Calculation method for external flow convective heat transfer of fluid with low Prandtt number

Abstract

The invention belongs to the field of numerical heat transfer calculation, and particularly relates to a low-Prandtt-number fluid external flow convective heat transfer calculation method, which introduces a neural network to calculate the turbulent heat flux of a low-Prandtt-number fluid, and can utilize different turbulent models to calculate the turbulent heat flux of the low-Prandtt-number fluid on the basis of an open source computational fluid mechanics program OpenFOAM. And in combination with a neural network turbulence heat flux model, the heat transfer calculation precision of the low-Prandtt-number fluid is improved.

Description

Technical Field

[0001] The present invention belongs to the field of numerical heat transfer calculation, and particularly relates to a calculation method for convective heat transfer of external flow of low Prandtl number fluids. Background Technique

[0002] During the flow process, a fluid can exchange heat with its surroundings, and the heat transfer law is related to the Prandtl number of its physical properties. The Prandtl number (Pr) is defined as: Pr = ν / α, where ν is the kinematic viscosity; α is the thermal diffusivity; Pr represents the relative magnitude of momentum diffusion and thermal diffusion capabilities.

[0003] The commonly used three-dimensional numerical simulation of fluid heat transfer in engineering adopts the Reynolds-Averaged Navier-Stokes (RANS) / Unsteady Reynolds-Averaged Navier-Stokes (URANS) method. When using this type of method to solve the temperature field in the energy equation, there are high-order terms in the equation that cannot be calculated by the time-averaged field: turbulent heat flux, and a turbulent heat flux model is required to close it.

[0004] The heat transfer law of low Prandtl number fluids is special, with a significant difference between the flow boundary layer and the temperature boundary layer, and the heat transfer and momentum transfer are no longer similar. Therefore, when conducting three-dimensional numerical calculation and analysis of its heat transfer law, the Reynolds analogy theory cannot be applied, and the relevant calculation methods of the velocity field cannot be directly used.

[0005] Among the existing turbulent heat flux closure models, few are applicable to low Prandtl number fluids; most of the few models modified based on low Prandtl numbers are based on internal flow heat transfer conditions such as channel flow and Rayleigh-Bénard convection, and their calculation accuracy is poor in complex conditions, especially in external flow heat transfer cases. Summary of the Invention

[0006] In order to solve the problem of poor calculation method accuracy of the existing turbulent heat flux closure model in complex conditions, the present invention discloses a calculation method for heat transfer of external flow of low Prandtl number fluids based on a neural network turbulent heat flux model, which improves the calculation accuracy of heat transfer of low Prandtl number fluids.

[0007] The technical solution of the present invention is as follows:

[0008] A calculation method for convective heat transfer of external flow of low Prandtl number fluids, the calculation method comprising the following steps:

[0009] Step 1: In OpenFOAM, based on the built-in URANS solver, establish a user-defined URANS transient incompressible single-phase forced convection heat transfer solver, and read the physical property parameters and the solution control function;

[0010] Step 2: Establish a variable field in the user-defined URANS transient incompressible single-phase forced convection heat transfer solver established in Step 1;

[0011] Step 3: Use the PIMPLE algorithm built into OpenFOAM to solve the continuity equation, momentum equation, and turbulence model equation at the new time step until the variable field reaches the set iterative convergence condition;

[0012] Step 4: Calculate the turbulent heat flux on each grid. For each grid, determine whether the turbulent kinetic energy <k>10 -3 and the original features If so, calculate the Prandtl number Pr through an empirical formula, and then calculate the turbulent heat flux; otherwise, use a neural network to calculate the turbulent heat flux on each grid to obtain the turbulent heat flux field;

[0013] Step 5: Discretize the turbulent heat flux field;

[0014] Step 6: Solve the energy equation until the residual is lower than the set convergence threshold;

[0015] Step 7: Repeat Steps 4 to 6;

[0016] Step 8: Determine whether the time has ended. If not, return to Step 2. If so, end the calculation and save the results.

[0017] Furthermore, the physical property parameters include the kinematic viscosity ν and the Prandtl number Pr.

[0018] Furthermore, the variable field includes, but is not limited to, temperature <t>, Pressure , speed , Turbulent kinetic energy <k>and the turbulent kinetic energy dissipation rate <ε>.

[0019] Furthermore, in step 4, the turbulent Prandtl number Pr is calculated through an empirical formula t , and then the turbulent heat flux is calculated, specifically as follows:

[0020]

[0021] In the formula, Re is the Reynolds number and Pr is the Prandtl number;

[0022] The calculation formula of the turbulent heat flux is as follows:

[0023]

[0024] where T represents temperature; α represents thermal diffusivity; '' represents fluctuating quantity; i represents the component along the coordinate axis; u is the velocity vector; < > represents ensemble average; Pr t represents the turbulent Prandtl number; v t represents the eddy viscosity coefficient.

[0025] Furthermore, in step 4, the turbulent heat flux on each grid is calculated by using a neural network to obtain a turbulent heat flux field, which specifically includes the following steps:

[0026] Step 4.1: Read the structure of the neural network, including weights, bias parameters, and activation functions;

[0027] Step 4.2: Read or calculate the original input feature field, including: turbulent kinetic energy <k>, turbulent kinetic energy dissipation rate <ε>, strain rate tensor <s>, rotation tensor <r>, temperature gradient turbulent kinetic energy gradient modified local Reynolds number Re based on the wall distance d , Prandtl number Pr;

[0028] Among them, the calculation methods of S and R are as follows: The superscript "T" represents transpose;

[0029] Step 4.3: Nondimensionalize each of the original input feature fields (except Red and Pr) obtained in Step 4.2 with different nondimensionalization factors:

[0030]

[0031] Among them: q represents the original input feature, represents the input feature after nondimensionalization, q * represents the nondimensionalization factor, || || represents the L2 norm of a vector or scalar; ||<S)|| and || <r>The calculation method of || is as follows: where tr() represents the trace of the tensor;

[0032] Step 4.4: From the dimensionless original features Re d and Pr, 30 invariants are calculated. The calculation methods of the first 26 invariants λ1 to λ 26 are as follows:

[0033]

[0034]

[0035] The last four invariants are respectively Re d and ln(Pr);

[0036] Step 4.5: According to the neural network operation rules, using the 30 invariants calculated in Step 4.4 as the input of the neural network, calculate the coefficients g1 to g 12 ;

[0037] Step 4.6: Calculate 12 form invariants to Specifically as follows:

[0038]

[0039]

[0040] Step 4.7: Calculate the linear term of the turbulent heat flux <-u'T'> || :

[0041]

[0042] Step 4.8: Calculate the non - linear term of the turbulent heat flux

[0043]

[0044] Furthermore, Step 5 is specifically: For each grid, judge whether it satisfies <k>10 -3 and If so, implicitly discretize the turbulent heat flux at that location; otherwise, the linear term of the turbulent heat flux < -u'T' > || Using implicit discretization, the non - linear term of the turbulent heat flux Use explicit discretization.

[0045] Furthermore, in step 6, the energy equation is:

[0046]

[0047] where, T is temperature; t is time; α represents thermal diffusivity; 'represents pulsation; represents the gradient operator; u is the velocity vector; < > represents the ensemble average.

[0048] Compared with the prior art, the present invention has the following beneficial effects:

[0049] (1) The present invention introduces a neural network to calculate the turbulent heat flux of low - Prandtl - number fluids. Based on the open - source computational fluid dynamics program OpenFOAM, different turbulence models can be utilized, and combined with the neural network turbulent heat flux model, to improve the heat transfer calculation accuracy of low - Prandtl - number fluids.

[0050] (2) In the present invention, for relatively high turbulent pulsation intensity and temperature gradient (i.e., <k>>10 -3 and ) position, a neural network turbulent heat flux calculation model with higher calculation accuracy developed for the external flow heat transfer condition of low Prandtl number fluids is introduced to obtain more accurate turbulent heat flux, thereby better improving the calculation accuracy of convective heat transfer of low Prandtl number fluids.

[0051] (3) For the case where the turbulent pulsation intensity and temperature gradient are small (i.e., <k>≤10 -3 or ) position, Pr with higher theoretical accuracy is introduced t calculation formula, so as to obtain more accurate turbulent heat flux, thereby better improving the calculation accuracy of the external convective heat transfer of low Prandtl number fluids.

[0052] (4) Split the turbulent heat flux into the sum of a linear term and a non-linear term; when calculating the divergence of the turbulent heat flux, the implicit discretization is used for the linear term and the explicit discretization is used for the non-linear term. The coefficient g2 of the linear term is forced to be non-negative, ensuring that the coefficient before the linear diffusion term is non-negative and increasing the stability of the calculation method.

[0053] (5) Based on the open-source platform, different turbulent models can be called according to the needs of specific calculation and analysis conditions, improving the calculation accuracy of the velocity field, pressure field and turbulent variables, and further improving the calculation accuracy of the temperature field. Brief Description of the Drawings

[0054] Figure 1 is the calculation flow chart of the method of the present invention;

[0055] Figure 2 is the comparison chart of the heat transfer calculation results between the calculation method of the present invention and the traditional calculation method. Detailed Embodiments

[0056] The present invention will be described in detail below with reference to the drawings and specific embodiments.

[0057] See Figure 1 , a calculation method for external flow convective heat transfer of low Prandtl number fluids, the calculation method comprising the following steps:

[0058] Step 1: In OpenFOAM, based on the built-in URANS solver, establish a user-defined URANS transient incompressible single-phase forced convective heat transfer solver, and read the physical property parameters and the solution control function;

[0059] Step 2: In the user-defined URANS transient incompressible single-phase forced convective heat transfer solver established in Step 1, establish a variable field;

[0060] Step 3: Use the PIMPLE algorithm built in OpenFOAM to solve the continuity equation, momentum equation and turbulent model equation at the new time until the variable field reaches the set iteration convergence condition;

[0061] Step 4: Calculate the turbulent heat flux on each grid, and for each grid, judge whether the turbulent kinetic energy is satisfied <k>10 -3 and the original features If so, calculate the Prandtl number Pr through an empirical formula and then calculate the turbulent heat flux; otherwise, use a neural network to calculate the turbulent heat flux on each grid to obtain the turbulent heat flux field;

[0062] Step 5: Discretize the turbulent heat flux field;

[0063] Step 6: Solve the energy equation until the residual is lower than the set convergence threshold;

[0064] Step 7: Repeat Steps 4 to 6;

[0065] Step 8: Determine whether the time is over. If not, go back to Step 2. If so, end the calculation and save the results.

[0066] Among them, the physical property parameters include the kinematic viscosity ν and the Prandtl number Pr;

[0067] The variable field includes but is not limited to temperature <t>, pressure< / t> < / k> < / k> < / k> < / k> < / r> < / r> < / s> < / k> < / k> <s>, speed , Turbulent kinetic energy <k>and the turbulent kinetic energy dissipation rate <ε>.

[0068] In another embodiment of the present invention, in step 4, the turbulent Prandtl number Pr is calculated through an empirical formula t , and then the turbulent heat flux is calculated, specifically as follows:

[0069]

[0070] In the formula, Re is the Reynolds number;

[0071] The calculation formula of the turbulent heat flux is as follows:

[0072]

[0073] Among them, T represents temperature; α represents thermal diffusivity;'' represents the pulsation quantity; i represents the component along the coordinate axis; u is the velocity vector; < > represents the ensemble average; Pr t represents the turbulent Prandtl number; v t represents the eddy viscosity coefficient.

[0074] In one embodiment of the present invention, in step 4, the turbulent heat flux on each grid is calculated by using a neural network to obtain a turbulent heat flux field, which specifically includes the following steps:

[0075] Step 4.1: Read the structure of the neural network, including weights, bias parameters, and activation functions;

[0076] Step 4.2: Read or calculate the original input feature field, including: turbulent kinetic energy <k>, turbulent kinetic energy dissipation rate <ε>, strain rate tensor <s>, rotation tensor <r>, temperature gradient turbulent kinetic energy gradient modified local Reynolds number Re based on the wall distance d , Prandtl number Pr;

[0077] Among them, the calculation methods of S and R are as follows: The superscript "T" represents transpose;

[0078] Step 4.3: Nondimensionalize each of the original input feature fields (except Red and Pr) obtained in Step 4.2 with different nondimensionalization factors:

[0079]

[0080] Among them: q represents the original input feature, represents the input feature after nondimensionalization, q * represents the nondimensionalization factor, |||| represents the L2 norm of a vector or scalar;

[0081] ||<S)|| and || <r>The calculation method of || is as follows: Among them, tr() represents the trace of the tensor.

[0082] The original input features of the neural network and the dimensionless factors are shown in Table 1 below:

[0083]

[0084] Step 4.4: From the dimensionless original features Re d and Pr, 30 invariants are calculated. The calculation methods of the first 26 invariants λ1 to λ 26 are shown in Table 2 below, and the last four invariants are respectively Re d and ln(Pr);

[0085] Table 2

[0086]

[0087] Step 4.5: According to the neural network operation rules, using the 30 invariants calculated in Step 4.4 as the input of the neural network, calculate the coefficients g1 to g 12 ;

[0088] Step 4.6: Calculate 12 form invariants to Specifically as shown in Table 3 below:

[0089] Table 3

[0090]

[0091] Step 4.7: Calculate the linear term of the turbulent heat flux <-u'T'> || :

[0092]

[0093] Step 4.8: Calculate the non-linear term of the turbulent heat flux

[0094]

[0095] In an embodiment of the present invention, Step 5 is specifically: for each grid, determine whether it satisfies <k>10 -3 and If so, perform implicit discretization on the turbulent heat flux at that location; otherwise, for the linear term of the turbulent heat flux < -u′T′ > || Adopt implicit discretization for the non - linear term of the turbulent heat flux Adopt explicit discretization

[0096] In an embodiment of the present invention, in step 6, the energy equation is as follows:

[0097]

[0098] where T is temperature; t is time; the superscript ′ represents the pulsation quantity; represents the gradient operator; u is the velocity vector; < > represents the ensemble average.

[0099] After the final physical quantities reach the set iterative convergence conditions, a calculation method for external - flow convective heat transfer applicable to low - Prandtl - number fluids based on the neural - network turbulent heat flux model can be obtained. This method overcomes the limitations of the Reynolds analogy, combines the neural network with the calculation of the turbulent heat flux of low - Prandtl - number fluids, provides a high - precision calculation method for studying the external - flow heat - transfer characteristics of low - Prandtl - number fluids, and belongs to the secondary development and application of combining the neural network with the turbulent heat flux model of low - Prandtl - number fluids on the open - source computational fluid dynamics program OpenFOAM platform.

[0100] The following is a specific application scenario of the present invention:

[0101] For the neural - network turbulent heat flux model proposed by the present invention, when the liquid lead - bismuth flows over the tube bundle of the steam generator of the nuclear reactor, the calculation accuracy of the temperature field is significantly improved. Taking the error between the numerical simulation and the experimental value as an index, the method proposed in this paper improves the calculation accuracy of the Nusselt number of heat transfer on the tube - bundle surface by 15% - 27% compared with the simple gradient diffusion model (SGDH method) under different working conditions (different Peclet numbers), as shown in Figure 2 .

[0102] The above are only the embodiments of the present invention, and do not limit the patent scope of the present invention accordingly. Any equivalent structural or equivalent process transformation made by using the content of the specification and drawings of the present invention, or directly or indirectly applied in other related technical fields, shall be equally included in the patent protection scope of the present invention.< / k> < / r> < / r> < / s> < / k> < / k> < / s> < / t> < / k>

Claims

1. A calculation method for convective heat transfer of external flow of a low Prandtl number fluid, characterized in that, The calculation method includes the following steps: Step 1: In OpenFOAM, based on the built-in URANS solver, establish a user-defined URANS transient incompressible single-phase forced convection heat transfer solver, and read the physical property parameters and solution control functions; Step 2: In the user-defined URANS transient incompressible single-phase forced convection heat transfer solver established in Step 1, establish a variable field; Step 3: Use the PIMPLE algorithm built in OpenFOAM to solve the continuity equation, momentum equation and turbulence model equation at the new time until the variable field reaches the set iterative convergence condition; Step 4: Calculate the turbulent heat flux on each grid. For each grid, determine whether the turbulent kinetic energy is satisfied <k>10 -3 and the original features If so, calculate the Prandtl number Pr through the empirical formula and then calculate the turbulent heat flux;< / k> Otherwise, use a neural network to calculate the turbulent heat flux on each grid to obtain the turbulent heat flux field; Step 5: Discretize the turbulent heat flux field; Step 6: Solve the energy equation until the residual is lower than the set convergence threshold; Step 7: Repeat Steps 4 to 6; Step 8: Judge whether the time is over. If not, go back to Step 2. If so, end the calculation and save the results.

2. The calculation method for convective heat transfer of external flow of a low Prandtl number fluid according to claim 1, characterized in that, The physical property parameters include kinematic viscosity ν and Prandtl number Pr.

3. A calculation method for convective heat transfer of external flow of a low Prandtl number fluid according to claim 1, characterized in that The variable field includes but is not limited to temperature <t>, Pressure , speed , Turbulent kinetic energy <k>And turbulent kinetic energy dissipation rate <ε>.< / k> < / t> 4. A calculation method for convective heat transfer of external flow of a fluid with a low Prandtl number according to claim 1, characterized in that, Calculating the turbulent Prandtl number Pr through the empirical formula described in step 4 t , and then calculating the turbulent heat flux, specifically as follows: In the formula, Re is the Reynolds number and Pr is the Prandtl number; The calculation formula of the turbulent heat flux is as follows: where, T represents temperature; α represents thermal diffusivity;'represents pulsation; i represents the component along the coordinate axis; u is the velocity vector; <> represents ensemble average; Pr t represents the turbulent Prandtl number; v t represents the eddy viscosity coefficient.

5. A calculation method for convective heat transfer of external flow of a low Prandtl number fluid according to claim 1, characterized in that, In Step 4, the method of using a neural network to calculate the turbulent heat flux on each grid to obtain the turbulent heat flux field specifically includes the following steps: Step 4.1: Read the structure of the neural network, including weight, bias parameters and activation functions; Step 4.2: Read or calculate the original input feature field, including: turbulent kinetic energy <k>, turbulent kinetic energy dissipation rate <ε>, strain rate tensor <s>, rotation tensor (R>, temperature gradient Turbulent kinetic energy gradient Modified local Reynolds number Re based on the wall distance d , Prandtl number Pr;< / s> < / k> <s> Among them, the calculation methods of S and R are: The superscript "T" represents transpose; Step 4.3: Nondimensionalize each of the original input feature fields (except Red and Pr) obtained in Step 4.2 with different nondimensionalization factors: where: q represents the original input feature, represents the input feature after dimensionless transformation, q * represents the dimensionless factor, |||| represents the L2 norm of a vector or scalar; || <s>||and|| <r>The calculation method of || is:< / r> < / s> <s> where tr() represents the trace of a tensor; Step 4.4: From the dimensionless original features Re d and Pr, 30 invariants are calculated, and the calculation methods of the first 26 invariants λ1 to λ 26 are as follows: The last four invariants are respectively Re d and ln(Pr); Step 4.5: According to the neural network operation rules, use the 30 invariants calculated in Step 4.4 as the input of the neural network, and calculate the coefficients g1 to g 12 ; Step 4.6: Calculate 12 form invariants to Specifically as follows: Step 4.7: Calculate the linear term of the turbulent heat flux < -u'T' > || : Step 4.8: Calculate the non - linear term of turbulent heat flux 6. The calculation method for convective heat transfer of external flow of a fluid with a low Prandtl number according to claim 1, wherein Step 5 specifically is: For each grid, determine whether it satisfies <k>10 -3 and If so, the turbulent heat flux at that location is discretized implicitly; otherwise, the linear term of the turbulent heat flux < -u′T′>| | Using implicit discretization, the non - linear term of the turbulent heat flux is discretized explicitly.< / k> 7. A calculation method for convective heat transfer of external flow of a low Prandtl number fluid according to claim 1, characterized in that, In Step 6, the energy equation is: where, T is temperature; t is time; α represents thermal diffusivity; ′ represents pulsation; represents the gradient operator; u is the velocity vector; < > represents the ensemble average. < / s> < / s>

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