Method for calculating transient operating performance of non-gray strongly scattering droplet radiator

Abstract

The application discloses a kind of non-gray strong scattering droplet radiator transient working performance calculation method, steps are as follows:1, build space droplet radiator radiation heat dissipation model.2, based on radiation heat dissipation model, fast iteration is carried out, and the steady temperature field of droplet layer is calculated.3, change the inlet temperature of droplet generator based on the steady temperature field, carry out time step iteration, save transient temperature field in iteration process.4, based on the transient temperature field, the transient working performance calculation of space droplet radiator is carried out.The method of the application realizes the calculation of the transient working performance of the space droplet radiator of non-gray body strong scattering working medium, and has excellent calculation performance.

Description

Technical Field

[0001] This invention relates to the field of Monte Carlo ray tracing and Mie scattering theory, specifically to a method for calculating the transient performance of a non-gray strong scattering droplet radiator. Background Technology

[0002] Since the beginning of the 21st century, with the development of aerospace science and technology, conventional energy sources have become insufficient to meet the needs of an increasing number of space missions. Advanced space nuclear reactor power sources (space reactors) have become the inevitable, and even the only, choice. The thermal management system of a space nuclear-powered spacecraft mainly consists of three modules: the nuclear reactor module, the thermoelectric conversion module, and the waste heat removal module. Currently, most space reactor waste heat removal systems employ liquid metal loop or heat pipe radiators to dissipate heat to the space environment. Due to the weight limitations of the radiators, the designed electrical power of the space reactor is limited to the hundreds of kilowatts. In contrast, liquid droplet radiators, compared to traditional heat pipe radiators, have advantages such as low thermal resistance, high heat dissipation power per unit mass, simple structure, and less susceptibility to impacts from space kinetic energy.

[0003] The droplet radiator mainly relies on the external radiation of the droplet layer to dissipate heat and realize the waste heat discharge of the space stack. Therefore, the radiation heat dissipation performance of the droplet layer is crucial to the working performance of the droplet radiator. Most of the droplets in the droplet layer are in the hundreds of micrometers, which is close to the wavelength of the droplet radiation light. Therefore, it is not appropriate to use Rayleigh scattering or geometric optics to calculate its optical performance. Summary of the Invention

[0004] In order to overcome the problems existing in the prior art, the purpose of this invention is to provide a method for calculating the transient operating performance of a non-gray strong scattering droplet radiator. The method of this invention realizes the calculation of the transient operating performance of a space droplet radiator with a non-gray strong scattering working medium and has excellent calculation performance.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A method for calculating the transient performance of a non-gray strong scattering droplet radiator is proposed. This method considers the anisotropic scattering and transmission processes during the non-gray body emission, absorption, and working fluid transfer processes in the radiative heat dissipation of the space droplet radiator, taking into account the influence of solar thermal radiation, and can complete the calculation of transient operating characteristics. The method includes the following steps:

[0007] Step 1: Construct a space droplet radiator radiation heat dissipation model:

[0008] The space droplet radiator system includes a droplet generator, a droplet collector, a liquid storage tank, a circulating pump, a heat exchanger, and a fluid transfer pipeline. The working fluid droplets fly at a constant speed and form a droplet layer between the droplet collector and the droplet radiator. Since the radiative heat dissipation of the liquid working fluid takes place almost entirely in the droplet layer, the radiative heat transfer capacity of the space droplet radiator is determined by the radiative heat dissipation capacity of the droplet layer.

[0009] For the droplet generator, droplet collector, and droplet layer, the droplet layer is divided into several cuboid droplet layer control volumes of equal size, the surfaces of the droplet generator and droplet collector are divided into several rectangular surface control volumes of equal area, and the surface of the droplet layer exposed to sunlight is divided into several rectangular solar irradiation control volumes of equal area. The sum of these three types of control volumes constitutes the established geometric model of the droplet layer.

[0010] Taking a control volume i within the droplet layer, the energy conservation equation for this control volume, which is also the radiation heat dissipation model of the space droplet radiator, is as follows:

[0011]

[0012] In the formula:

[0013] Vp,i — Volume of droplet layer control volume i / m -3

[0014] ρ p,i —Density of droplet layer control volume i / kg·m -3

[0015] h p,i ——Control volume enthalpy value / J·kg -1

[0016] t — time / s -1

[0017] q r — Thermal radiation flux / W·m -2

[0018] Q—Local heat source / W·m -2

[0019] N P —Total number of droplet layer control volumes

[0020] N En ——Total number of surface control volumes

[0021] N solar — Number of control volumes on surfaces subject to solar radiation

[0022] A j —Total emission surface area of ​​droplet layer control volume j / m 2

[0023] ε j — Emissivity of droplet layer control volume j

[0024] σ — Stefan-Boltzmann constant

[0025] T j —Temperature of droplet layer control volume j / K

[0026] —Radiative transfer factor of droplet layer control volume j to droplet layer control volume i

[0027] A k —Total emission surface area of ​​surface control volume k / m 2

[0028] ε k — Emissivity of surface control volume k

[0029] T k —Temperature of surface control volume k / K

[0030] —Radiative transfer factor of surface control volume k to droplet layer control volume i

[0031] A i —Total emission surface area of ​​droplet layer control volume i / m 2

[0032] ε i — Emissivity of droplet layer control volume i

[0033] T i —Temperature of droplet layer control volume i / K

[0034] S l — Irradiated area of ​​solar irradiance control body l / K

[0035] P solar —Solar irradiance / W·m 2

[0036] —Radiative transfer factor of solar irradiance control volume l to droplet layer control volume i

[0037] In the energy conservation equation for the control volume, the volume and density of the droplet layer control volume i are given by the thermophysical properties of the working fluid of the space droplet radiator and the geometric properties of the droplet layer. The enthalpy is calculated based on the thermophysical properties of the working fluid of the space droplet radiator and the temperature of the control volume. The temperature of the control volume is the dependent variable, and time is the independent variable. The total number of control volumes is given by the method of dividing the control volumes. The total emission surface area of ​​the control volumes is given by the geometric properties of the droplet layer. The emissivity of the control volumes is given by the thermophysical properties of the working fluid of the space droplet radiator and the thermophysical properties of the surface materials of the droplet generator and the droplet collector.

[0038] The radiative transfer factor was obtained by Monte Carlo ray tracing simulation, and the geometric model simulated by Monte Carlo ray tracing was given by the established droplet layer geometric model. For non-gray body emission processes, the emitted light wavelength was re-solved using Monte Carlo ray tracing and the emission characteristics of the liquid working fluid in the space droplet radiator.

[0039]

[0040] In the formula:

[0041] E emissive —Emission characteristics of liquid working fluid in space droplet radiators

[0042] Random—random numbers generated in Monte Carlo ray tracing.

[0043] λ — wavelength of emitted light / m

[0044] For non-gray body absorption and anisotropic scattering transport processes, the method of changing the droplet layer absorption factor, extinction factor, and droplet scattering phase function input into the Monte Carlo method is employed. These three parameters should be re-solved based on the droplet geometry model and the thermal properties of the working fluid in the space droplet radiator, using Mie scattering theory.

[0045]

[0046] α λ =1.5Q aλ f v / D d (4)

[0047] K λ =1.5(Q) aλ +Q sλ )f v / D d (5)

[0048] In the formula:

[0049] D d —Droplet diameter / m

[0050] n optical,λ ,k optical,λ —The real and imaginary parts of the complex refractive index of the liquid working medium in a space droplet radiator at the incident light wavelength

[0051] φ λ (θ,η)——Scattering phase function of liquid working fluid droplets in a space droplet radiator

[0052] Q aλ —Droplet absorption cross section / m 2

[0053] Q sλ —Droplet scattering cross section / m 2

[0054] α λ —Droplet layer absorption factor / m

[0055] K λ — Droplet layer extinction factor / m

[0056] f v — Droplet volume fraction

[0057] Solar irradiance is:

[0058]

[0059] In the formula:

[0060] P0 – Solar irradiance at 1 AU (Earth-Sun distance) / W·m 2

[0061] R—AU (Earth-Sun distance) is the distance from the Sun to a space-based reactor system in units.

[0062] Step 2: Perform rapid iterative calculations based on the radiation heat dissipation model of the space droplet radiator to obtain the steady-state temperature field of the droplet layer;

[0063] For the radiative heat dissipation model of the space droplet radiator established in step 1, assuming that the temperature of the droplet layer control volume has reached a steady-state condition and is a constant value, the time term dt is replaced by the droplet flight velocity:

[0064]

[0065] In the formula:

[0066] u i —Droplet layer control volume i Droplet flight speed

[0067] dt——Time is longer than a walk

[0068] dx — the length of the droplet layer control volume i traveling at the droplet's velocity during time dt.

[0069] According to equation (7), the droplet layer control body i moves by dx along the droplet flight velocity after time dt. Based on this, the new position reached by the droplet layer control body i after time dt is determined, and the droplet layer control body that coincides with the droplet layer control body i at the new position is denoted as droplet layer control body i. dt Based on this, the radiation heat dissipation model of the space droplet radiator is discretized into a steady-state iterative equation:

[0070]

[0071] In the formula:

[0072] —Droplet layer control volume i at the (m+1)th iteration dt enthalpy value

[0073] —Enthalpy of droplet layer control volume i at the m-th iteration

[0074] Enthalpy value at the m-th iteration Based on the temperature at the m-th iteration The thermal properties of the working fluid in the space droplet radiator are solved, and the enthalpy value at the (m+1)th iteration is obtained according to equation (8).

[0075] When the droplet layer control body i is in close contact with the droplet generator, it is assumed that the temperature of the droplet layer control body is equal to the outlet temperature of the droplet generator.

[0076] T i =T in,generator (9)

[0077] T i —Temperature of droplet layer control volume i

[0078] T in,generator — Droplet generator outlet temperature

[0079] For the steady-state temperature field solution process, a fast iterative method is adopted, such that the chosen dt makes dx exactly the distance between the two droplet layer control volumes in the direction of droplet flight velocity in the droplet layer = the distance between the droplet layer control volumes i. dt The droplet layer control volume i+1 is exactly adjacent to droplet layer control volume i along the droplet velocity direction. At this point, the solution is started from the droplet generator exit along the droplet flight velocity direction within the droplet layer. After solving, the solution is directly... Assign to And utilize reassignment Continue solving using equation (8) The change in enthalpy of the entire droplet layer was recorded between the two iterations.

[0080] in:

[0081] —Enthalpy of droplet layer control volume i+1 at the (m+1)th iteration

[0082] —The enthalpy of droplet layer control volume i+1 at the m-th iteration

[0083] —The enthalpy of the droplet layer control volume i+2 at the (m+1)th iteration

[0084] When the error is less than 10 -6 When the enthalpy field of the droplet layer has converged, it is considered that the convergence criterion is:

[0085]

[0086] h i m+1 —Enthalpy of droplet layer control volume i in the (m+1)th iteration

[0087] h i m —Enthalpy of droplet layer control volume i in the m-th iteration

[0088] Step 3: Based on the steady-state temperature field, change the inlet temperature of the droplet generator and perform time step iterations, saving the transient temperature field during the iteration process;

[0089] The radiative heat dissipation model of the space droplet radiator established in step 1 is discretized in time:

[0090]

[0091] —Enthalpy of the iterative droplet layer control volume idt at time t+dt

[0092] — The enthalpy of the droplet layer control volume i at time t.

[0093] Assuming that at t=0, the temperature of each droplet layer control volume i is either the given initial temperature or the temperature calculated in step 2 during steady-state operation, the initial enthalpy of each droplet layer control volume i can be calculated based on the temperature and the thermophysical properties of the working fluid in the space droplet radiator. Based on equation (11), the droplet layer temperature is retained in each step of the solution, that is, the transient temperature change of all droplet control volumes i at the time step is solved.

[0094] Step 4: Calculate the transient operating performance of the space droplet radiator based on the transient temperature field;

[0095] The transient operating characteristics that need to be calculated for the space droplet radiator system include transient temperature distribution, transient droplet collector outlet average enthalpy, and transient radiative force of the droplet layer; the enthalpy of the droplet layer control volume i at time t is obtained through step 3. The transient temperature of droplet layer control volume i can be calculated by combining the thermophysical properties of the liquid working fluid in the space droplet radiator. The average enthalpy at the outlet of the transient droplet collector and the transient radiative force of the droplet layer are calculated as follows:

[0096]

[0097]

[0098] In the formula:

[0099] h t collector —The average enthalpy of the droplet collector's transient outlet at time t.

[0100] n high —Total number of droplet control volumes in the thickness direction

[0101] n wide —Total number of droplet layer control volumes in the width direction

[0102] E t power —Transient radiation force of the droplet layer at time t

[0103] —Radiative transfer factor of droplet layer control volume i to droplet layer control volume j

[0104] —Radiative transfer factor of droplet layer control volume i to surface control volume k

[0105] —Radiative transfer factor of surface control volume i to droplet layer control volume j

[0106] —Radiative transfer factor of surface control volume i to surface control volume k.

[0107] Compared with the prior art, the present invention has the following outstanding features:

[0108] For the non-gray body characteristics in the droplet layer, the anisotropic scattering and transport processes during the non-gray body emission, absorption, and working fluid transport processes in the radiative heat dissipation of the space droplet radiator were considered, along with the influence of solar thermal radiation. For the calculation of transient-steady-state operating performance, a combination of fast iteration and time iteration was employed to reduce the computational load required for simulation. This method utilizes Monte Carlo ray tracing and Mie scattering theory to provide a research methodology for the transient operating performance of droplet radiators. Attached Figure Description

[0109] Figure 1 This is a flowchart of the method of the present invention;

[0110] Figure 2 This is the structure of the space droplet radiator system in this invention;

[0111] Figure 3 An example of using this method to calculate a steady-state temperature field.

[0112] Figure 4 An example of using this method to calculate a transient temperature field.

[0113] Figure 5 An example of using this method to calculate a transient temperature field.

[0114] Figure 6 An example of using this method to calculate a transient temperature field.

[0115] Figure 7 An example of using this method to calculate a transient temperature field.

[0116] Figure 8 An example of using this method to calculate a transient temperature field. Detailed Implementation

[0117] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0118] like Figure 1 As shown, the transient performance calculation method for the non-gray strong scattering droplet radiator of the present invention includes the following steps:

[0119] Step 1: Construct a radiative heat dissipation model of a space droplet radiator. This example uses a rectangular space droplet radiator system with PDMS silicone oil as the working fluid, and its structure is as follows: Figure 2 As shown, the system includes a droplet generator, a droplet collector, a storage tank, a circulating pump, a heat exchanger, and fluid transfer pipelines. The liquid working fluid absorbs waste heat from the reactor system in the heat exchanger, then enters the droplet generator and forms hundreds of millions of tiny droplets. These droplets travel at a constant speed to the droplet collector, dissipating heat through thermal radiation during their flight. During this process, the droplets form a droplet layer between the droplet collector and the droplet radiator. The cooled droplets are collected by the droplet collector and then pumped back to the heat exchanger, repeating this cycle. Since the radiative heat dissipation of the liquid working fluid occurs almost entirely within the droplet layer, the radiative heat transfer capacity of the space droplet radiator is determined by the radiative heat dissipation capacity of the droplet layer.

[0120] For the droplet generator and droplet collector, as well as the cuboid droplet layer between them, the droplet layer is divided into several cuboid droplet layer control volumes of equal size, the surface of the droplet generator and the surface of the droplet collector are divided into several rectangular surface control volumes of equal area, and the surface of the droplet layer exposed to sunlight is divided into several rectangular solar irradiation control volumes of equal area. The sum of these three types of control volumes constitutes the established geometric model of the droplet layer.

[0121] Taking a control volume i within the droplet layer, the energy conservation equation for this control volume, which is also the radiation heat dissipation model of the space droplet radiator, is as follows:

[0122]

[0123] In the formula:

[0124] Vp,i — Volume of droplet layer control volume i / m -3

[0125] ρ p,i —Density of droplet layer control volume i / kg·m -3

[0126] h p,i ——Control volume enthalpy value / J·kg -1

[0127] t — time / s -1

[0128] q r — Thermal radiation flux / W·m -2

[0129] Q—Local heat source / W·m -2

[0130] N P —Total number of droplet layer control volumes

[0131] N En ——Total number of surface control volumes

[0132] N solar — Number of control volumes on surfaces subject to solar radiation

[0133] A j —Total emission surface area of ​​droplet layer control volume j / m 2

[0134] ε j — Emissivity of droplet layer control volume j

[0135] σ — Stefan-Boltzmann constant

[0136] T j —Temperature of droplet layer control volume j / K

[0137] —Radiative transfer factor of droplet layer control volume j to droplet layer control volume i

[0138] A k —Total emission surface area of ​​surface control volume k / m 2

[0139] ε k — Emissivity of surface control volume k

[0140] T k —Temperature of surface control volume k / K

[0141] —Radiative transfer factor of surface control volume k to droplet layer control volume i

[0142] A i —Total emission surface area of ​​droplet layer control volume i / m 2

[0143] ε i — Emissivity of droplet layer control volume i

[0144] T i —Temperature of droplet layer control volume i / K

[0145] S l — Irradiated area of ​​solar irradiance control body l / K

[0146] P solar —Solar irradiance / W·m 2

[0147] —Radiative transfer factor of solar irradiance control volume l to droplet layer control volume i

[0148] In the energy conservation equation of the control volume, the volume and density of the droplet layer control volume i are given by the PDMS thermophysical properties and the geometric properties of the droplet layer. The enthalpy is calculated based on the PDMS thermophysical properties and the control volume temperature. The control volume temperature is the dependent variable, and time is the independent variable. The total number of control volumes is given by the method of dividing the control volumes. The total emission surface area of ​​the control volumes is given by the geometric properties of the droplet layer. The emissivity of the control volumes is given by the PDMS thermophysical properties and the thermophysical properties of the surface materials of the droplet generator and droplet collector.

[0149] The radiative transfer factor was obtained through Monte Carlo ray tracing simulation. In Monte Carlo ray tracing, the geometric model of the simulated object is given by the established geometric model of the droplet layer. For non-gray body emission, non-gray body absorption, and anisotropic scattering transport conditions, the gray body assumption and isotropic scattering assumption in the usual Monte Carlo ray tracing method for solving droplet radiators do not hold. Therefore, for the non-gray body emission process, the emitted light wavelength is re-solved using the Monte Carlo ray tracing method and the emission characteristics of the liquid working fluid in the space droplet radiator.

[0150]

[0151] In the formula:

[0152] E emissive —Emission characteristics of liquid working fluid in space droplet radiators

[0153] Random—random numbers generated in Monte Carlo ray tracing.

[0154] λ — wavelength of emitted light / m

[0155] For non-gray volume absorption and anisotropic scattering transport processes, the method of changing the droplet layer absorption factor, extinction factor, and droplet scattering phase function input into the Monte Carlo method is employed. These three parameters should be re-solved based on the droplet geometry model and PDMS thermal properties, using Mie scattering theory.

[0156]

[0157] α λ =1.5Q aλ f v / D d (4)

[0158] K λ =1.5(Q) aλ +Q sλ )f v / D d (5)

[0159] In the formula:

[0160] D d —Droplet diameter / m

[0161] λ—Incident light wavelength / m

[0162] n optical,λ ,k optical,λ —Real and imaginary parts of the complex refractive index of PDMS working fluid at the incident light wavelength

[0163] φ λ (θ,η)——PDMS droplet scattering phase function

[0164] Q aλ —Droplet absorption cross section / m 2

[0165] Q sλ —Droplet scattering cross section / m 2

[0166] α λ —Droplet layer absorption factor / m

[0167] K λ — Droplet layer extinction factor / m

[0168] f v —Droplet volume fraction

[0169] Solar irradiance is:

[0170]

[0171] In the formula:

[0172] P0 – Solar irradiance at 1 AU (Earth-Sun distance) / W·m 2

[0173] R—AU (Earth-Sun distance) is the distance from the Sun to a space-based reactor system in units.

[0174] Step 2: Perform rapid iterative calculations based on the radiation heat dissipation model of the space droplet radiator to obtain the steady-state temperature field of the droplet layer;

[0175] For the radiative heat dissipation model of the space droplet radiator established in step 1, assuming that the temperature of the droplet layer control volume has reached a steady-state constant, the time term dt is replaced by the droplet flight velocity:

[0176]

[0177] In the formula:

[0178] u i —Droplet layer control volume i Droplet flight speed

[0179] dt——Time is longer than a walk

[0180] dx — the length of the droplet layer control volume i traveling at the droplet's velocity during time dt.

[0181] According to equation (7), the droplet layer control body i moves by dx along the droplet flight velocity after time dt. Based on this, the new position reached by the droplet layer control body i after time dt is determined, and the droplet layer control body that coincides with the droplet layer control body i at the new position is denoted as droplet layer control body i. dt Based on this, the radiation heat dissipation model of the space droplet radiator is discretized into a steady-state iterative equation:

[0182]

[0183] In the formula:

[0184] —Droplet layer control volume i at the (m+1)th iteration dt enthalpy value

[0185] —Enthalpy of droplet layer control volume i at the m-th iteration

[0186] Enthalpy value at the m-th iteration Based on the temperature at the m-th iteration By solving the PDMS thermophysical properties, the enthalpy value at the (m+1)th iteration can be obtained according to equation (8).

[0187] When the droplet layer control body i is in close contact with the droplet generator, it is assumed that the temperature of the droplet layer control body is equal to the outlet temperature of the droplet generator.

[0188] T i =T in,generator (9)

[0189] T i —Temperature of droplet layer control volume i

[0190] T in,generator — Droplet generator outlet temperature

[0191] For the steady-state temperature field solution process, it is not required that the data at each iteration step have specific meanings regarding the transient droplet radiator's performance. Therefore, a fast iteration method is adopted. Even if the chosen dt makes dx exactly the distance between the two droplet layer control volumes in the direction of the droplet's flight velocity, the droplet layer control volume i at this time... dt The droplet layer control volume i+1 is exactly adjacent to droplet layer control volume i along the droplet velocity direction. At this point, the solution is started from the droplet generator exit along the droplet flight velocity direction within the droplet layer. After solving, the solution is directly... Assign to And utilize reassignment Continue solving using equation (8) The change in enthalpy of the entire droplet layer was recorded between the two iterations.

[0192] in:

[0193] —Enthalpy of droplet layer control volume i+1 at the (m+1)th iteration

[0194] —The enthalpy of droplet layer control volume i+1 at the m-th iteration

[0195] —The enthalpy of the droplet layer control volume i+2 at the (m+1)th iteration

[0196] When the error is less than 10 -6 When the enthalpy field of the droplet layer has converged, it is considered that the convergence criterion is:

[0197]

[0198] h i m+1 —Enthalpy of droplet layer control volume i in the (m+1)th iteration

[0199] h i m —Enthalpy of droplet layer control volume i in the m-th iteration

[0200] Compared to calculating the control volume of the entire droplet layer in m iterations. Then based on calculate In the rapid iterative step-by-step assignment method, the enthalpy value at each step cannot represent the process of the droplet layer's enthalpy changing over time. However, under convergence conditions, it conforms to the steady-state iterative equation proposed in this step, which can greatly reduce the amount of computation.

[0201] The temperature distribution of the droplet layer at an outlet temperature of 360 K is calculated in the width-thickness cross section and in the droplet velocity-width cross section as follows: Figure 4 As shown, Figure 4 (a) shows the temperature distribution of the droplet layer on the thickness-width section under steady-state calculation, with the coordinates from top to bottom being 0m, 25m, 50m, 75m, and 100m in the direction of droplet flight velocity. Figure 4 Figure (b) shows the temperature distribution of the central layer of the droplet in the droplet velocity-width cross section when the coordinates of the droplet layer in the thickness direction are taken at half the value under steady-state calculation.

[0202] Step 3: Based on the steady-state temperature field, change the inlet temperature of the droplet generator and perform time step iterations, saving the transient temperature field during the iteration process;

[0203] The radiative heat dissipation model of the space droplet radiator established in step 1 is discretized in time:

[0204]

[0205] —Enthalpy of the iterative droplet layer control volume idt at time t+dt

[0206] — The enthalpy of the droplet layer control volume i at time t.

[0207] Assuming that at t=0, the temperature of each droplet layer control volume i is either the given initial temperature or the temperature calculated in step 2 during steady-state operation, the initial enthalpy of each droplet layer control volume i can be calculated based on the temperature and PDMS thermophysical properties. Based on equation (11), the droplet layer temperature is retained in each step of the solution, that is, the transient temperature change of all droplet control volumes i at the time step is solved.

[0208] This example uses a cold start condition. It assumes the droplet radiator starts at a cold temperature of 200K, with the initial temperature of each droplet layer control volume i at 200K, making the droplet generator inlet temperature 360K. The transient temperature field change of the droplet layer from the start-up condition to the steady-state condition is calculated, eventually reaching a steady state. Figure 4 , Figure 5 , Figure 6 , Figure 7 , Figure 8 As shown, the temperature fields were calculated for times of 2.5s, 5s, 7.5s, 10s, and 13.6s (convergence steady state). In each group of figures, Figure (a) shows the temperature distribution of the droplet layer on the thickness-width cross section under steady-state calculation, with coordinates from top to bottom representing the droplet velocity direction: 0m, 25m, 50m, 75m, and 100m. Figure 4 (a) The temperature distributions at 25m, 50m, 75m, and 100m overlap. Figure 5 (a) The temperature distributions at 50m, 75m, and 100m overlap. Figure 6 Figure (a) shows the temperature distributions at 75m and 100m, which overlap. Figure (b) shows the temperature distribution of the droplet center layer on the droplet velocity-width cross section when the coordinates of the droplet layer in the thickness direction are halved under steady-state calculation. As can be seen from the figure, the temperature field after the cold start calculation converges is basically the same as the inlet temperature of 360K in step 3. The transient operating characteristics can be calculated based on this temperature field.

[0209] Step 4: Calculate the transient operating performance of the space droplet radiator based on the transient temperature field;

[0210] The transient operating characteristics that need to be calculated for the space droplet radiator system include transient temperature distribution, transient droplet collector outlet average enthalpy, and transient radiative force of the droplet layer; the enthalpy of the droplet layer control volume i at time t is obtained through step 3. The transient temperature of droplet layer control volume i can be calculated using PDMS thermophysical properties. The average enthalpy at the outlet of the transient droplet collector and the transient radiative force of the droplet layer are calculated as follows:

[0211]

[0212]

[0213] In the formula:

[0214] h t collector —The average enthalpy of the droplet collector's transient outlet at time t.

[0215] n high —Total number of droplet control volumes in the thickness direction

[0216] n wide —Total number of droplet layer control volumes in the width direction

[0217] E t power —Transient radiation force of the droplet layer at time t

[0218] —Radiative transfer factor of droplet layer control volume i to droplet layer control volume j

[0219] —Radiative transfer factor of droplet layer control volume i to surface control volume k

[0220] —Radiative transfer factor of surface control volume i to droplet layer control volume j

[0221] —Radiative transfer factor of surface control volume i to surface control volume k.

Claims

1. A method for calculating the transient operating performance of a non-gray strong scattering droplet radiator, characterized by: The anisotropic scattering and transport processes during the non-gray body emission, non-gray body absorption, and working fluid transport processes of the space droplet radiator are considered, along with the influence of solar thermal radiation. The transient operating characteristics can also be calculated. The calculation includes the following steps: Step 1: Construct a space droplet radiator radiation heat dissipation model: The space droplet radiator system includes a droplet generator, a droplet collector, a liquid storage tank, a circulating pump, a heat exchanger, and a fluid transfer pipeline. The working fluid droplets fly at a constant speed and form a droplet layer between the droplet collector and the droplet radiator. Since the radiative heat dissipation of the liquid working fluid takes place almost entirely in the droplet layer, the radiative heat transfer capacity of the space droplet radiator is determined by the radiative heat dissipation capacity of the droplet layer. Step 2: Perform rapid iterative calculations based on the radiation heat dissipation model of the space droplet radiator to obtain the steady-state temperature field of the droplet layer; Step 3: Based on the steady-state temperature field, change the inlet temperature of the droplet generator and perform time step iterations, saving the transient temperature field during the iteration process; Step 4: Calculate the transient operating performance of the space droplet radiator based on the transient temperature field; The transient operating characteristics that need to be calculated for the space droplet radiator system include transient temperature distribution, transient droplet collector outlet average enthalpy, and transient radiative force of the droplet layer; the time obtained from step 3... t Iterative droplet layer control volume i enthalpy value The thermophysical properties of the working fluid in a space droplet radiator can be used to calculate the droplet layer control volume. i transient temperature The average enthalpy at the outlet of the transient droplet collector and the transient radiative force of the droplet layer are calculated as follows: (12) (13) In the formula: --time t Transient outlet average enthalpy of droplet collector n high —Total number of droplet control volumes in the thickness direction n wide —Total number of droplet layer control volumes in the width direction --time t Transient radiation force of droplet layer —Droplet layer control volume i Control volume of droplet layer j Radiative transfer factor —Droplet layer control volume i For surface control body k Radiative transfer factor ——Surface control body i Control volume of droplet layer j Radiative transfer factor ——Surface control body i For surface control body k Radiative transfer factor —Droplet layer control volume j Total launch surface area / m 2 —Droplet layer control volume j Emission rate σ — Stefan-Boltzmann constant —Droplet layer control volume j Temperature / K.

2. The method for calculating the transient operating performance of a non-gray strong scattering droplet radiator according to claim 1, characterized in that: In step 1, for the droplet generator, droplet collector, and droplet layer, the droplet layer is divided into several cuboid droplet layer control bodies of equal size, the surfaces of the droplet generator and droplet collector are divided into several rectangular surface control bodies of equal area, and the surface of the droplet layer exposed to sunlight is divided into several rectangular solar irradiation control bodies of equal area. The sum of these three types of control bodies constitutes the established geometric model of the droplet layer. Take the droplet layer control volume in the droplet layer i The energy conservation equation of the control volume, i.e., the radiative heat dissipation model of the space droplet radiator, is as follows: (1) In the formula: Vp,i —Droplet layer control volume i Volume / m -3 —Droplet layer control volume i Density / kg·m -3 ——Control volume enthalpy value / J·kg -1 t ——Time / s -1 — Thermal radiation flux / W·m -2 Q ——Local heat source / W·m -2 N P —Total number of droplet layer control volumes N En ——Total number of surface control volumes N solar — Number of control volumes on surfaces subject to solar radiation —Droplet layer control volume j Control volume of droplet layer i Radiative transfer factor ——Surface control body k Total launch surface area / m 2 ——Surface control body k Emission rate ——Surface control body k Temperature / K ——Surface control body k Control volume of droplet layer i Radiative transfer factor —Droplet layer control volume i Total launch surface area / m 2 —Droplet layer control volume i Emission rate —Droplet layer control volume i Temperature / K —Solar Irradiance Control System l Irradiated area / K —Solar irradiance / W·m 2 —Solar Irradiance Control System l Control volume of droplet layer i Radiative transfer factor In the energy conservation equation of the control volume, the droplet layer control volume i The volume and density are given by the thermophysical properties of the working fluid of the space droplet radiator and the geometric properties of the droplet layer. The enthalpy is calculated based on the thermophysical properties of the working fluid of the space droplet radiator and the temperature of the control body. The temperature of the control body is the dependent variable and time is the independent variable. The total number of control bodies is given by the way the control bodies are divided. The total emission surface area of ​​the control bodies is given by the geometric properties of the droplet layer. The emissivity of the control bodies is given by the thermophysical properties of the working fluid of the space droplet radiator and the thermophysical properties of the surface materials of the droplet generator and the droplet collector. The radiative transfer factor was obtained by Monte Carlo ray tracing simulation, and the geometric model simulated by Monte Carlo ray tracing was given by the established droplet layer geometric model. For non-gray body emission processes, the emitted light wavelength was re-solved using Monte Carlo ray tracing and the emission characteristics of the liquid working fluid in the space droplet radiator. (2) In the formula: —Emission characteristics of liquid working fluid in space droplet radiators Random numbers generated in Monte Carlo ray tracing —Emitted light wavelength / m For non-gray body absorption and anisotropic scattering transport processes, the method of changing the droplet layer absorption factor, extinction factor, and droplet scattering phase function input into the Monte Carlo method is adopted. These three parameters should be re-solved based on the droplet geometric model and the thermal properties of the working fluid of the space droplet radiator, using Mie scattering theory. (3) (4) (5) In the formula: D d —Droplet diameter / m —The real and imaginary parts of the complex refractive index of the liquid working medium in a space droplet radiator at the incident light wavelength —Phase function of liquid working fluid droplet scattering in a space droplet radiator —Droplet absorption cross section / m 2 —Droplet scattering cross section / m 2 —Droplet layer absorption factor / m — Droplet layer extinction factor / m — Droplet volume fraction Solar irradiance is: (6) In the formula: ——1 AU Solar irradiance at Earth-Sun distance / W·m 2 R —— AU The distance from the Sun to the Earth-Sun distance is the distance between the Earth-Sun stack system and the Sun.

3. The method for calculating the transient operating performance of a non-gray strong scattering droplet radiator according to claim 1, characterized in that: Step 2 is as follows: For the radiative heat dissipation model of the space droplet radiator established in step 1, assuming that the temperature of the droplet layer control volume has reached a steady-state condition and is a constant value, the time term d is calculated using the droplet flight velocity. t Replace: (7) In the formula: —Droplet layer control volume i Droplet flight speed d t —Time is long before a walk d x ——d t Time-dependent droplet layer control volume i The length of flight at the droplet's flight speed According to equation (7), the droplet layer control volume i After time dt, the droplet moves at a velocity d. x Based on this, the droplet layer control volume was determined. i After time d t The new position reached after the motion will be aligned with the droplet layer control volume at the new position. i The overlapping droplet layer control volume is denoted as the droplet layer control volume. i Based on this, the radiation heat dissipation model of the space droplet radiator is discretized into a steady-state iterative equation: (8) In the formula: —Droplet layer control volume at the (m+1)th iteration i enthalpy value —Droplet layer control volume at the m-th iteration i enthalpy value Enthalpy value at the m-th iteration Based on the temperature at the m-th iteration The thermal properties of the working fluid in the space droplet radiator are solved, and the enthalpy value at the (m+1)th iteration is obtained according to equation (8). ; When the droplet layer control body i When in close proximity to the droplet generator, it is assumed that the temperature of the droplet layer control volume is equal to the droplet generator outlet temperature. (9) —Droplet layer control volume i temperature — Droplet generator outlet temperature A fast iterative method is used to solve the steady-state temperature field, so that the chosen d t Make dx exactly the distance between the two droplet layer control volumes in the direction of droplet flight velocity in the droplet layer = make the droplet layer control volume i It is exactly the control volume adjacent to the droplet layer along the droplet velocity direction. i droplet layer control body i+ 1. At this point, the solution is started from the droplet generator outlet along the direction of the droplet flight velocity in the droplet layer. After the solution is obtained, the result is directly... Assign to and utilize reassignment Continue solving using equation (8) And record the change in the enthalpy of the entire droplet layer between the two iterations; in: —Droplet layer control volume at the (m+1)th iteration i+ Enthalpy of 1 —Droplet layer control volume at the m-th iteration i+ Enthalpy of 1 —Droplet layer control volume at the (m+1)th iteration i+ enthalpy of 2 When the error is less than 10 -6 When the enthalpy field of the droplet layer has converged, it is considered that the convergence criterion is: (10) —The droplet layer control volume in the (m+1)th iteration i enthalpy value —The droplet layer control volume in the m-th iteration i The enthalpy value.

4. The method for calculating the transient operating performance of a non-gray strong scattering droplet radiator according to claim 1, characterized in that: Step 3 is as follows: Discretize the heat dissipation model of the space droplet radiator established in Step 1 in time: (11) --time t+dt Iterative droplet layer control volume idt enthalpy value --time t Iterative droplet layer control volume i enthalpy value Assumption t When =0, each droplet layer control volume i The temperature is either the given initial temperature or the temperature calculated in step 2 during steady-state operation. Based on the temperature and the thermophysical properties of the working fluid in the space droplet radiator, the control volume of each droplet layer can be calculated. i initial enthalpy value Based on equation (11), the droplet layer temperature is retained in each step of the solution, thus solving for all droplet control volumes. i Transient temperature changes over a time step.

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