. It becomes. Hereinafter, this point will be described based on experimental results.

  Assuming that the output gear blank material for automobiles whose cross-sectional shape from the central axis to the outer peripheral surface is the shape shown in FIG. 2 is a material to be processed, heat flow analysis is performed on the calculation region shown in FIG. 3 using a computer. went. At this time, the temperature of the material to be processed was constant, and only the gas flow field region excluding the material to be processed was used as the calculation region. In addition, assuming that the gas flow field is in a steady state, a steady heat flow analysis in the calculation domain was performed.

In steady-state heat flow analysis, equations (10) to (12) in which the time differential terms of equations (5) to (7) were eliminated were used to solve equations obtained by discretizing these equations (10) to (12). .

The cooling conditions were the cooling conditions 1 to 7 shown in Table 1, and steady heat flow analysis was performed for each cooling condition.

Feed gas mass flow rate ratio in Table 1 G _in / G _in1 is the ratio of the feed gas mass flow rate G _in the respective cooling conditions for supplying gas mass flow rate G _in1 of cooling conditions 1. The supply gas flow rate ratio _{U g, in / U g,} in1 is the ratio of the feed gas flow rate U _{g, in} each cooling condition to the feed gas flow rate U _{g, in1} of cooling conditions 1. The supply gas mass flow rate G _in1 was 339 (kg / (m ² / s)), and the supply gas flow rate U _{g, in1} was 10 (m / s). Further, the treated material surface temperature _{T w} at each cooling condition, three (cooling condition 5-7) or four (cooling condition 1-4) were prepared.

A steady heat flow analysis is performed under each cooling condition in Table 1, and the local heat transfer coefficient h () of each predetermined surface position x (upper1 to 4, outside1 to 3, lower1 to 6, inside1) of the material to be treated in FIG. x) and average heat transfer coefficient hm were calculated. Specifically, the temperature distribution in the boundary layer on the predetermined surface position x is obtained based on the equations (10) to (12), and based on the equations (9) and (4) using the obtained temperature distribution. Thus, the local heat transfer coefficient h (x) was obtained. Further, the average heat transfer coefficient hm was calculated based on the obtained local heat transfer coefficient h (x). In Equation (4), the local heat transfer coefficient h (x) was obtained with T _{t, s} = T _w .

  Based on the calculated local heat transfer coefficient h (x) and the average heat transfer coefficient hm, the similarity of the local heat transfer coefficient distribution was evaluated.

  First, the similarity of the heat transfer coefficient distribution with respect to the temperature change of the material to be processed will be described. 4 shows the average heat transfer coefficient hm when the surface temperature of the material to be treated is 1123 (K), 923 (K), 723 (K), and 523 (K) under the cooling condition 1, and FIG. Ratio of local heat transfer coefficient h (x) to average heat transfer coefficient hm at each predetermined surface position x when the surface temperature is 1123 (K), 923 (K), 723 (K), 523 (K) (h (x) / hm: hereinafter referred to as dimensionless local heat transfer coefficient (-)).

  4 and 5, the average heat transfer coefficient hm changed depending on the surface temperature of the material to be treated (FIG. 4). On the other hand, the dimensionless local heat transfer coefficient at each predetermined surface position x was substantially constant without depending on the change in the surface temperature of the material to be processed (FIG. 5). That is, the distribution shape of the local heat transfer coefficient h (x) was always similar to the change in the surface temperature of the material to be treated.

Next, the similarity of the distribution shape of the local heat transfer coefficient h (x) to changes _in the supply gas temperature T _{g, in} , the supply gas mass flow rate G _in , and the supply gas flow rate U _{g, in} will be described. FIG. 6 shows the average heat transfer coefficient hm in each of the cooling conditions 1 to 7 when the surface temperature of the material to be processed is 1123K, and FIG. 7 shows each of the cooling conditions 1 to 1 when the surface temperature of the material to be processed is 1123K. 7 shows a dimensionless local heat transfer coefficient at each predetermined surface position x in FIG.

  6 and 7, the average heat transfer coefficient hm varies depending on the cooling conditions (FIG. 6), but the dimensionless local heat transfer coefficient h (x) at each predetermined surface position x is It was almost constant regardless of the cooling conditions (FIG. 7). That is, the distribution shape of the local heat transfer coefficient h (x) was always similar to the change in cooling conditions.

From the above results, the distribution shape of the local heat transfer coefficient h (x), that is, the dimensionless local heat transfer coefficient, is almost constant without depending on the cooling condition. Therefore, the average heat transfer coefficient (hereinafter referred to as the reference average heat transfer coefficient) hm _ref and the local heat transfer coefficient (hereinafter referred to as the reference local heat transfer coefficient) h _ref ( x) and the average heat transfer coefficient (hereinafter referred to as the target average heat transfer coefficient) hm and the local heat transfer coefficient (hereinafter referred to as the target local heat transfer coefficient) under the cooling conditions different from the reference cooling conditions (hereinafter referred to as the target cooling conditions). h (x) has the relationship of the following formula (1).

h _ref (x) / hm _ref = h (x) / hm (1)

In the present invention, when the cooling condition is changed, the target local heat transfer coefficient h (x) is determined based on the above equation (1). That is, in the present invention, the reference local heat transfer coefficient h _ref (x) under the reference cooling condition is obtained in advance, and when the cooling condition is changed, the reference local heat transfer coefficient h _ref (x) is used to obtain the equation The target heat transfer coefficient h (x) is calculated from (1). Thus, in the present invention, it is not necessary to collect experimental data every time the cooling condition is changed, and it is not necessary to perform a heat flow analysis by a numerical analysis method every time the cooling condition is changed.

  [Target local heat transfer coefficient conversion formula]

Hereinafter, a conversion formula for determining the target local heat transfer coefficient h (x) will be described based on the above formula (1). It is known that the approximate function of the average heat transfer coefficient hm is represented by Expression (13).

Here, Pr is the Prandtl number and Re is the Reynolds number. L is a representative dimension and corresponds to the outer diameter dimension of the material to be treated in the present embodiment. T _b is an average temperature of the turbulent boundary layer formed on the predetermined surface position x (hereinafter referred to as film temperature). μ _G (T _b ) is a gas viscosity coefficient at the film temperature T _b . C _g (T _b ) is the gas specific heat at the film temperature T _b . λ _g (T _{g, in} ) is the thermal conductivity of the gas at the supply gas temperature T _{g, in} . These gas physical properties (viscosity coefficient, specific heat, thermal conductivity) depend on temperature. Therefore, in the present embodiment, gas property values corresponding to the supply gas temperature T _{g, in} and the film temperature T _b are used.

The film temperature _Tb is defined by the following equation (14).

  Α and m in equation (13) are coefficients identified when the approximate function is created.

  Generally, since the exponent m of the Reynolds number Re in the turbulent flow field is about 0.8, m = 0.8 may also be used in this embodiment. Alternatively, steady heat flow analysis may be performed in advance under a plurality of cooling conditions, and α and m may be obtained using the results. 8 and 9 show the average heat transfer coefficient hm (points in the figure) obtained as a result of the steady heat flow analysis under the cooling conditions 1 to 7, and the approximate function (solid line) of the equation (13). FIG. In FIG. 8, α in Equation (13) is 0.0286, m is 0.8478, FIG. 9 is α in Equation (13) = 0.0592, and m = 0.8. It can be said that any approximation function has high accuracy of approximation.

Based on the equation (13), the average heat transfer coefficient hm _ref under the reference cooling condition is expressed by the following equation (15).

Here, T _{g, in, ref} is the reference supply gas temperature. G _{in, ref} is the reference feed gas mass flow rate. T _{b, ref} is a reference film temperature under the reference cooling condition, and is expressed by the following equation (16) based on the equation (14).

Here, T _{w, ref} is the reference material surface temperature.

The determination formula of the local heat transfer coefficient h (x) under the target cooling condition in which at least one of the supply gas temperature, the supply gas mass flow rate, and the surface temperature of the material to be processed is different from the reference cooling condition is the expression (1), the expression (13) ) To Expression (16), the following Expression (17) is obtained.

From the above, if the local heat transfer coefficient h _ref (x) in the reference cooling condition is calculated by steady heat flow analysis, the local heat transfer coefficient h (x) in the target cooling condition different from the reference cooling condition is expressed by the equation (1). ) Can be easily determined by equation (17) derived from

  Hereinafter, the local heat transfer coefficient determination device according to the present embodiment will be described.

  [overall structure]

  Referring to FIG. 10, the local heat transfer coefficient determination device 1 according to the present embodiment includes a storage unit 10, a cooling condition setting unit 11, a calculation region setting unit 12, a steady heat flow analysis unit 13, and a reference. A local heat transfer coefficient calculating unit 14 and a target local heat transfer coefficient determining unit 15 are provided.

  The storage unit 10 stores a physical property value database 16 shown in FIG. In the physical property value database 16, gas physical property values are registered in correspondence with temperatures. The physical property value database 16 includes a field for registering a temperature, a field for registering the viscosity coefficient of the supply gas used for gas cooling, a field for registering the specific heat of the gas, and the thermal conductivity of the gas. And a field for registration. These gas property values are used when determining the target local heat transfer coefficient h (x).

The cooling condition setting unit 11 sets a reference cooling condition and a target cooling condition according to a user operation. As described above, the reference cooling condition is a cooling condition set when calculating the reference local heat transfer coefficient h _ref (x). The reference supply gas mass flow rate G _{in, ref} , the reference supply gas temperature T _{g, in, ref} and the reference material surface temperature _{Tw, ref} . The target cooling condition is a cooling condition set when determining the target local heat transfer coefficient, and includes a supply gas mass flow rate G _in , a supply gas temperature T _{g, in,} and a surface temperature T _{w of the} workpiece.

  The calculation area setting unit 12 sets a calculation area for performing steady heat flow analysis. Specifically, based on information such as the dimensions of the gas flow field region, the shape dimensions of the material to be processed, and the arrangement position of the material to be processed in the gas flow field region, which are input according to the user operation, the calculation region is determined. Set.

  Based on the input information, the calculation region setting unit 12 sets a gas flow field region in a predetermined range surrounding the material to be processed among the regions in the heat treatment furnace as the calculation region. That is, only the gas flow field region in a predetermined range excluding the material to be processed is set as the calculation region. The calculation area setting unit 12 further divides the calculation area into a plurality of minute areas.

The steady heat flow analysis unit 13 performs steady heat flow analysis on the reference cooling condition for the divided calculation region. Specifically, based on the reference cooling conditions, construed determined by discretizing the equation (10) to (12), to calculate the gas temperature T _g of each grid point (microscopic area). Thereby, the gas temperature distribution in the turbulent boundary layer in the vicinity of the surface of the material to be processed under the reference cooling condition is obtained.

The reference local heat transfer coefficient calculation unit 14 calculates a reference local heat transfer coefficient h _ref (x) from Expression (9) and Expression (4) based on the result obtained by steady heat flow analysis.

When the target cooling condition is set, the target local heat transfer coefficient determining unit 15 uses the calculated reference local heat transfer coefficient h _ref (x) to satisfy the target local heat transfer coefficient h ( x).

  FIG. 12 is a block diagram illustrating a hardware configuration of the computer apparatus 20. The computer device 20 includes a hard disk drive (HDD) 21, a memory 23, a CPU 24, a display 25, and an input unit 26. The HDD 21 stores a local heat transfer coefficient determination program 22. The HDD 21 further stores a physical property value database 16. The computer device 20 functions as the local heat transfer coefficient determination device 1 by loading the local heat transfer coefficient determination program 22 into the memory 23 and causing the CPU 24 to execute it. At this time, the storage unit 10 corresponds to the HDD 21 and the memory 23. The cooling condition setting unit 11, the calculation region setting unit 12, the steady heat flow analysis unit 13, the reference local heat transfer coefficient calculation unit 14, and the target local heat transfer coefficient determination unit 15 correspond to the CPU 24. Information necessary for setting the reference cooling condition, the target cooling condition, and the calculation region is input by the input unit 26 based on a user operation. The determined target heat transfer coefficient h (x) is displayed on the display 25.

  [Operation flow]

  Next, the process for determining the target local heat transfer coefficient h (x) by the local heat transfer coefficient determining apparatus 1 (hereinafter simply referred to as the determining apparatus 1) will be described.

  With reference to FIG. 13, the determination apparatus 1 first sets a calculation area (S1). Specifically, the determination apparatus 1 determines the material to be processed based on information such as the size of the material to be processed, the size of the gas flow field region, and the arrangement position of the material to be processed, which is input by the user using the input unit 26. A gas flow field region within a predetermined range surrounding the is set as a calculation region. After setting the calculation area, the determination apparatus 1 divides the calculation area into a plurality of minute areas based on the grid point number data input by the input unit 26.

Subsequently, the determining apparatus 1 calculates a reference local heat transfer coefficient h _ref (x) (reference heat transfer coefficient calculation process: S2). In the reference heat transfer coefficient calculation process, first, supply gas temperature Tg _{, in, ref} , supply gas mass flow rate _{Gin, ref,} and workpiece surface temperature _{Tw, ref} are set as reference cooling conditions (S21). The reference cooling condition is input by the input unit 26 based on a user operation.

After the reference cooling condition is set, the determination apparatus 1 performs steady heat flow analysis by a numerical analysis method on the calculation region based on the reference cooling condition (S22). At this time, the determination apparatus 1 assumes that the surface temperature of the material to be processed is uniform at T _{w, ref} and performs steady-state heat flow analysis of only the gas flow field. Specifically, an equation obtained by discretizing Equations (10) to (12) is obtained, and a gas flow rate U _g , a gas pressure P _g , and a gas temperature T _g in each minute region are calculated. The calculated gas flow rate U _g , gas pressure P _g, and gas temperature T _g of each micro region are stored in the storage unit 10 in association with the identification data of each micro region.

After the analysis, the reference heat transfer coefficient h _ref (x) at the predetermined surface position x of the material to be processed is calculated using the gas temperature T _g stored in the storage unit 10 (S23). Determining apparatus 1 first out of the distribution of the obtained gas temperature T _g in the step S22, it reads out the gas temperature T _g of the respective minute regions constituting a turbulent boundary layer on a predetermined surface position x from the storage unit 10. Determining apparatus 1 uses the read gas temperature T _g, and calculates the heat flux q (x) at a predetermined surface position x based on the equation (9). The determination apparatus 1 calculates the reference local heat transfer coefficient h _ref (x) based on the equation (4) using the calculated heat flux q (x). At this time, the supply gas temperature T _{g, in, ref in the} reference cooling condition is substituted for Tf in the equation (4), and the surface temperature T _{w of the} material to be treated is substituted for T _{t, s} in the equation (4). Substitute _ref . The calculated reference local heat transfer coefficient h _ref (x) is stored in the storage unit 10.

The determination device 1 further calculates the reference film temperature T _{b, ref} based on the equation (16) using the supply gas temperature T _{g, in, ref} and stores it in the storage unit 10 (S24). The reference film temperature T _{b, ref} is used for calculating the target local heat transfer coefficient h (x).

With the above operation, the determination device 1 determines the reference local heat transfer coefficient h _ref (x) in the reference cooling condition. When the cooling condition is changed from the reference cooling condition to the target cooling condition after calculating the reference local heat transfer coefficient h _ref (x), the determination device 1 executes a target local heat conductivity determination process (S3).

In the target local thermal conductivity determination process, the determination device 1 first sets a target cooling condition (S31). The target supply gas temperature T _{g, in} , the target supply gas mass flow rate G _in , and the target workpiece surface temperature T _w are input by the input unit 26 in accordance with a user operation, and target cooling conditions are set.

After setting the target cooling condition, the determination apparatus 1 calculates a film temperature (target film temperature) T _b under the target cooling condition based on the set target cooling condition (S32). Determining apparatus 1, the subject the supply gas temperature T _g, with _in and subject workpiece surface temperature T _w, and calculates the target film temperature T _b by equation (14). The calculated target film temperature T _b is stored in the storage unit 10.

Subsequently, the determining apparatus 1 reads out the reference gas property value corresponding to the reference film temperature T _{b, ref} and the target gas property value corresponding to the target film temperature T _b from the property value database 16 (S33). The determination device 1 refers to the temperature field in the physical property value database 16, and includes the viscosity coefficient μ _g (T _{b, ref} ) and gas specific heat Cg (T) included in the same record as the temperature corresponding to the reference film temperature T _{b, ref. b, ref} ) and thermal conductivity λ (T _{b, ref} ) are read out. The determination apparatus 1 also reads out the thermal conductivity λ (T _{g, in, ref} ) corresponding to the reference gas temperature T _{g, in, ref} from the physical property value database 16. The determination apparatus 1 further corresponds to μ _g (T _b ), C _g (T _b ) and λ (T _b ) corresponding to the target film temperature T _b and the target gas temperature T _{g, in} from the physical property value database 16. Read λ (T _{g, in} ).

After reading the physical property values, the determining apparatus 1 calculates the target local heat transfer coefficient h (x) so as to satisfy the expression (1) (S34). Specifically, the determination device 1 reads the reference local heat transfer coefficient h _ref (x) stored in the storage unit 10, and the physical property value read in step S33 and the reference heat transfer coefficient h _ref (x). And the target local heat transfer coefficient h (x) is determined by the equation (17). The value of the index m in Expression (17) is stored in the storage unit 10 in advance. The exponent m value may be 0.8, which is a general value in turbulent flow, and as shown in FIG. 8, the exponent m value (for example, the approximate function obtained based on the result of the steady heat flow analysis in advance, for example, m = 0.8478) may be used. The calculated target local heat transfer coefficient h (x) is stored in the storage unit 10 and displayed on the display 25.

When the user obtains the target local heat transfer coefficient h (x) under another target cooling condition different from the previous target cooling condition (YES in S4), the determination device 1 executes the operation of step S3 again. That is, it is not necessary to execute the steady heat flow analysis in step S2 again, and the time required for the steady heat flow analysis can be omitted. The determination apparatus 1 uses the reference heat transfer coefficient h _ref (x) already registered in the storage unit 10 and the physical property value in the physical property value database 16 to determine the target heat transfer coefficient h (x) by the operation of step S3. It can be determined in a short time (S3).

As described above, the determination device 1 according to the present embodiment uses the fact that the equation (1) is established in the flow field in the gas furnace, and thus the target heat transfer using the reference local heat transfer coefficient h _ref (x). The rate h (x) can be calculated in a short time. Therefore, the determination device 1 does not need to perform a heat flow analysis or acquire experimental data every time the cooling condition is changed as in the prior art, and obtains the target local heat transfer coefficient h (x). Can be greatly shortened.

  The physical property value database 16 described above may be created for each gas composition. In that case, the cooling condition setting unit 11 sets the gas composition in addition to the cooling conditions. The target local heat transfer coefficient determining unit 15 reads a predetermined gas property value from the property value database of the corresponding gas composition.

In the above embodiment, the reference average heat transfer coefficient hm _ref is specified by the physical property value read from the physical property value database, and the target local heat transfer coefficient h (x) is obtained using the equation (17). The reference average heat transfer coefficient hm _ref may be specified by another method, and the target local heat transfer coefficient h (x) may be obtained based on Expression (1). For example, the average heat transfer coefficient hm _ref may be calculated based on the result analyzed by the steady heat flow analyzing unit 13 and used for calculating the target local heat transfer coefficient h (x).

Moreover, although the film temperature _Tb is defined by the equation (14), another defining equation may be used.

  For the calculation region shown in FIG. 3, the local heat transfer coefficient h (x) is calculated by the determination apparatus 1 (example of the present invention) in the present embodiment and the conventional technique 2 (comparative example). The calculation times were compared.

  [Calculation time of heat transfer coefficient]

  First, the calculation time of the local heat transfer coefficient was measured in the inventive example and the comparative example. As shown in FIG. 14, two types of grid points (number of minute regions) used for analysis were prepared. However, in the example of the present invention, since the steady heat flow analysis was performed using only the gas flow field as a calculation region, the grid inside the material to be processed was not used.

The gas composition is nitrogen, the reference supply gas temperature is 298 (K), the supply gas mass flow rate is 339 (kg / m ² / s), the reference workpiece surface temperature is 1123 (K), and the reference cooling conditions are used. The heat transfer rate was calculated. For the conventional example, the cooling condition at the start of cooling was set as the above-mentioned reference cooling condition, the time step width Δt was set to 0.01 seconds, an unsteady heat flow analysis was performed for 50 seconds after the start of cooling, and the local heat transfer coefficient was calculated. In the example of the present invention, steady heat flow analysis was performed to calculate the reference local heat transfer coefficient. The finite volume method was used as a numerical analysis method for both the inventive example and the comparative example.

Table 2 shows the measurement results of the calculation time.

Referring to Table 2, in the example of the present invention, the calculation time could be shortened to 1/100 or less of the conventional one regardless of the number of grid points. Table 3 shows the reference local heat transfer coefficient at each predetermined surface position x obtained by the analysis according to the example of the present invention.

  [Calculation of temperature of material to be treated]

  Using the local heat transfer coefficient obtained in the above-described experiment, the temperature of the material to be treated was calculated in the present invention example and the comparative example, and the calculation results of both were compared.

As shown in Table 4, with respect to the cooling conditions C1 to C3, temperature transitions at predetermined positions L1 to L4 immediately below the surface of the material to be processed shown in FIG. 15 were calculated.

  In the comparative example, similarly to the above-described experiment, a simulation was performed for 50 seconds after the start of cooling with the time step width Δt being 0.01 seconds for each of the cooling conditions C1 to C3.

In the example of the present invention, using the reference local heat transfer coefficient h _ref (x) in Table 3, step S3 in FIG. 13 is executed based on the change in the cooling condition and the surface temperature of the material to be processed, and the local heat transfer coefficient h (x) (x = surface position immediately above L1 to L4) was determined. A heat conduction analysis was performed using the obtained local heat transfer coefficient h (x), and temperature transitions at positions L1 to L4 in 50 seconds from the start of cooling were calculated.

  The calculation results are shown in FIGS. 16 shows the calculation result under the cooling condition C1, FIG. 17 shows the calculation result under the cooling condition C2, and FIG. 18 shows the calculation result under the cooling condition C3. Each marker (point) in the figure indicates the calculation result according to the present invention. “◯” indicates the temperature at L1, “Δ” indicates the temperature at L2, “□” indicates the temperature at L3, and “◇” indicates the temperature at L4. On the other hand, the curve in the figure shows the calculation result obtained by the comparative example. In the middle curve, the thin solid line indicates the temperature at L1, the dotted line indicates the temperature at L2, the alternate long and short dash line indicates the temperature at L3, and the thick solid line indicates the temperature at L4.

  Referring to FIGS. 16 to 18, the calculation result of the present invention example was equivalent to the calculation result of the comparative example under any cooling condition. Moreover, the calculation time of this experiment was 1/10 or less of the calculation time of a comparative example. The inventive example can shorten the calculation time compared with the comparative example, and the calculation result shows the same accuracy as the comparative example.

  While the embodiments of the present invention have been described above, the above-described embodiments are merely examples for carrying out the present invention. Therefore, the present invention is not limited to the above-described embodiment, and can be implemented by appropriately modifying the above-described embodiment without departing from the spirit thereof.

It is a flowchart which shows the determination process of the local heat transfer coefficient by unsteady heat flow analysis. It is sectional drawing from the center axis | shaft of a to-be-processed material shape used for the steady heat flow analysis to an outer peripheral surface. It is a figure which shows the calculation area | region containing the to-be-processed material shown in FIG. It is a figure which shows the relationship between an average heat transfer rate and the to-be-processed material surface temperature obtained by steady-state heat-flow analysis with respect to the calculation area | region shown in FIG. It is a figure which shows the relationship between each temperature of a to-be-processed material, and the dimensionless local heat transfer coefficient in each predetermined surface position of a to-be-processed material. It is a figure which shows the relationship between an average heat transfer rate and cooling conditions obtained by steady-state heat flow analysis with respect to the calculation area | region shown in FIG. It is a figure which shows the relationship between each cooling condition and the dimensionless local heat transfer coefficient in each predetermined surface position of a to-be-processed material. It is a figure which shows the correlation with the approximate function of an average heat transfer coefficient, and the steady heat flow analysis result. It is a figure which shows the correlation with the approximate function of another average heat transfer coefficient different from FIG. 8, and a steady heat flow analysis result. It is a functional block diagram which shows the function structure of the local heat transfer coefficient determination apparatus in this Embodiment. It is a figure which shows the data structure of the physical property value database in FIG. It is a functional block diagram which shows the hardware constitutions of a computer apparatus. It is a flowchart which shows operation | movement of the local heat transfer coefficient determination apparatus shown in FIG. It is a figure which shows the calculation area | region used in the Example. It is a figure which shows the extraction position of the temperature transition of the to-be-processed material used in the Example. It is a figure which shows the temperature transition of the to-be-processed material surface of this invention example and a comparative example. It is a figure which shows the temperature transition of the to-be-processed material surface of the example of this invention and a comparative example on the cooling conditions different from FIG. It is a figure which shows the temperature transition of the to-be-processed material surface of the example of this invention and a comparative example on the cooling conditions different from FIG.16 and FIG.17.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Local heat transfer coefficient determination apparatus 11 Cooling condition setting part 12 Calculation area | region setting part 13 Steady heat flow analysis part 14 Reference | standard local heat transfer coefficient calculation part 15 Target local heat transfer coefficient determination part 16 Physical property value database 22 Local heat transfer coefficient determination program

Claims (2)

A local heat transfer coefficient determination program for determining a local heat transfer coefficient of the surface of the material to be processed in gas cooling for supplying gas into the heat treatment furnace to cool the material to be processed,
Of the region in the heat treatment furnace, setting a gas flow field region of a predetermined range surrounding the material to be processed as a calculation region;
Setting a reference cooling condition including a supply gas temperature, a supply gas mass flow rate, and a material surface temperature;
Based on the reference cooling condition, performing a steady heat flow analysis of the calculation region by a numerical analysis method;
Obtaining a reference local heat transfer coefficient h _ref (x) at a predetermined surface position x of the material to be processed under the reference cooling condition based on the result of the steady heat flow analysis;
Setting a target cooling condition in which at least one of the supply gas temperature, the supply gas mass flow rate, and the material surface temperature to be processed is different from the reference cooling condition;
After obtaining the reference local heat transfer coefficient h _ref (x), the reference average heat transfer coefficient hm _ref determined by the reference cooling condition, the target average heat transfer coefficient hm determined by the target cooling condition, The target local heat transfer coefficient h _ref (x) and the target local heat transfer coefficient h (x) at the predetermined surface position x under the target cooling condition satisfy the expression (1). A local heat transfer coefficient determination program for causing a computer to execute the step of determining the rate h (x).
h (x) / hm = h _ref (x) / hm _ref (1) A local heat transfer coefficient determining device for determining a local heat transfer coefficient of the surface of the material to be processed in gas cooling for supplying a gas into the heat treatment furnace to cool the material to be processed,
A calculation region setting means for setting a gas flow field region of a predetermined range surrounding the material to be processed as a calculation region among the regions in the heat treatment furnace,
Reference cooling conditions including supply gas temperature, supply gas mass flow rate, and material surface temperature to be processed, and at least one of the supply gas temperature, supply gas mass flow rate, and material surface temperature to be processed is different from the reference cooling conditions Cooling condition setting means for setting cooling conditions;
Based on the reference cooling conditions, steady heat flow analysis means for performing steady heat flow analysis of the calculation region by a numerical analysis method,
Based on the analysis result of the steady heat flow analyzing means, a reference local heat transfer coefficient determining means for obtaining a reference local heat transfer coefficient h _ref (x) at a predetermined surface position x of the material to be processed under the reference cooling condition;
After obtaining the reference local heat transfer coefficient h _ref (x), the reference average heat transfer coefficient hm _ref determined by the reference cooling condition, the target average heat transfer coefficient hm determined by the target cooling condition, The target local heat transfer coefficient h _ref (x) and the target local heat transfer coefficient h (x) at the predetermined surface position x under the target cooling condition satisfy the expression (1). A local heat transfer coefficient determining device, comprising: a target local heat transfer coefficient determining means for determining the rate h (x).
h (x) / hm = h _ref (x) / hm _ref (1)

Images