A method for determining the average flow velocity of a steady flow section in a slender uniform straight circular tube based on the principle of heat diffusion

Abstract

The present invention provides a method for determining the average flow velocity of a steady flow cross section in a slender, uniform, straight circular tube based on the principle of heat diffusion, and belongs to the technical field of flow velocity measurement. The present invention utilizes a heater to input dynamically changing heat at any position of a circular tube, and uses thermal imaging technology to synchronously and non-invasively measure the spatiotemporal distribution changes of the average cross-sectional temperature along the length direction of the slender, uniform, straight circular tube in the heating area. Based on the principles of fluid mechanics and heat transfer, a heat diffusion equation is obtained that describes the quantitative relationship between the average cross-sectional temperature along the length direction of a slender, uniform, straight circular tube and the average flow velocity of the cross section in the tube. An objective function is established based on the equation, and the average velocity of the fluid along the cross section in the slender, uniform, straight circular tube is solved by the idea of ​​minimizing the objective function in the optimization method. Furthermore, a deep neural network method is established to achieve rapid solution of the average flow velocity of the circular tube cross section based on the spatiotemporal temperature distribution of the measurement area.

Description

Technical Field

[0001] The present invention belongs to the technical field of flow velocity measurement, and relates to a method for determining the average flow velocity of a steady flow section in a slender uniform straight circular tube based on the principle of heat diffusion. The method is based on relevant principles such as fluid mechanics, heat transfer, and thermal imaging. Background Art

[0002] Slender uniform straight round tubes are widely used in chemistry, life sciences, clinical medicine and other fields. The flow behavior of liquids in slender uniform straight round tubes is crucial for the delivery of chemicals, biological agents and disease treatment drugs. Under steady flow conditions, the average velocity along the cross section of the pipe is one of the most important characteristic parameters of liquid flow in slender uniform straight round tubes. Therefore, the measurement of the average flow velocity of the cross section is of great significance for the precise control of chemical reactions and the precise control of the dosage of biological agents and drugs.

[0003] So far, there are a large number of technologies for measuring the flow rate of circular pipes (corresponding to the average flow velocity of the pipe cross section), including: electromagnetic induction flow sensing technology, ultrasonic Doppler flow sensing technology, laser Doppler flow measurement detection technology, etc. These technologies have their own advantages and have different applications for different occasions. Based on the principle of heat transfer, people have invented a method of using thermal film sensors to detect flow velocity near solid walls. However, this method requires the thermal film sensor to be implanted into the inner wall of the pipe, thereby destroying the structure of the pipe itself. This invasive method is greatly limited when applied to chemistry, life sciences, clinical medicine and other fields. Therefore, there is an urgent need for a method based on the principle of heat transfer to non-invasively detect the flow rate (or cross-sectional average flow velocity) in a uniform straight circular pipe.

[0004] The invention is based on the heat transfer theory and proposes a method for inverting the average flow velocity on the cross section of a circular tube according to the dynamic heat diffusion equation in a steady flow in a circular tube. Summary of the invention

[0005] The present invention is a method for inverting the average flow velocity on the cross section of a tube according to the dynamic heat diffusion effect in a circular tube flow field. The method is based on the heat transfer principle in a circular tube flow field to obtain a formula describing the quantitative relationship between the average flow velocity and the average temperature on the cross section of the tube; a heater is used to periodically input dynamically changing heat into a slender uniform straight circular tube to cause the temperature of the fluid in the tube to change periodically, and in the heating area along the length direction of the slender uniform straight circular tube, thermal imaging technology is used to non-invasively and synchronously measure the spatiotemporal distribution changes of the average temperature of the cross section along the length direction of the tube; an objective function is established according to the formula describing the quantitative relationship between the average flow velocity and the average temperature, and an optimization method is used to calculate the size of the average flow velocity in the tube. Furthermore, a deep neural network model can be established to accelerate the calculation, and the average flow velocity in the tube can be quickly calculated directly through the spatiotemporal distribution of the average temperature of the corresponding area of ​​the circular tube.

[0006] The technical solution of the present invention is as follows:

[0007] The present invention is a method for determining the average flow velocity of a steady flow cross section in a slender uniform straight circular tube based on the principle of heat diffusion. The flow velocity in the straight circular tube to be measured is the average flow velocity along the cross section of the slender uniform straight circular tube. Figure 1 As shown in the figure, a polar coordinate system is established with the center of the slender uniform straight circular tube as the pole, the length direction is the z axis, the radius direction is the r axis, the angle direction is the θ axis, and the inner and outer radii of the slender uniform straight circular tube are R i and R o are much smaller than (characteristic length L is R i and R o The characteristic length L is 10-100 times of the length L. The device structure is as follows Figure 2 As shown, a constant flow of fluid is introduced into the slender uniform straight round tube 1, and any position of the slender uniform straight round tube is marked as A (taken as the coordinate origin z = 0), and the heater 2 is used to periodically input heat Q (t). The transfer process of heat Q (t) in the tube wall and the liquid in the tube satisfies the energy equation

[0008]

[0009] Among them, T(r,θ,z,t) is temperature; ρ is material density; c is material specific heat capacity; t is time; U is heat diffusion velocity; κ is material thermal conductivity; heat Q(t) and temperature T(r,θ,z,t) satisfy

[0010]

[0011] Where T0. is the initial temperature of the liquid in the tube before the heater works; the heat diffusion velocity U satisfies

[0012]

[0013] In the formula, is the average velocity of the liquid flowing in the tube.

[0014] Due to the inner and outer radius R of the slender uniform straight circular tube i and R o The length of the straight tube is much smaller than the characteristic length L, and the temperature T is easy to form a uniform distribution on the cross section. Therefore, this method only considers the average temperature along the cross section of the straight tube. Defined as

[0015]

[0016] Satisfy the heat diffusion equation

[0017]

[0018] in

[0019]

[0020]

[0021] In the above formula,

[0022]

[0023] and

[0024]

[0025]

[0026]

[0027] Among them, B satisfies

[0028]

[0029] The boundary conditions are

[0030]

[0031] Furthermore, assuming that the density of the pipe wall material is w Specific heat capacity c w , thermal conductivity κ w are constants, the density of the liquid ρ f Specific heat capacity c f , thermal conductivity κ f are also constants, then the average heat diffusion velocity in equation (5) can be deduced from equations (6)-(14): satisfy

[0032]

[0033] in

[0034]

[0035]

[0036] In equation (5) satisfy

[0037]

[0038] in,

[0039]

[0040] and

[0041]

[0042]

[0043]

[0044]

[0045] like Figure 2 As shown, assuming that the heater 2 inputs periodically changing heat Q(t) at point A of the slender uniform straight circular tube 1, the average cross-sectional temperature at point A is Then the boundary condition of equation (5) is

[0046]

[0047]

[0048] like Figure 2 As shown, the infrared thermal imaging system is used to synchronously measure the continuous position ( Figure 2 The waveform of the average temperature of the cross section (the shaded position in the middle) changing with time. The spatial discrete step length along the tube length is Δz, and the time sampling step length is Δt. Then at time k, z i The average cross-sectional temperature at can be expressed as Where (i=1,2,3…N z +1, k = 1, 2, 3…N t +1). Using the finite difference method, equation (5) is approximated as:

[0049]

[0050] Then the following objective function can be constructed to solve the average flow velocity of the pipe section:

[0051]

[0052] in is the objective function and Ω is the constraint.

[0053] Set the optimization parameters and substitute the time-space distribution value of the average temperature of the cross section etc., use optimization algorithms (such as simplex method, Lagrange method, Lemke method, etc.) to optimize the objective function under constraints and obtain the optimal solution, which is t k The average cross-sectional velocity at time Similarly, repeat the optimization process by setting the optimization parameters repeatedly and substituting the average temperature distribution values ​​of the cross section at different times into the average velocity distribution values ​​of the cross section at different times.

[0054] Furthermore, a neural network can be constructed to directly calculate the average velocity of the straight circular tube section through the temporal and spatial distribution of the temperature in the straight circular tube. The artificial neural network used is a deep feedforward network, including an input layer, a hidden layer and an output layer. Figure 3 As shown in the figure, the input of the neural network is the temperature distribution of the straight circular tube at two consecutive moments; the output is the average flow velocity of the cross section at the corresponding moment. The input layer and the output layer are connected in a fully connected manner. The network between the input layer and the output layer is called the hidden layer, which is represented by z l (l=1,2,3,…,L), the size of the hidden layer actually used needs to be determined according to the sampled temperature distribution. Figure 3 The size of the hidden layer is for illustration only. The connection between two adjacent layers is as follows:

[0055] z l =σ l (W l ·z l-1 +b l ), (28)

[0056] where σ l is the activation function of the lth layer, W l represents the neural network weight vector of layer l, b l Represents the deviation value of layer l. The prediction result of the neural network is represented as the output of layer L, that is:

[0057]

[0058] in, represents the average velocity of the straight circular tube section predicted by the neural network. Next, the loss function of the neural network is constructed. In addition to the difference between the predicted value of the neural network and the true value, the heat diffusion equation (5) derived above can also be added as a penalty term to the loss function to make it have physical condition constraints. Therefore, the loss function L(W,b) is defined as follows:

[0059]

[0060] Finally, the above loss function and the constructed data set are used to train the neural network, and the optimization algorithm used in the training can be the SGD algorithm, the Adam algorithm, etc. Finally, the training is completed, and the weight parameters of the neural network are obtained. The average velocity of the pipeline section can be directly obtained by inputting the spatiotemporal distribution data of the temperature into the trained neural network.

[0061] Beneficial effects of the invention: The invention combines the heat transfer principle with fluid mechanics and establishes the relationship between the cross-sectional average flow velocity and the temporal and spatial distribution of the temperature in the straight circular tube. By using a heater to input dynamically changing heat into the straight circular tube, when there is a cross-sectional average temperature gradient caused by convection and diffusion in the slender and uniform straight circular tube, the average flow velocity in the slender and uniform straight circular tube can be accurately calculated by the method of the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 It is a schematic diagram of the geometric structure of a slender uniform straight circular tube and the polar coordinate system.

[0063] Figure 2 The figure is a schematic diagram of the device structure of the present invention. In the figure: 1 is a slender uniform straight round tube; 2 is a heater; 3 is an infrared thermal imager; and 4 is a schematic diagram of the temperature distribution of the pipeline in the measurement area.

[0064] Figure 3 It is a schematic diagram of the framework of a fully connected artificial neural network model. Its input is the spatial distribution of temperature at two consecutive moments, and its output is the average flow velocity of the pipe section at that moment. The deep neural network includes an input layer, a hidden layer, and an output layer. The number of neurons and layers in the figure are only for reference.

[0065] Figure 4 It is the result of solving the average flow velocity in the pipe section using the optimization method.

[0066] Figure 5 It is the result of using neural network to solve the average flow velocity in the pipe section. DETAILED DESCRIPTION

[0067] The following examples will further illustrate the present invention, but are not intended to limit the scope of the present invention.

[0068] This embodiment uses numerical simulation to illustrate the effectiveness of the method of the present invention, and the simulation parameter settings are consistent with the actual situation. Figure 2 As shown, the device used in this embodiment includes 4 parts. Among them, 1 is a slender uniform straight round tube of the flow rate to be measured, 2 is an (infrared) heater for inputting dynamically changing heat, 3 is an infrared thermal imager for measuring the temperature distribution of the round tube, and 4 is a schematic diagram of the obtained temperature distribution of the round tube. The slender round tube involved is a PVC round tube with an inner diameter of 2.5 mm and an outer diameter of 4 mm, wherein the fluid in the tube is water, and the specific physical parameters are shown in Table 1.

[0069] Table 1 Physical parameter values

[0070]

[0071] The average flow velocity of the steady flow section in the slender uniform straight circular tube is set to 2.1221 mm / s. At the same time, assuming that the ambient temperature is 20°C, the heater dynamically inputs heat to the fluid flowing through this area in the circular tube, so that the temperature of the fluid in the tube changes dynamically over time, that is:

[0072] T0(t)=23+3sin(0.2πt), (31)

[0073] The temperature distribution of the round tube below the heating area is measured by an infrared thermal imager with a sampling frequency of 100 Hz. The measured temperature distribution of the round tube is subjected to noise reduction and discretized with a step size of 1 mm along the length of the tube to calculate the average temperature distribution of the cross section of the round tube. The temperature change of a continuous area of ​​1 cm in length along the length of the tube in the temperature measurement area for 5 seconds is used for velocity calculation.

[0074] (I) Optimization method

[0075] For the optimization method to solve the speed. First, based on the spatial and temporal distribution data of the temperature in the area, the numerical difference method is used to calculate the first-order and second-order spatial gradients and first-order time derivatives of the temperature at each discrete point. Then, the coefficients in the heat diffusion equation (Formula 5) are calculated based on the known physical properties of the circular tube and the fluid. The unknown term in the diffusion equation is only the average flow velocity of the cross section. Therefore, t k The average flow velocity of the pipeline section at the moment is used as the optimal solution to be solved to construct the following optimization problem:

[0076]

[0077] In this example, we use the simplex method to solve the optimization problem. The solution range and the initial basic feasible solution are given according to the actual situation of pipeline flow. First, substitute the initial solution into the objective function and plan the objective function value. Then calculate the simplex multiplier and calculate the discriminant number for the non-basic variables. If the discriminant number of the basic variable is equal to zero, stop the calculation and the current basic feasible solution is the optimal solution. Otherwise, further calculate the out-of-basis variables and the in-basis variables to obtain a new basis matrix and repeat the above process. The optimal solution finally obtained is t calculated according to the spatiotemporal distribution of temperature. k Average flow velocity in the pipe section at time.

[0078] Repeat the above optimization process to calculate the average flow velocity of the pipeline section at different times during the sampling time. Finally, perform sliding average on the obtained results to obtain the following: Figure 4 The average flow velocity of the pipe section shown, the relative error of the velocity solution is 1.82%. This error is only for reference, and the actual implementation error is related to sampling accuracy, infrared imager measurement error, noise and other factors.

[0079] Compared with the neural network method, the optimization method has clear physical and mathematical mechanisms in the solution process, and does not require pre-constructed data sets for training. However, it requires the physical properties of the pipeline and fluid to be known, and has higher requirements for sampling accuracy and noise conditions.

[0080] 2. Neural Network Method

[0081] For the neural network method to solve the velocity. First, it is necessary to construct a data set for neural network training. The 22 temperature values ​​at different positions of the sampling area at two consecutive moments are used as input vectors, and the average velocity of the cross section at the corresponding moment is used as output, which together constitute a data element. 50,000 data elements are used to form the required data set, and noise reduction and normalization are performed. The training set in actual implementation can be obtained by the above optimization method or the method of measuring the temperature distribution of a given flow velocity.

[0082] The structure of the neural network is as follows Figure 3 As shown in the figure, according to the constructed temperature spatiotemporal distribution data set, the hidden layer of the neural network is set to 4 layers, and each hidden layer contains 128 neurons. The data set is randomly divided into three categories, 80% of which is used as a training set for neural network training. 10% is used as a validation set to verify whether the network is generalizing and stop training before overfitting. The last 10% is used as a test set for independent testing of the neural network. Define the loss function as shown in formula (30), use the Adam optimizer to train the neural network, and supervise the changes in the loss function value and mean square error of the training set and the validation set with the number of iterations during the training process. Use the test set to verify the accuracy of the neural network training results and predictions.

[0083] After the trained neural network is obtained, the temperature spatiotemporal distribution data of the sampled 5s is processed and input into the neural network. The output obtained is the average flow velocity of the pipeline section. The result is as follows: Figure 5 As shown in the figure, the relative error of the solution speed is 0.58%. This error is only for reference, and the actual implementation error is related to factors such as sampling accuracy and the data set used for training.

[0084] Compared with the optimization method, the neural network method is faster in the implementation process, does not need to know the exact physical properties of the pipe and fluid, and is more robust to noise. However, as a black box system, the mechanism of the neural network solution process is not clear, and the corresponding data set needs to be built in advance for network training.

Claims

1. A method for determining the average flow velocity of a steady flow section in a slender uniform straight circular tube based on the principle of heat diffusion, characterized in that: Follow these steps: The flow velocity in the straight circular tube to be measured is the average flow velocity along the cross section of the slender uniform straight circular tube. A polar coordinate system is established with the center of the slender uniform straight circular tube as the pole. The length direction is the z axis, the radius direction is the r axis, and the angle direction is the θ axis. The inner and outer radii of the slender uniform straight circular tube are R i and R o are much smaller than the characteristic length L; a constant flow of fluid is introduced into the slender uniform straight round tube (1), any position of the slender uniform straight round tube is marked as A and the coordinate origin z=0 is taken, and heat Q(t) is periodically input using a heater (2), then the heat Q(t) transfer process in the tube wall and the liquid in the tube satisfies the energy equation Among them, T(r, θ, z, t) is temperature; ρ is material density; c is material specific heat capacity; t is time; U is heat diffusion velocity; κ is material thermal conductivity; heat Q(t) and temperature T(r, θ, z, t) satisfy Where T0 is the initial temperature of the liquid in the tube before the heater works; the heat diffusion velocity U satisfies In the formula, is the average flow velocity of the liquid in the tube; Average temperature along the cross section of the straight circular tube Defined as Satisfy the heat diffusion equation in In the above formula, and Among them, B satisfies The boundary conditions are Assume that the density of the tube wall material is w Specific heat capacity c w , thermal conductivity κ w are constants, the density of the liquid ρ f Specific heat capacity c f , thermal conductivity κ f are also constants, then the average heat diffusion velocity in equation (5) can be deduced from equations (6)-(14): satisfy in In equation (5) satisfy in, and Assume that when the heater (2) inputs periodically changing heat Q(t) at point A of the slender uniform straight circular tube (1), the average cross-sectional temperature at point A is Then the boundary condition of equation (5) is In the heating area, along the length of the slender uniform straight circular tube, an infrared thermal imaging system is used to synchronously measure the waveform of the average cross-sectional temperature at continuous positions as a function of time; the spatial discrete step length along the tube length is Δz, and the time sampling step length is Δt. Then, at time k, z i The average cross-sectional temperature at can be expressed as where i = 1, 2, 3, ... N z +1, k = 1, 2, 3...N t +1; using the finite difference method, equation (5) is approximated as: Then the following objective function can be constructed to solve the average flow velocity of the pipe section: in is the objective function, Ω is the constraint; Set the optimization parameters and substitute the time-space distribution value of the average temperature of the cross section where i = 1, 2, 3, ... N z +1,; use the optimization algorithm to optimize the objective function under the constraints and get the optimal solution, which is t k The average cross-sectional velocity at time Similarly, repeat the optimization parameters, repeat the optimization process, and substitute the average temperature distribution values ​​of the cross section at different times to obtain the average velocity of the cross section at different times.

2. A method for determining the average flow velocity of a steady flow section in a slender uniform straight circular tube based on the principle of heat diffusion according to claim 1, characterized in that: A deep neural network is constructed to directly calculate the average velocity of the straight circular tube cross section through the temporal and spatial distribution of the temperature in the straight circular tube. The artificial neural network used is a deep feedforward network, including an input layer, a hidden layer and an output layer. The input of the neural network is the temperature distribution of the straight circular tube at two consecutive moments. The output is the average flow velocity of the cross section at the corresponding moment. The input layer and the output layer are connected in a fully connected manner. The network between the input layer and the output layer is called the hidden layer, which is represented by z l , l = 1, 2, 3, ..., L, the size of the hidden layer actually used needs to be determined according to the sampled temperature distribution; the connection between two adjacent layers is as follows: With l =σ l (IN l ·With l-1 +b l ), (28) where σ l is the activation function of the lth layer, W l represents the neural network weight vector of layer l, b l Represents the deviation value of layer l; the prediction result of the neural network is represented as the output of layer L, that is: in, represents the average velocity of the straight circular tube section predicted by the neural network; Construct the loss function of the neural network. In addition to the difference between the predicted value and the true value of the neural network, the heat diffusion equation (5) derived above can also be added as a penalty term to the loss function to make it have physical condition constraints. Therefore, the loss function L(W, b) is defined as follows: Finally, the neural network is trained using the above loss function and the constructed data set. Finally, the training is completed and the weight parameters of the neural network are obtained. The average velocity of the pipeline section can be directly obtained by inputting the spatiotemporal distribution data of temperature into the trained neural network.

3. The method for determining the average flow velocity of a steady flow section in a slender uniform straight circular tube based on the heat diffusion principle according to claim 1, characterized in that: The method uses a heater to non-invasively input dynamically changing heat into a slender uniform straight circular tube periodically, so that the fluid temperature in the heating area changes periodically; at the same time, in the heating area along the length direction of the slender uniform straight circular tube, thermal imaging technology is used to non-invasively and synchronously measure the changes in the temporal and spatial distribution of the average temperature of the cross section along the length of the tube; based on the dynamic heat diffusion effect in the straight circular tube flow field, the average flow velocity on the cross section of the straight circular tube is directly inverted through the temporal and spatial distribution of the average temperature of the cross section of the straight circular tube.

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