Method for assessing radioactivity based on plume dispersion pattern in limited space

Abstract

The application provides a method for evaluating radioactivity in a limited space based on a plume diffusion mode, which is mainly used for evaluating radioactivity concentration distribution in the limited space, and the method comprises the following steps: equivalent processing of a radioactivity diffusion process, regarding the radioactivity diffusion process as a plume bundle composed of a plurality of smoke clusters, and obtaining the radioactivity concentration distribution through a Gaussian smoke cluster diffusion model; improving a traditional Gaussian smoke cluster model by considering radioactivity source intensity variation, gravity settlement and environmental wind speed, considering the variation of the radioactivity intensity of the smoke cluster according to radioactivity decay, considering the offset amount of the gravity settlement to the center line of the plume according to Stokes formula, and synthesizing and superimposing diffusion speed according to the parallelogram rule to combine the environmental wind speed and the radioactivity self-diffusion speed; and superimposing the radioactivity concentrations of all the smoke clusters according to the improved smoke cluster model to evaluate the radioactivity concentration in the limited space.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of nuclear radiation protection, and particularly relates to a radioactive evaluation method based on a plume diffusion mode in a limited space. BACKGROUND

[0002] Nuclear facilities, especially when they are in a serious deviation from normal operating conditions or in an accident, will have radioactive effects on the environment and the public, so it is of great significance to evaluate nuclear radiation. The calculation of the radiation dose of radioactive airborne matter to the environment through atmospheric diffusion is an important indicator for evaluating the harm of nuclear radiation.

[0003] Radioactive hazards are different from general environmental pollution, which are often difficult to detect in advance but are fierce, and can cause serious pollution and damage to the environment and the public in a moment or a short time of emission of nuclear pollutants. In order to protect the health and safety of the public around the nuclear facilities, appropriate protective facilities need to be taken, and the prerequisite is to evaluate the pollution range and intensity of radioactivity. At present, the widely used diffusion model for nuclear evaluation is the Gaussian plume model, but the traditional Gaussian plume model is suitable for relatively uniform and stable radioactive airborne flow, and does not comprehensively consider the influence of related factors, so the reliability and accuracy of the evaluation results in actual application are often low: 1. The influence of radioactive decay is not considered, and it is often considered that the concentration of the radioactive source is stable, which does not conform to the actual situation that the concentration changes with time; 2. The influence of gravity sedimentation is not considered, when the particle size of radioactive substances is larger than a certain size, gravity sedimentation will make the center line of the plume deviate significantly, and then affect the plume diffusion path, resulting in that the radioactive concentration distribution derived by the traditional plume model is no longer applicable; 3. The influence of environmental wind speed is not considered, the superposition of environmental wind speed and the diffusion speed of radioactive substances themselves will change the diffusion trajectory and diffusion range of radioactive substances, and further affect the distribution of radioactive concentration.

[0004] The radioactive evaluation method based on the plume diffusion mode in a limited space adopts an improved Gaussian plume model, regards the radioactive plume as a group of air masses, considers the change of radioactive source intensity through the radioactive decay characteristics, and considers the offset amount of gravity sedimentation to the center line of the plume. At the same time, by superimposing the diffusion speed of radioactive substances themselves and the environmental wind speed in a limited space, the superimposed diffusion speed which plays a key role in gas diffusion is obtained, and then the concentration distribution of the diffusion of radioactive substances in space is better evaluated. SUMMARY

[0005] To address the shortcomings of traditional Gaussian plume models used for gas diffusion assessment, this invention aims to provide an improved plume model for evaluating radioactivity concentration within a confined space. This method is based on the traditional Gaussian plume model and improves upon it in three main ways: by treating the plume as individual plumes to account for changes in radioactive source concentration during diffusion; by considering the offset of the plume centerline to account for the gravitational settling effect of radioactive materials; and by superimposing the diffusion velocity of the radioactive material itself with the ambient wind speed to obtain a superimposed diffusion velocity. This approach better reflects actual diffusion conditions and provides a more accurate assessment of radioactivity intensity within a confined space.

[0006] The technical solution of the present invention includes the following process:

[0007] Step 1: Based on the plume model, the plume formed during radioactive diffusion is considered as a stream composed of continuous plumes. The concentration is obtained according to the Gaussian plume model as follows:

[0008]

[0009]

[0010] In the formula, Representing a spatial point The concentration at the location; H is the effective height; Q is the intensity of the radioactive source; This represents the rate of radioactive diffusion. These are the standard deviations of the smoke plume in the x, y, and z directions, respectively.

[0011] Step 2: Consider the change in the intensity Q of the radioactive source. In reality, the intensity of the radioactive source changes over time, generally following an exponential distribution of decay laws.

[0012]

[0013] In the formula, This is an initial estimate of the intensity of the radioactive source. The decay constant is This is the time elapsed since the beginning;

[0014] Step 3: Consider gravity settling and its impact on the plume model. Gravity settling acts on the plume diffusion trajectory, thus affecting the radioactive diffusion effect. This is considered in two steps:

[0015] Step 31: Calculate the settling velocity. The settling velocity depends on air resistance and gravity balance. Use Stokes' theorem to calculate the settling velocity:

[0016]

[0017] In the formula, Particle density; g is the acceleration of gravity; D is the particle diameter; C is the dynamic viscosity coefficient of air;

[0018] Step 32: Calculate the offset of the plume centerline, the gravitational settling effect is superimposed on the plume centerline, which causes the centerline to be offset downward, and the effect is equivalent to that the radioactive particles move vertically downward at a speed of , and the height of the downward movement is:

[0019]

[0020] wherein, is the offset height of the plume centerline, is the settling time, and is the time for moving to the coordinate x at a speed of :

[0021]

[0022] Therefore, after considering the gravitational settling, the effective height is:

[0023]

[0024] Step 4: Obtain the superimposed diffusion speed, the gas diffusion speed of the spatial point is determined by the wind speed and the diffusion speed of the gas itself, and the superimposed diffusion speed is calculated according to the wind direction, the observation point, the position and the included angle relationship of the radioactive source. In a limited space, the environmental wind speed is basically stable, and has a stable wind direction and wind speed. The calculation of the superimposed diffusion speed includes three steps:

[0025] Step 41: Determine the included angle ψ between the wind direction and the diffusion direction, according to the included angle between the spatial point, the radioactive source connecting line and the x-axis of the coordinate system with the radioactive source as the origin, and the included angle between the wind direction and the x-axis, the included angle ψ between the wind direction and the diffusion direction is obtained:

[0026]

[0027] Step 42: Determine the wind speed conversion coefficient, convert the wind speed to the spatial point, the radioactive source connecting line direction according to the principle of orthogonal decomposition, and the wind speed conversion coefficient in this direction is :

[0028]

[0029] wherein, 1 represents downwind diffusion, represents partial downwind diffusion, 0 represents no wind diffusion, -1<ψ<0 represents partial upwind diffusion, ​-1 represents the inverse wind diffusion;

[0030] Step 43: Determine the superimposed diffusion velocity, integrate the wind speed conversion coefficient and the diffusion velocity of the radioactive material itself to obtain the superimposed diffusion velocity :

[0031]

[0032] In the formula, u is the diffusion velocity of the radioactive material, and v is the wind speed;

[0033] Step 5: The concentration formula of the smoke plume model obtained after improvement in steps 2, 3, and 4:

[0034]

[0035]

[0036] Step 6: Calculate the sum of the radioactive concentration of the smoke plume in the beam, in a limited space, according to the smoke plume model, the radioactive concentration is equivalent to the accumulation of the radioactive effect of all smoke plumes in the smoke plume, within the time range [0, T] of interest, the spatial point radioactive concentration is obtained by integration.

[0037]

[0038] The radioactive diffusion process is quantitatively calculated by twice equivalent, once the radioactive diffusion process is equivalent to the smoke plume model, and once the smoke plume model is equivalent to the smoke plume beam composed of numerous smoke plumes, so that the decay characteristics of the radioactive material can be fully considered in the radioactive evaluation model.

[0039] Considering the settling effect of radioactive particles, the settling velocity is obtained by balancing the air resistance and gravity according to the Stokes formula, the settling velocity acts on the center line of the smoke plume, causing the center line of the smoke plume to produce a deviation in the vertical direction, changing the effective height of radioactive diffusion, and further affecting the radioactive concentration distribution.

[0040] Considering the influence of environmental wind speed on radioactive diffusion, through the angle between the wind direction and the diffusion direction, not only can the spatial point be known in the radioactive diffusion downwind or in the radioactive diffusion upwind, but also the superimposed diffusion velocity formed by the environmental wind speed and the diffusion velocity of the radioactive material itself, further affecting the radioactive concentration distribution of the smoke plume model, fully considering the important factor of wind speed affecting the radioactive concentration in the smoke plume model.

[0041] The radioactive diffusion effect of each smoke plume is obtained according to the improved smoke plume model, and the radioactive concentration in the limited space is the accumulation of the diffusion effect of each smoke plume. According to the time period of radioactive evaluation, all the smoke plume diffusion effects in the time period of interest are accumulated to obtain the radioactive concentration of the whole plume model, which is an important result of the radioactive evaluation in the limited space. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 The positional relationship among the environmental wind speed, the radioactive source and the space point is exemplarily shown.

[0043] Figure 2 The offset amount of the gravity settling on the center line of the plume is exemplarily shown. DETAILED DESCRIPTION

[0044] The invention content of the present application is further explained below in combination with the drawings and specific embodiments, and the method comprises the following main steps:

[0045] Step 1: Based on the smoke plume model, the plume flow formed in the radioactive diffusion process is regarded as a flow beam continuously composed of individual smoke plumes, and the concentration is obtained according to the Gaussian smoke plume model:

[0046]

[0047]

[0048] In the formula, represents the concentration at the space point ; H is the effective height; Q is the intensity of the radioactive source; is the radioactive diffusion velocity; is the standard deviation of the smoke plume in x, y and z directions, respectively;

[0049] Step 2: Considering the change of the radioactive source intensity Q, in the actual situation, the intensity of the radioactive source changes with time, and the overall exponential distribution is subject to the decay law:

[0050]

[0051] In the formula, is the initial estimation of the radioactive source intensity, is the decay constant, is the distance from the initial time;

[0052] Step 3: Considering the gravity settling and its influence on the plume model, the gravity settling acts on the diffusion trajectory of the plume, and then affects the radioactive diffusion effect, which is considered in two steps:

[0053] Step 31: Calculate the settling velocity, which depends on the balance of air resistance and gravity, and use the Stokes formula to calculate the settling velocity:

[0054]

[0055] where, is the particle density; is the gravity acceleration; D is the particle diameter; is the dynamic viscosity coefficient of air;

[0056] Step 32: Calculate the offset of the plume centerline, as shown in Figure 1 The gravitational settling effect is superimposed on the plume centerline, causing the centerline to shift downward, which is equivalent to the radioactive particles moving vertically downward at a speed of during the plume diffusion process, and the height of the downward movement is:

[0057]

[0058] where, is the plume centerline offset height, is the settling time, and is the time to move to coordinate x at a speed of :

[0059]

[0060] Therefore, after considering the gravitational settling, the effective height is:

[0061]

[0062] Step 4: Obtain the superimposed diffusion velocity, the gas diffusion velocity at a spatial point is determined by the wind speed and the gas's own diffusion velocity, as shown in Figure 2 The relationship between the wind direction, observation point, and the position and angle of the radioactive source is given, from which the superimposed diffusion velocity is calculated. In a limited space, the environmental wind speed is basically stable, with a stable wind direction and speed, and the calculation of the superimposed diffusion velocity includes three steps:

[0063] Step 41: Determine the angle ψ between the wind direction and the diffusion direction, according to the angle between the space point, the radioactive source connecting line, and the x-axis of the coordinate system with the radioactive source as the origin, and the angle between the wind direction and the x-axis, the angle ψ between the wind direction and the diffusion direction is obtained:

[0064]

[0065] Step 42: Determine the wind speed conversion coefficient, convert the wind speed to the direction of the space point, the radioactive source connecting line according to the principle of orthogonal decomposition, and the wind speed conversion coefficient in this direction is :

[0066]

[0067] In the formula, 1 represents downwind diffusion, represents partial downwind diffusion, 0 represents no wind diffusion, -1 < u < 0 represents partial upwind diffusion, -1 represents upwind diffusion;

[0068] Step 43: Determine the superimposed diffusion velocity, integrate the wind speed conversion coefficient and the diffusion velocity of the radioactive material itself to obtain the superimposed diffusion velocity :

[0069]

[0070] In the formula, u is the diffusion velocity of the radioactive material, and v is the wind speed;

[0071] Step 5: The smoke plume model concentration formula obtained after improvement in steps 2, 3, and 4:

[0072]

[0073]

[0074] Step 6: Calculate the sum of the smoke plume radioactivity concentration in the smoke plume beam. In a limited space, according to the smoke plume model, the radioactivity concentration is equivalent to the accumulation of the radioactivity effect of all smoke plumes in the smoke plume. If one smoke plume is generated per unit time, then from the initial time to the T time, a total of N smoke plumes are generated, and the space point radioactivity concentration is obtained by summation.

[0075]

[0076] The radioactive diffusion process is quantitatively calculated by twice equivalent, once the radioactive diffusion process is equivalent to the smoke plume model, and once the smoke plume model is equivalent to the smoke plume beam composed of numerous smoke plumes, so that the decay characteristics of the radioactive material can be fully considered in the radioactive evaluation model.

[0077] Considering the settling effect of radioactive particles, the settling velocity is obtained by balancing the air resistance and gravity according to the Stokes formula. The settling velocity acts on the smoke plume center line, causing the smoke plume center line to produce a deviation in the vertical direction, changing the effective height of radioactive diffusion, and further affecting the radioactive concentration distribution.

[0078] Considering the influence of environmental wind speed on radioactive diffusion, through the angle between the wind direction and the diffusion direction, not only can we know whether the space point is in the downwind direction of radioactive diffusion or in the upwind direction of radioactive diffusion, but also can we combine the environmental wind speed and the diffusion speed of the radioactive itself to form the superposition diffusion speed, which further influences the radioactive concentration distribution of the plume model. The important factor of wind speed influencing the radioactive concentration is fully considered in the plume model.

[0079] According to the improved plume model, the radioactive diffusion effect of each plume is obtained, and the radioactive concentration in the limited space is the accumulation of the diffusion effect of each plume. According to the time period of radioactive evaluation, the diffusion effects of all plumes in the concerned time period are accumulated to obtain the overall radioactive concentration of the plume model, which is an important result of the radioactive evaluation in the limited space.

Claims

1. A method for evaluating radioactivity concentration in a limited space based on a plume diffusion model, for evaluating radioactivity concentration in a limited space, characterized by, The process comprises the following steps: Step 1: Based on the plume model, the plume formed in the radioactive diffusion process is regarded as a flow beam composed of a plurality of plumes in succession, and the concentration is obtained according to the Gaussian plume model: ； ； where C(x, y, z) represents the concentration at spatial point H is the effective height; Q is the intensity of the radioactive source; is the radioactive diffusion velocity; is the standard deviation of the cloud in the x, y, z directions, respectively; Step 2: Considering the change of the radioactive source intensity Q, in the actual situation, the intensity of the radioactive source changes with time, and the overall distribution is subject to the exponential distribution of the decay law: ； wherein is the initial estimate of the source strength, is the decay constant, is the time since the initial time; Step 3: Considering the effect of gravity settling and its effect on the plume model, the gravity settling acts on the diffusion trajectory of the plume, and further affects the radioactive diffusion effect, which is considered in two steps: Step 31: Calculate the settling velocity, which depends on the balance of air resistance and gravity, and the settling velocity is calculated by using the Stokes formula: ； wherein is the particle density; is the acceleration due to gravity; D is the particle diameter; is the dynamic viscosity coefficient of air; Step 32: Calculate the offset of the plume centerline, the gravitational settling effect superimposed on the plume centerline, resulting in the centerline offset downward, the effect is equivalent to the radioactive particles in the process of plume diffusion, vertically downward movement at a speed of , the height of the downward movement is: ； wherein is the plume centerline offset height, is the settling time, is the velocity Time to move to coordinate x: ； Therefore, after considering the gravity settling, the effective height is: ； Step 4: Obtain the superimposed diffusion velocity, the gas diffusion velocity of the space point is determined by the wind speed and the diffusion velocity of the gas itself, and the superimposed diffusion velocity is calculated according to the relationship between the wind direction, the observation point, the position and the angle of the radioactive source. In a limited space, the environmental wind speed is basically stable, with a stable wind direction and speed, and the calculation of the superimposed diffusion velocity includes three steps: Step 41: Determine the angle ψ between the wind direction and the direction of dispersion, according to the angle between the spatial point, the connecting line of the radioactive source and the x-axis of the coordinate system with the radioactive source as the origin , and the angle between the wind direction and the x-axis , to obtain the angle ψ between the wind direction and the direction of dispersion: ； Step 42: determining the wind speed conversion factor, converting the wind speed to the direction of the space point and the radiation source connecting line according to the principle of orthogonal decomposition, the wind speed conversion factor in this direction : ； wherein 1 indicates downwind diffusion, 0.5 indicates partial downwind diffusion, 0 indicates no wind diffusion, -1 -0.5 indicates partial upwind diffusion, -1 indicates upwind diffusion; Step 43: determine the superimposed diffusion velocity, integrate the wind speed conversion coefficient and the diffusion velocity of the radioactive material itself to obtain the superimposed diffusion velocity : ； In the formula, u is the diffusion velocity of the radioactive material, and v is the wind speed; Step 5: The plume model concentration formula obtained after improvement in steps 2, 3 and 4: ； ； Step 6: Calculate the sum of the radioactive concentration of the plume in the plume beam, in a limited space, according to the plume model, the radioactive concentration is equivalent to the cumulative effect of all the plumes in the plume, and in the time range [0, T] concerned, the space point radioactive concentration is obtained by integration: 。 2. The method for assessing radioactivity based on plume dispersion pattern in a confined space according to claim 1, characterized in that The radioactive diffusion process is quantitatively calculated by twice equivalent, once the radioactive diffusion process is equivalent to the plume model, and once the plume model is equivalent to the plume beam composed of a large number of plumes, so that the decay characteristics of the radioactive material can be fully considered in the radioactive evaluation model.

3. The method for assessing radioactivity based on plume dispersion pattern in a confined space according to claim 1, characterized in that Considering the settling effect of radioactive particles, the settling velocity is obtained by the balance of air resistance and gravity according to the Stokes formula, the settling velocity acts on the center line of the plume, so that the center line of the plume is offset in the vertical direction, the effective height of the radioactive diffusion is changed, and the radioactive concentration distribution is further affected.

4. The method for assessing radioactivity based on plume dispersion pattern in a confined space according to claim 1, characterized in that Considering the effect of environmental wind speed on radioactive diffusion, through the angle between the wind direction and the diffusion direction, not only can the space point be known in the radioactive diffusion downwind or in the radioactive diffusion upwind, but also the superimposed diffusion velocity is formed by combining the environmental wind speed and the diffusion velocity of the radioactive material, which further affects the radioactive concentration distribution of the plume model, and the important factor of wind speed affecting the radioactive concentration is fully considered in the plume model.

5. The method for assessing radioactivity based on plume dispersion pattern in a confined space according to claim 1, characterized in that According to the improved plume model, the radioactive diffusion effect of each plume is obtained, and the radioactive concentration in a limited space is the cumulative effect of each plume diffusion, according to the time period of radioactive evaluation, the diffusion effect of all the plumes in the concerned time period is accumulated, and the overall radioactive concentration of the plume model is obtained, which is an important result of the radioactive evaluation in a limited space.

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