A numerical simulation method for nonequilibrium flow heat transfer during phase change sweating cooling

Abstract

This invention discloses a numerical simulation method for nonequilibrium flow heat transfer in phase change sweating cooling. After initialization, the method calculates the mixing density, mixed viscosity, mixing enthalpy, convection coefficient, and diffusion coefficient based on the liquid and gas phase properties obtained from the fluid temperature. Boundary conditions are assigned to the cooling fluid continuity equation, cooling fluid momentum equation, cooling fluid energy equation, and porous framework energy equation. The cooling fluid continuity equation and cooling fluid momentum equation are solved. The terms in the cooling fluid energy equation and porous framework energy equation are divided into unsteady-state terms, convection terms, diffusion terms, and source terms. These four terms are expressed by writing UDF functions and then loaded into the UDS equation in FLUENT. The new mixing velocity, new mixing pressure, new mixing enthalpy, and new solid phase temperature are solved. The difference between these values ​​and the corresponding initial values ​​in the current iteration is determined. If the requirements are met, the calculation ends; otherwise, the solid phase temperature and fluid saturation are updated, and the iteration is restarted.

Description

Technical Field

[0001] This invention relates to a numerical simulation method for non-equilibrium flow heat transfer during phase change sweating cooling, belonging to the field of aircraft thermal protection technology. Background Technology

[0002] Aerospace technology is at the forefront of modern scientific and technological development. Besides meeting the requirements of flying higher and faster, cost-saving and reusable launch vehicles are also inevitable development trends for future aerospace vehicles. This brings with it a series of key technical problems, one of which is thermal protection. The development speed of aerospace vehicles has exceeded the development speed of high-temperature resistant materials. Relying solely on the development of high-temperature resistant materials science is no longer sufficient to meet the design needs of future aerospace flights; active cooling technology must be combined to provide higher thermal protection capabilities. Sweating cooling exhibits excellent thermal protection effects and helps reduce wall friction drag, thus it is considered one of the most promising cooling technologies for solving the thermal protection problem of high-speed aircraft. Because experimental research on sweating cooling requires high-end equipment and is difficult to observe internal flow fields, numerical simulation of the sweating cooling process is an important research method. Currently, numerical simulation methods for single-phase flow heat transfer in sweating cooling are relatively mature, while numerical simulation methods for phase change sweating cooling are scarce, especially since existing commercial software cannot directly simulate the non-equilibrium flow heat transfer process of phase change sweating cooling. Summary of the Invention

[0003] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a numerical simulation method for non-equilibrium flow heat transfer in phase change sweating cooling. Based on the FLUENT platform, a secondary development is carried out to achieve accurate and rapid prediction of the non-equilibrium flow heat transfer performance of phase change sweating cooling, providing support for the engineering design of phase change sweating cooling.

[0004] The technical solution of this invention is: a numerical simulation method for non-equilibrium flow heat transfer during phase change sweating cooling, comprising the following steps:

[0005] Step 1: For the mixing velocity u in the continuity equation of the cooling fluid, the mixing pressure p in the momentum equation of the cooling fluid, the mixing enthalpy h in the energy equation of the cooling fluid, and the solid phase temperature T in the energy equation of the porous framework... s Perform initialization assignment;

[0006] Step 2: Adjust the fluid saturation s and fluid temperature T. f Perform initialization assignment;

[0007] Step 3, based on the fluid temperature T f Obtain the physical properties of the liquid and gas phases;

[0008] Step 4: Based on the liquid and gas phase physical properties and fluid saturation s obtained in the previous step, calculate the mixing density ρ, the mixed viscosity μ, the convection coefficient γ, and the diffusion coefficient Γ. h ;

[0009] Step 5: Assign boundary conditions to the cooling fluid continuity equation, cooling fluid momentum equation, cooling fluid energy equation, and porous skeleton energy equation;

[0010] Step 6: Solve the continuity equation and momentum equation of the cooling fluid;

[0011] The cooling fluid energy equation and the porous framework energy equation are divided into unsteady-state terms, convection terms, diffusion terms, and source terms. These four terms are expressed using a UDF function, which is then loaded into the UDS equations in FLUENT. Solving the cooling fluid energy equation and the porous framework energy equation separately yields the new mixing velocity u. new New mixed pressure p new New enthalpy of mixing h new The new solid-state temperature T s-new ;

[0012] Step 7: Determine the new u new p new h new T s-new Compared with the initial u, p, h, T in this iteration s If the difference between them meets the requirements, the calculation can end; otherwise, u will be... new p new h new T s-new Assign values ​​to u, p, h, and T respectively. s According to h and T f Update the relationship between and s T f After step 's', return to Step 3 to iterate again.

[0013] Preferably, the solution is obtained by writing a function using a UDF program, specifically as follows:

[0014] The initialization function is used to initialize the saturation s and the fluid temperature T. f ;

[0015] The characteristic definition function is used to define and calculate the fluid mixing density ρ, the hybrid viscosity μ, the convection coefficient γ, and the diffusion coefficient Γ. h ;

[0016] The parameter adjustment function is used to adjust the fluid saturation s and temperature T after each iteration. f Mixed density ρ, hybrid viscosity μ, convection coefficient γ, and diffusion coefficient Γ h;

[0017] The unsteady-state term definition function defines and solves the unsteady-state terms of the energy equations for fluids and porous frameworks.

[0018] The convection term definition function is used to define and solve the convection term in the fluid energy equation;

[0019] The diffusion term definition function is used to define and solve the diffusion term in the fluid energy equation;

[0020] The heat exchange definition function is used to define and solve for the heat exchange between the fluid and the porous framework;

[0021] Boundary definition functions are used to define the boundary conditions for the energy equations of the porous skeleton and the cooling fluid.

[0022] Preferably, based on the fluid temperature T f The physical properties of the liquid and gas phases are determined by looking up tables or fitting formulas. These physical properties include: liquid density ρ. l Gas phase density ρ v Liquid phase dynamic viscosity μ l Gas phase dynamic viscosity μ v Enthalpy of liquid phase saturation h l enthalpy of gas phase saturation h v , latent heat of vaporization h fg Liquid phase heat c l Compared to air, heat c v .

[0023] Preferably, the mixing density ρ, the hybrid viscosity μ, the convection coefficient γ, and the diffusion coefficient Γ are... h The calculation methods are as follows:

[0024] ρ=sρ l +(1-s)ρ v

[0025]

[0026]

[0027]

[0028] Where s is the liquid phase saturation, ρ l ρ is the density of the liquid phase. v Let k be the gas phase density. rl The relative permeability of the liquid phase, μ l k is the dynamic viscosity of the liquid phase. rv The relative permeability of the gas phase, μ v Let λ be the gas phase dynamic viscosity, λ be the liquid phase relative mobility, and h be the liquid phase relative mobility. l For liquid phase saturation enthalpy, hv For gas-phase saturation enthalpy, k f,eff T is the effective thermal conductivity of the fluid. f h is the fluid temperature, h is the enthalpy of mixing, h fg Where is the latent heat of vaporization, and D(s) is the capillary diffusion coefficient.

[0029] Preferably, boundary conditions are assigned to the cooling fluid continuity equation, cooling fluid momentum equation, cooling fluid energy equation, and porous skeleton energy equation, specifically as follows:

[0030] The cooling fluid inlet is given a given velocity and temperature value, the cooling fluid outlet is given a given pressure value, the cold end of the porous skeleton is under adiabatic conditions, and the hot end of the porous skeleton is given a given heat flux density value.

[0031] Preferably, the cooling fluid energy equation is:

[0032]

[0033] in, This is the unsteady-state term of the cooling fluid energy equation. For the convection term of the cooling fluid energy equation, For the diffusion term in the cooling fluid energy equation, q sf The source term represents the heat exchange between the fluid and the solid.

[0034] ε is porosity, t is time, ρ is mixing density, h is mixing enthalpy, γ is convection coefficient, u is mixed viscosity, and Γ is... h Here is the diffusion term coefficient. This represents the Hamiltonian operator.

[0035] Preferably, the energy equation for the porous framework is:

[0036]

[0037] This is the unsteady-state term of the energy equation for porous frameworks. For the diffusion term in the porous framework energy equation, q sf The source term represents the heat exchange between the fluid and the solid.

[0038] ε is porosity, t is time, and ρ s Let c be the solid density. p,s For solid phase heat, k f,eff For the effective thermal conductivity of the solid phase, T s Solid-state temperature This represents the Hamiltonian operator.

[0039] Preferably, in Step 1, the initialization functions provided by the FLUENT platform are used to initialize the mixing velocity u in the cooling fluid continuity equation, the mixing pressure p in the cooling fluid momentum equation, the mixing enthalpy h in the cooling fluid energy equation, and the solid phase temperature T in the porous framework energy equation. s Perform initialization assignment;

[0040] In Step 6, boundary conditions are assigned to the cooling fluid continuity equation and cooling fluid momentum equation using the FLUENT platform, and the cooling fluid continuity equation and cooling fluid momentum equation are solved using its built-in flow model.

[0041] Compared with the prior art, the present invention has the following advantages:

[0042] (1) This invention proposes a new simulation model for heat and mass transfer of phase change sweating cooling considering non-equilibrium effects, which improves the simulation prediction accuracy under extreme conditions and can support the refined design of phase change sweating cooling thermal protection for the next generation of high-speed aircraft.

[0043] (2) This invention develops a numerical simulation method based on the secondary development of the FLUENT platform for a new model of non-equilibrium heat and mass transfer, laying the foundation for rapid iteration in the scheme stage. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of the technical solution of the present invention;

[0045] Figure 2 This is a schematic diagram of the solution process of this invention. Detailed Implementation

[0046] like Figure 1 As shown, the typical physical model of phase change sweating cooling is that the cooling fluid enters the porous skeleton region 2 through inlet 1, and forms a cooling fluid domain 3 within the porous skeleton. After the fluid in the cooling fluid domain 3 completes phase change heat transfer with the porous skeleton, it flows out through outlet 4.

[0047] The technical solution of this invention is as follows: the control equations describing the non-equilibrium flow heat transfer process of phase change sweating cooling are shown in equations (1) to (4), and the meanings and determination methods of the parameters in the control equations are shown in Table 1; this invention solves the continuity equation and momentum equation of the cooling fluid using the existing functions of FLUENT software; on this basis, a UDF (User-defined functions) program is developed to solve the energy equation of the cooling fluid and the energy equation of the porous skeleton; the UDF program includes the DEFINE_INIT function, DEFINE_PROPERTY function, DEFINE_ADJUST function, DEFINE_UDS_USNTEADY function, DEFINE_UDS_FLUX function, DEFINE_UDS_DIFFUSIVITY function, DEFINE_SOURCE function, and DEFINE_PROFILE function; the DEFINE_INIT function is used to initialize the saturation s and the fluid temperature T. f The DEFINE_PROPERTY function is used to define and calculate the fluid mixing density, mixed viscosity, diffusion coefficient, and convection coefficient; the DEFINE_ADJUST function is used to adjust the fluid saturation s and temperature T after each iteration step. f The functions defined and solved are: mixing density and hybrid viscosity; DEFINE_UDS_USNTEADY function for defining and solving the unsteady-state terms of the fluid and porous framework energy equations; DEFINE_UDS_FLUX function for defining and solving the convection terms of the fluid energy equations; DEFINE_UDS_DIFFUSIVITY function for defining and solving the diffusion terms of the fluid energy equations; DEFINE_SOURCE function for defining and solving the source terms (heat exchange between the fluid and the porous framework); and DEFINE_PROFILE function for defining the boundary conditions of the cooling fluid energy equations and the porous framework energy equations.

[0048] When assigning boundary conditions to the cooling fluid continuity equation, cooling fluid momentum equation, cooling fluid energy equation, and porous skeleton energy equation: the cooling fluid inlet is given a velocity and temperature value, the cooling fluid outlet is given a pressure value, the cold end of the porous skeleton is under adiabatic conditions, and the hot end of the porous skeleton is given a heat flux density value.

[0049] Equations (1) to (4) and the parameter calculations in Table 1 constitute a new simulation model for heat and mass transfer during phase change sweating and cooling that can consider non-equilibrium effects. Specifically:

[0050] Cooling fluid continuity equation:

[0051]

[0052] Cooling fluid momentum equation:

[0053]

[0054] Cooling fluid energy equation:

[0055]

[0056] in, This is the unsteady-state term of the cooling fluid energy equation. For the energy convection term of cooling fluid, For the energy diffusion term of the cooling fluid, q sf For source terms;

[0057] Energy equation for porous framework:

[0058]

[0059] in, This is the unsteady-state term of the energy equation for porous frameworks. For the porous framework energy diffusion term, q sf For source terms;

[0060] Table 1. Meaning and determination method of parameters in the governing equations.

[0061]

[0062]

[0063]

[0064]

[0065] The workflow of this invention is as follows: Figure 2 As shown, the details are as follows:

[0066] ① Using FLUENT's built-in initialization function, the mixing rate u, mixing pressure p, mixing enthalpy h, and solid phase temperature T in equations (1) to (4) are initialized. s Perform initialization assignment;

[0067] ② The fluid saturation s and fluid temperature T are determined using the DEFINE_INIT function in the UDF program. f Perform initialization assignment;

[0068] ③ Based on fluid temperature T f The physical properties of the liquid and gas phases are solved by looking up tables or fitting formulas. The physical properties of the liquid and gas phases include: liquid density ρ. l Gas phase density ρ vLiquid phase dynamic viscosity μ l Gas phase dynamic viscosity μ v Enthalpy of liquid phase saturation h l enthalpy of gas phase saturation h v , latent heat of vaporization h fg Liquid phase heat c l Compared to air, heat c v ;

[0069] ④ Based on the liquid and gas phase physical properties and fluid saturation s obtained in the previous step, calculate the mixing density ρ, mixed viscosity μ, convection coefficient γ, and diffusion coefficient Γ using the DEFINE_PROPERTY function in the UDF program. h :

[0070] ρ=sρ l +(1-s)ρ v

[0071]

[0072]

[0073]

[0074] Where s is the liquid phase saturation, ρ l ρ is the density of the liquid phase. v Let k be the gas phase density. rl The relative permeability of the liquid phase, μ l k is the dynamic viscosity of the liquid phase. rv The relative permeability of the gas phase, μ v Let λ be the gas phase dynamic viscosity, λ be the liquid phase relative mobility, and h be the liquid phase relative mobility. l For liquid phase saturation enthalpy, h v For gas-phase saturation enthalpy, k f,eff T is the effective thermal conductivity of the fluid. f h is the fluid temperature, h is the enthalpy of mixing, h fg Where is the latent heat of vaporization, and D(s) is the capillary diffusion coefficient.

[0075] ⑤ Apply boundary conditions to equation (1) (cooling fluid continuity equation) and equation (2) (cooling fluid momentum equation) through the FLUENT platform, and apply boundary conditions to equation (3) and equation (4) through the DEFINE_PROFILE function;

[0076] ⑥ Use the Boundary Conditions panel in FLUENT to assign boundary conditions to equations (1) and (2), and solve equations (1) and (2) using the built-in flow model;

[0077] The cooling fluid energy equation is divided into unsteady terms. Convection term in the cooling fluid energy equation The diffusion term in the energy equation of cooling fluid and source item q sf The porous framework energy equation is divided into unsteady-state terms. Diffusion term in the energy equation of porous framework and source item q sf ;

[0078] Solve equations (3) and (4) using the functions DEFINE_UDS_USNTEADY, DEFINE_UDS_FLUX, DEFINE_UDS_DIFFUSIVITY, and DEFINE_SOURCE to obtain the new u. new P new h new T s-new ;

[0079] ⑦ Determine the new mixing speed u new New mixed pressure P new New enthalpy of mixing h new The new solid-state temperature T s-new Compared with the initial u, P, h, T in this iteration s If the difference between them meets the requirements, the calculation can end; otherwise, u will be... new P new h new T s-new Assign values ​​to u, P, h, and T respectively. s According to h and T f The relationship between and s is updated by the DEFINE_ADJUST function. f , s, then repeat ③~⑦.

[0080] DEFINE_ADJUST function updates T f The basis for s is the calculation method in items 18 and 34 of Table 1, specifically:

[0081]

[0082]

[0083] Where, ρ l ρ is the density of the liquid phase. v ρ is the gas phase density, ρ is the mixed density, and h is the enthalpy of mixing. l For liquid enthalpy, h v For gas enthalpy, c p,l For liquid phase heat, c p,vAs for the relative heat of gas, T sat This is the saturation temperature.

[0084] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

Claims

1. A numerical simulation method for non-equilibrium flow heat transfer during phase change sweating cooling, characterized in that... include: Step 1: The mixing velocity *u* in the continuity equation of the cooling fluid, the mixing pressure *p* in the momentum equation of the cooling fluid, the mixing enthalpy *h* in the energy equation of the cooling fluid, and the solid phase temperature *T* in the energy equation of the porous framework. s Perform initialization assignment; Step 2: Adjust the fluid saturation s and fluid temperature T. f Perform initialization assignment; Step 3, based on the fluid temperature T f Obtain the physical properties of the liquid and gas phases; Step 4: Based on the obtained liquid and gas phase physical properties and fluid saturation s, calculate the mixing density ρ, the mixed viscosity μ, the convection coefficient γ, and the diffusion coefficient Γ. h ; Step 5: Assign boundary conditions to the cooling fluid continuity equation, cooling fluid momentum equation, cooling fluid energy equation, and porous skeleton energy equation; Step 6: Solve the continuity equation and momentum equation of the cooling fluid; The cooling fluid energy equation and the porous framework energy equation are divided into unsteady-state terms, convection terms, diffusion terms, and source terms. These terms are expressed using a UDF function and loaded into the UDS equations in FLUENT. The cooling fluid energy equation and the porous framework energy are then solved separately to obtain the new mixing velocity u. new New mixed pressure p new New enthalpy of mixing h new The new solid-state temperature T s-new ; Step 7: Determine the new u new p new h new T s-new Compared with the initial u, p, h, T in this iteration s If the difference between them meets the requirements, the calculation can end; otherwise, u will be... new p new h new T s-new Assign values ​​to u, p, h, and T respectively. s According to h and T f Update the relationship between and s T f After step 's', return to Step 3 to iterate again.

2. The numerical simulation method for non-equilibrium flow heat transfer during phase change sweating cooling according to claim 1, characterized in that: The solution is obtained by writing a function using a UDF program, specifically: The initialization function is used to initialize the saturation s and the fluid temperature T. f ; The characteristic definition function is used to define and calculate the fluid mixing density ρ, the hybrid viscosity μ, the convection coefficient γ, and the diffusion coefficient Γ. h ; The parameter adjustment function is used to adjust the fluid saturation s and temperature T after each iteration. f Mixed density ρ, hybrid viscosity μ, convection coefficient γ, and diffusion coefficient Γ h ; The unsteady-state term definition function defines and solves the unsteady-state terms of the energy equations for fluids and porous frameworks. The convection term definition function is used to define and solve the convection term in the fluid energy equation; The diffusion term definition function is used to define and solve the diffusion term in the fluid energy equation; The heat exchange definition function is used to define and solve for the heat exchange between the fluid and the porous framework; Boundary definition functions are used to define the boundary conditions for the energy equations of the porous skeleton and the cooling fluid.

3. The numerical simulation method for non-equilibrium flow heat transfer during phase change sweating cooling according to claim 1, characterized in that: Based on fluid temperature T f The physical properties of the liquid and gas phases are determined by looking up tables or fitting formulas. These physical properties include: liquid density ρ. l Gas phase density ρ v Liquid phase dynamic viscosity μ l Gas phase dynamic viscosity μ v Liquid phase saturation enthalpy h l enthalpy of gas phase saturation h v , latent heat of vaporization h fg Liquid phase heat c l Compared to air, heat c v .

4. The numerical simulation method for non-equilibrium flow heat transfer during phase change sweating cooling according to claim 1, characterized in that: Mixed density ρ, hybrid viscosity μ, convection coefficient γ, and diffusion coefficient Γ h The calculation methods are as follows: p = s p l +(1-s)ρ v Where s is the liquid phase saturation, ρ l ρ is the density of the liquid phase. v k is the gas phase density. rl The relative permeability of the liquid phase, μ l k is the dynamic viscosity of the liquid phase. rv The relative permeability of the gas phase, μ v Let λ be the gas phase dynamic viscosity, λ be the liquid phase relative mobility, and h be the liquid phase relative mobility. l For liquid phase saturation enthalpy, h v For gas-phase saturation enthalpy, k f,eff T represents the effective thermal conductivity of the fluid. f h is the fluid temperature, h is the enthalpy of mixing, h fg Where is the latent heat of vaporization, and D(s) is the capillary diffusion coefficient.

5. The numerical simulation method for non-equilibrium flow heat transfer during phase change sweating cooling according to claim 1, characterized in that: Boundary conditions are assigned to the cooling fluid continuity equation, cooling fluid momentum equation, cooling fluid energy equation, and porous skeleton energy equation, specifically as follows: The cooling fluid inlet is given a given velocity and temperature value, the cooling fluid outlet is given a given pressure value, the cold end of the porous skeleton is under adiabatic conditions, and the hot end of the porous skeleton is given a given heat flux density value.

6. The numerical simulation method for non-equilibrium flow heat transfer during phase change sweating cooling according to claim 1, characterized in that: The energy equation for the cooling fluid is: in, This is the unsteady-state term of the cooling fluid energy equation. For the convection term of the cooling fluid energy equation, For the diffusion term in the cooling fluid energy equation, q sf The source term represents the heat exchange between the fluid and the solid. ε is porosity, t is time, ρ is mixing density, h is mixing enthalpy, γ is convection coefficient, u is mixed viscosity, and Γ is... h The coefficient of the diffusion term, This represents the Hamiltonian operator.

7. The numerical simulation method for non-equilibrium flow heat transfer during phase change sweating cooling according to claim 1, characterized in that: The energy equation for the porous framework is: This is the unsteady-state term of the energy equation for porous frameworks. For the diffusion term in the energy equation of the porous framework, q sf The source term represents the heat exchange between the fluid and the solid. ε is porosity, t is time, and ρ s Let c be the solid density. p,s For solid phase heat, k f,eff For the effective thermal conductivity of the solid phase, T s Solid-state temperature This represents the Hamiltonian operator.

8. The numerical simulation method for non-equilibrium flow heat transfer during phase change sweating cooling according to claim 1, characterized in that: In Step 1, the built-in initialization function of the FLUENT platform is used to initialize the mixing velocity u in the cooling fluid continuity equation, the mixing pressure p in the cooling fluid momentum equation, the mixing enthalpy h in the cooling fluid energy equation, and the solid phase temperature T in the porous framework energy equation. s Perform initialization assignment; In Step 6, boundary conditions are assigned to the cooling fluid continuity equation and cooling fluid momentum equation using the FLUENT platform, and the cooling fluid continuity equation and cooling fluid momentum equation are solved using its built-in flow model.

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