CFD inflow boundary condition construction method for wind-heat environment

Abstract

The invention discloses a CFD inflow boundary condition construction method for a wind-heat environment, and relates to the technical field of computational fluid mechanics and the wind-heat environment, a mathematical model of an equilibrium state boundary layer wind field under a neutral condition is constructed based on a Reynolds average method, and expressions of average wind speed, turbulent kinetic energy and specific dissipation rate are determined; a gradient diffusion hypothesis closed equation is adopted and a temperature expression is deduced based on an energy equation in combination with a steady-state condition and a horizontal uniformity constraint; the to-be-determined parameters are determined through experimental data fitting, and CFD inflow boundary conditions with the self-holding characteristic are formed. According to the method, the defect that in the prior art, the CFD inflow boundary condition is difficult to maintain the self-holding performance in wind-heat coupling simulation is overcome, the precision and reliability of CFD numerical simulation are remarkably improved, and a key technical support is provided for precise simulation of the urban wind-heat environment.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of computational fluid dynamics (CFD) and wind-thermal environment, and more particularly to a CFD inflow boundary condition construction method for wind-thermal environment. BACKGROUND

[0002] Currently, in the process of urban development, the underlying surface is covered with a large area of asphalt, concrete and other materials, combined with a large amount of waste heat emitted by human activities, which together leads to the increasingly serious urban wind-thermal environment problem. The problem is essentially a typical multi-physical field coupling system, and its core performance is the complex interaction between the flow field and the temperature field in the urban near-surface atmosphere. This coupling further triggers a series of multi-level negative effects: not only intensifies the heat island effect, directly endangers human health and comfort, but also changes the diffusion conditions of pollutants, leading to deterioration of air quality, and poses a serious challenge to the urban ecological system, energy structure and the quality of life of residents.

[0003] In order to scientifically deal with the above problems, computational fluid dynamics (CFD) provides an efficient research approach. Compared with traditional methods such as field measurement and wind tunnel experiment, CFD can effectively overcome the limitations of traditional methods in cost, measurement point coverage and full-field information reproduction by numerically solving the control equations of fluid flow and heat and mass transfer (such as Navier-Stokes equation, energy equation, etc.). Specifically, CFD technology has three core advantages: first, it can realize full-scale, full-three-dimensional refined simulation, and can completely reproduce the spatial distribution of wind speed, pressure, temperature and pollutant concentration in the region by constructing a virtual city model including buildings, streets and green spaces; second, it can deeply analyze the coupling mechanism between the flow field and the temperature field, and reveal the internal physical mechanism such as the cause of "high-temperature dead angle" and the cooling effect of ventilation corridor; third, it supports the simulation and comparison of the wind-thermal environment impact of various planning schemes (such as adjusting building layout, adding green space and water body, etc.) before construction, so as to provide a scientific basis for optimizing the scheme and realizing accurate decision-making before construction.

[0004] However, when using CFD to simulate urban wind-thermal environment, the setting of inlet boundary condition has become a key link affecting the accuracy of simulation. The ideal inflow boundary condition not only needs to accurately reflect the basic characteristics of the atmospheric boundary layer, but also needs to maintain the stability of its initial flow and thermodynamic characteristics in the entire calculation domain, i.e. has the property of "self-maintenance", so as to effectively avoid the simulation deviation caused by distorted boundary conditions. Unfortunately, the existing inflow boundary condition technology still has obvious limitations in this regard, and it is difficult to maintain the necessary self-maintenance performance in wind-thermal coupling simulation, thereby restricting the further improvement of the overall simulation accuracy of CFD.

[0005] Therefore, how to provide a CFD inflow boundary condition construction method capable of maintaining self-maintaining characteristics is a problem that those skilled in the art urgently need to solve. SUMMARY

[0006] Therefore, the present application provides a CFD inflow boundary condition construction method capable of maintaining self-maintaining characteristics. Based on the energy equation and the RANS equation, the wind speed profile of the exponential law is fused to construct a CFD inflow boundary condition for a hot and windy environment, thereby significantly improving the accuracy and reliability of CFD numerical simulation.

[0007] In order to achieve the above purpose, the present application adopts the following technical solutions: A CFD inflow boundary condition construction method for a hot and windy environment, comprising: Based on the Reynolds average method, a mathematical model for simulating the equilibrium boundary layer wind field under neutral conditions is constructed, and the expressions of the average wind speed, turbulent kinetic energy and specific dissipation rate of the inflow boundary are determined; Based on the energy equation, the steady state condition and the horizontal uniform constraint are combined, the equation is closed by using the gradient diffusion hypothesis, and the temperature expression is derived; The undetermined parameters in the average wind speed, turbulent kinetic energy, specific dissipation rate and temperature expression of the inflow boundary are determined by fitting experimental data, and the CFD inflow boundary condition with self-maintaining characteristics is formed.

[0008] Optionally, the average wind speed expression of the inflow boundary is:

[0009] In the formula, u is the average wind speed, unit m / s; is the dimensionless ground roughness exponent; z is the height from the ground, unit m; is the reference height wind speed, unit m / s; is the reference height, unit m.

[0010] Optionally, the expression of the turbulent kinetic energy is:

[0011] In the formula, z is the height from the ground; is the dimensionless ground roughness exponent; and is a constant.

[0012] Optionally, the expression of the specific dissipation rate is:

[0013] In the formula, is the specific dissipation rate, unit s -1 ; It is a dimensionless surface roughness index; is the constant of the turbulence model; u is the average wind speed in m / s; z is the height above the ground in m.

[0014] Optionally, the energy equation can be expressed as follows:

[0015] In the formula, Indicates thermal diffusivity (m) 2 / s), It is a temperature vector. It is a velocity vector. It is a volumetric heat source.

[0016] Optionally, it also includes requirements based on steady-state conditions. The energy equation is simplified to a steady-state form:

[0017] In the formula, For Hamiltonian operators, for The average Reynolds.

[0018] Optionally, the mathematical expression of the gradient diffusion hypothesis is as follows:

[0019] In the formula, This represents the average temperature, measured in Kelvin (K). and These represent the velocity fluctuation components in the x and z directions, respectively, with units of m / s; Represents temperature fluctuations, measured in Kelvin (K). Represents the turbulent thermal diffusivity; is the Prandtl constant for turbulence.

[0020] Optionally, the temperature expression is:

[0021] In the formula, Represents wall heat flux, in W / m² 2 ; Specific heat capacity at constant pressure, expressed in J / (kg·K); Density, unit: kg / m³ 3 ; For reference height z ref Turbulent kinetic energy at the location; For reference height z ref The speed at that location; For reference temperature; This is a reference temperature.

[0022] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a method for constructing CFD inflow boundary conditions for wind-thermal environments, which has the following beneficial effects: (1) By combining the energy equation and the RANS equation and constrained by Yang’s mathematical physics equation, this invention derives a self-sustaining CFD inflow boundary condition applicable to wind-heat environment. (2) The CFD inflow boundary conditions derived in this invention fundamentally guarantee the horizontal uniformity of the flow variables in the computational domain (i.e., self-sustaining characteristics), thereby significantly reducing numerical errors caused by the incoordination between the inlet and the internal flow field. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0024] Figure 1 This is a schematic diagram of the method flow provided by the present invention; Figure 2 The wind tunnel test non-isothermal ABL inflow profile and corresponding fitting curve provided by the present invention, wherein (a) is the average velocity profile, (b) is the turbulent kinetic energy profile, and (c) is the temperature profile; Figure 3 A schematic diagram of the computational boundary conditions provided by this invention; Figure 4 This is a schematic diagram comparing the inlet and outlet non-isothermal ABL profiles provided by the present invention, wherein (a) is the average velocity profile, (b) is the turbulent kinetic energy profile, and (c) is the temperature profile. Figure 5 The following are cloud maps of the non-isothermal ABL flow field within the domain provided by the present invention, wherein (a) is a velocity cloud map, (b) is a turbulent kinetic energy cloud map, and (c) is a temperature cloud map. Detailed Implementation

[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0026] This invention discloses a method for constructing CFD inflow boundary conditions for wind-thermal environments, such as... Figure 1 As shown, it includes: Based on the Reynolds-averaged method, a mathematical model for simulating the equilibrium boundary layer wind field under neutral conditions is constructed, and the expressions for the mean wind speed, turbulent kinetic energy, and specific dissipation rate at the inflow boundary are determined. Based on the energy equation, combined with steady-state conditions and horizontal uniformity constraints, and using the gradient diffusion hypothesis closed equation, the temperature expression is derived. By fitting experimental data, the mean wind speed, turbulent kinetic energy, specific dissipation rate, and undetermined parameters in the temperature expression of the inflow boundary are determined, thus forming a CFD inflow boundary condition with self-holding characteristics.

[0027] Specifically, the CFD method used in this invention is the Reynolds Average Method (RANS) based on time averaging. Under the inflow boundary, ensuring the horizontal uniformity of the ABL model is a key prerequisite for CFD wind load and environmental simulation. Under isothermal (neutral) conditions, the wind speed (u), turbulent kinetic energy (k), and specific dissipation rate (ω) at the inflow boundary are given by a new mathematical model for simulating the equilibrium boundary layer wind field proposed in this invention, as shown in equations (1) to (3). This model can ensure that the inflow boundary conditions can be realized throughout the entire computational domain under neutral conditions.

[0028] (1) (2) (3) in: The wind speed is the average wind speed, in m / s. Height above the ground, in meters (m). Wind speed at reference altitude, unit: m / s; Reference height, unit: meters; It is a dimensionless surface roughness index; Turbulent kinetic energy, unit m 2 / s 2 ; and It is a constant that can be obtained by fitting data from field measurements or wind tunnel tests. Specific dissipation rate, in seconds. -1 ; This is a constant for the turbulence model, with a value of 0.028.

[0029] In CFD, the general expression for the energy equation is: (4) In the formula, α Thermal diffusivity (m) 2 / s);T This is a temperature vector; V It is the velocity vector; R This is the heat source term. Assuming no additional anthropogenic heat sources are considered, then... .

[0030] Based on steady-state conditions, it is required that Equation (4) can be simplified to equation (5) in steady-state form: (5) In the formula, For Hamiltonian operators, for The average Reynolds.

[0031] Assuming no wind direction shift, the thermal and wind fields of the ABL flow are considered non-uniform only in the vertical direction. This means that the three-dimensional flow can be simplified to a two-dimensional flow containing only the flow direction and the vertical direction. Furthermore, in this case, the average velocity value is only in the x-direction. ,and Therefore, combining the principles of RANS, equation (5) can be simplified and extended to the following RANS form: (6) in, This represents the average temperature, measured in Kelvin (K). Represents the thermal diffusivity, with units of m. 2 / s; These represent velocity fluctuations in the x and z directions, respectively, with units of m / s; This represents temperature fluctuations, measured in Kelvin (K).

[0032] To close the above equation, the eddy current viscosity hypothesis is adopted, so that the Reynolds stress can be expressed as eddy current viscosity. For modeling, the gradient diffusion hypothesis (SGDH) is used, which assumes that the turbulent heat flux is proportional to the vertical gradient of the mean temperature T. The mathematical expression of SGDH is as follows: (7) in, Represents the turbulent thermal diffusivity; For turbulence Prandtl constant, .

[0033] Substituting equation (7) into equation (6), and simultaneously utilizing the horizontal uniform constraint, the temperature gradient is required. Equation (6) can be transformed into equation (8): (8) Equation (8) can be transformed into equation (9): (9) According to Fourier's law, the vertical gradient of the average temperature under one-dimensional natural heat conduction is proportional to the heat flux per unit time and per unit area of ​​the inner wall surface, thus: (10) in, Represents wall heat flux, in W / m² 2 ; Specific heat capacity at constant pressure, expressed in J / (kg·K); Density, unit: kg / m³ 3 .

[0034] Combining equations (10) and (9), we can naturally assume and Their behavior is similar in thermal diffusion, therefore it is assumed It also obeys Fourier's law and concludes that: (11) Substituting equation (7) into equation (11) yields: (12) Eddy viscosity The calculation can be expressed by equation (13): (13) Substituting equations (1) and (3) into equation (13) yields: (14) Substituting equation (14) into equation (11) yields: (15) make Then equation (14) can be simplified to: (16) make Then equation (15) can be further simplified to: (17) Then we can get: (18) Integrating both sides simultaneously yields the temperature. The expression: (19) By referencing the temperature and velocity at the corresponding altitude, the constant can be determined. : (20) The final temperature expression is: (twenty one) Thus, through theoretical derivation, the CFD inflow boundary conditions applicable to wind-heat environments that can maintain self-sustaining characteristics were obtained, namely equations (1)(2)(3)(21).

[0035] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings.

[0036] I. Establishment of Numerical Wind Tunnel

[0037] First, a numerical wind tunnel airspace with dimensions of height × width × length = 1m × 1.2m × 2.4m was established. This size was chosen to match the data used in subsequent fitting, and the relevant data were obtained from experimental results from the thermal stratification wind tunnel at Tokyo Institute of Technology. The airspace and boundary conditions of the numerical wind tunnel are set as follows: Figure 3 As shown. In terms of boundary condition configuration, the two sides and top of the computational domain are set as no-slip walls (symmetry), the inlet is set as a velocity inlet, and the outlet is set as a pressure outlet.

[0038] II. Data Fitting

[0039] Based on experimental data from the thermal stratification wind tunnel at Tokyo Institute of Technology, the fitting process of this invention (e.g.) Figure 2 The data curve shown is compared with the fitted curve. The specific process is as follows, and the calculation is performed sequentially using equations (1), (2), (3), and (21): (1) (2) (3) (19) (1) First, select the reference height and reference wind speed, respectively. and Based on formula (1), the average wind speed profile is fitted to obtain the parameters. The fitting results are as follows Figure 2 As shown in (a).

[0040] (2) Determine the parameters as well as Based on formulas (2) and (21), the turbulent kinetic energy profile is fitted to obtain... and The fitting results are as follows Figure 2 As shown in (b).

[0041] (3) Determine as well as Select reference temperature Reference height Compared with reference speed And based on formula (3), the temperature profile is fitted to obtain and The fitting results are as follows Figure 2 As shown in (c).

[0042] Through the above steps, the following set of equations for defining the inflow boundary conditions is finally obtained, namely equations (20) to (23): (twenty two) (twenty three) (twenty two) (twenty four) III. Numerical Calculation The fitted equations obtained above, i.e., equations (22) to (24), are compiled into user-defined functions (UDFs) and imported into the ANSYS Fluent simulation platform for calculation. The solver settings are as follows: the pressure-velocity coupling uses the SIMPLEC algorithm, and the nonlinear convection terms in the momentum equation and the turbulence model equation are discretized using the second-order upwind scheme. The bottom surface roughness constant is set to... The roughness height is The convergence criterion for the residuals of all variables, including those in the continuity equation, is set to 10. - ¹¹ To ensure calculation accuracy.

[0043] IV. Results and Analysis

[0044] Comparison of non-isothermal atmospheric boundary layer (ABL) profiles at the inlet and outlet of the numerical wind tunnel is as follows: Figure 4 As shown in the figure. Comparative analysis of the average velocity (a), turbulent kinetic energy (b), and temperature profile (c) reveals that their distribution patterns and specific values ​​remain highly consistent from the inlet to the outlet. Meanwhile, the flow field contour plot within the computational domain is shown below. Figure 5 As shown, the velocity contour plot (a), turbulent kinetic energy contour plot (b), and temperature contour plot (c) further visually present the spatial distribution of each physical quantity. The above results collectively verify that the inflow boundary conditions generated by this invention possess excellent self-sustaining characteristics, indicating that the core statistical characteristics of key physical quantities such as wind speed, turbulent kinetic energy, and temperature do not undergo significant distortion or attenuation during their development along the computational domain.

[0045] The above results clearly demonstrate that the CFD inflow boundary conditions proposed in this invention for wind-thermal environment simulation can effectively and accurately reproduce non-isothermal ABL flow, ensuring the uniformity and sustainability of the flow in the horizontal direction, thereby significantly improving the accuracy and reliability of CFD numerical simulation of wind-thermal environment under non-isothermal ABL conditions.

[0046] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0047] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for constructing CFD inflow boundary conditions for wind-thermal environments, characterized in that, include: Based on the Reynolds-averaged method, a mathematical model for simulating the equilibrium boundary layer wind field under neutral conditions is constructed, and the expressions for the mean wind speed, turbulent kinetic energy, and specific dissipation rate at the inflow boundary are determined. Based on the energy equation, combined with steady-state conditions and horizontal uniformity constraints, and using the gradient diffusion hypothesis closed equation, the temperature expression is derived. By fitting experimental data, the mean wind speed, turbulent kinetic energy, specific dissipation rate, and undetermined parameters in the temperature expression of the inflow boundary are determined, thus forming a CFD inflow boundary condition with self-holding characteristics.

2. The method for constructing CFD inflow boundary conditions for wind-thermal environments according to claim 1, characterized in that, The expression for the average wind speed at the inflow boundary is: In the formula, u The wind speed is the average wind speed, in m / s. Z is the dimensionless ground roughness index; z is the ground clearance in meters. Wind speed at reference altitude, unit: m / s; For reference height, unit is meters (m).

3. The method for constructing CFD inflow boundary conditions for wind-thermal environments according to claim 1, characterized in that, The expression for the turbulent kinetic energy is: In the formula, z is the height above the ground; It is a dimensionless surface roughness index; and It is a constant.

4. The method for constructing CFD inflow boundary conditions for wind-thermal environments according to claim 1, characterized in that, The expression for the specific dissipation rate is: In the formula, Specific dissipation rate, in seconds. -1 ; It is a dimensionless surface roughness index; is the constant of the turbulence model; u is the average wind speed in m / s; z is the height above the ground in m.

5. The method for constructing CFD inflow boundary conditions for wind-thermal environments according to claim 1, characterized in that, The expression for the energy equation is: In the formula, The value m represents thermal diffusivity. 2 / s, It is a temperature vector. It is a velocity vector. It is a volumetric heat source.

6. The method for constructing CFD inflow boundary conditions for wind-thermal environments according to claim 5, characterized in that, It also includes requirements based on steady-state conditions. The energy equation is simplified to a steady-state form: In the formula, For Hamiltonian operators, for The average Reynolds.

7. The method for constructing CFD inflow boundary conditions for wind-thermal environments according to claim 6, characterized in that, The mathematical expression for the gradient diffusion hypothesis is as follows: In the formula, This represents the average temperature, measured in Kelvin (K). and These represent the velocity fluctuation components in the x and z directions, respectively, with units of m / s; Represents temperature fluctuations, measured in Kelvin (K). Density, unit: kg / m³ 3 ; Represents the turbulent thermal diffusivity; is the Prandtl constant for turbulence.

8. The method for constructing CFD inflow boundary conditions for wind-thermal environments according to claim 7, characterized in that, The temperature expression is: In the formula, Represents wall heat flux, in W / m² 2 ; Specific heat capacity at constant pressure, expressed in J / (kg·K); It is a constant; These are constants for the turbulence model; For reference height z ref Turbulent kinetic energy at the location; For reference height z ref The speed at that location; For reference temperature; This is a reference temperature.

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