Pressure drop prediction method for continuous gradient porous structure in flowing direction

Abstract

The invention belongs to the technical field of porous structure heat exchangers, and provides a pressure drop prediction method for a continuous gradient porous structure in the flowing direction, and the method comprises the steps: calculating the pressure drop of each single-porosity porous structure at different inlet fluid velocities, and building a correlation between the inlet fluid velocities of the single-porosity porous structures and the pressure drops; calculating an inertia coefficient and a permeability coefficient of each single-porosity porous structure; drawing an inertia coefficient-porosity graph and a permeability coefficient-porosity graph, and performing linear fitting to obtain an inertia coefficient-porosity fitting curve and a permeability coefficient-porosity fitting curve; calculating an average inertia coefficient and an average permeability coefficient; and constructing a continuous gradient porous structure model, inputting the average inertia coefficient and the average permeability coefficient into the continuous gradient porous structure model to obtain a continuous gradient porous structure prediction model, and predicting the pressure drop of the continuous gradient porous structure. According to the method, the experiment and simulation cost can be reduced, and the prediction speed is higher.

Description

Technical Field

[0001] The invention belongs to the technical field of porous structure heat exchangers, and specifically discloses a method for predicting the pressure drop of a continuous gradient porous structure along a flow direction. Background Art

[0002] Pressure drop is a very important indicator in the design of porous structure heat exchangers, which involves key issues such as energy consumption in the heat exchange system used. The porous structure in the porous structure heat exchanger includes uniform porous structure and non-uniform porous structure. At present, the pressure drop prediction models for uniform porous structure include Ergun equation, Darcy equation and Darcy-Forchheimer equation. In recent years, research on non-uniform porous structure has become a hot topic, and some people have invented a modeling method for continuous gradient structure. For example, patent CN117906417A discloses a porous medium heat exchanger based on gradient skeleton diameter lattice unit structure. However, there are few reports on the pressure drop prediction method of continuous gradient porous structure along the flow direction. At present, the pressure drop data prediction of continuous gradient porous structure can only be carried out by experimental or simulation methods. It is impossible to quickly and accurately predict the pressure drop of continuous gradient porous structure along the flow direction, and the experimental method requires 3D printing, which greatly increases the cost, and the quality of 3D printing is uneven, and the pressure drop value cannot be accurately obtained. In view of the above-mentioned problems, it is necessary to study and design a new pressure drop prediction method for continuous gradient porous structures along the flow direction to overcome the problems existing in the existing pressure drop prediction of continuous gradient porous structures. Summary of the invention

[0003] In order to solve the problem that the existing prediction method of the pressure drop of the continuous gradient porous structure is complicated and cannot be predicted quickly and accurately, the present invention proposes a method for predicting the pressure drop of the continuous gradient porous structure along the flow direction.

[0004] The present invention provides a method for predicting the pressure drop of a continuous gradient porous structure along a flow direction, comprising the following steps: S1. establishing physical models of single porosity porous structures of different specifications, calculating the pressure drop of each single porosity porous structure at different inlet fluid velocities, and establishing a correlation between the inlet fluid velocity and the pressure drop of the single porosity porous structure; S2. calculating the inertia coefficient and permeability coefficient of each single porosity porous structure according to the correlation between the inlet fluid velocity and the pressure drop of the single porosity porous structure obtained in step S1; S3. According to the inertia coefficient and permeability coefficient obtained in step S2, a coefficient of inertia-porosity diagram and a permeability-porosity diagram are drawn respectively. After the drawing is completed, the data in the coefficient of inertia-porosity diagram and the permeability-porosity diagram are linearly fitted to obtain a coefficient of inertia-porosity fitting curve and a permeability-porosity fitting curve; S4. Calculate the average inertia coefficient and average permeability coefficient of the single porosity porous structure of all specifications established in step S1 according to the inertia coefficient-porosity fitting curve and permeability coefficient-porosity fitting curve obtained in step S3; S5. Construct a continuous gradient porous structure model, input the average inertia coefficient and average permeability coefficient obtained in step S4 into the continuous gradient porous structure model to obtain a continuous gradient porous structure prediction model, and predict the pressure drop of the continuous gradient porous structure by using the continuous gradient porous structure prediction model.

[0005] According to a method for predicting the pressure drop of a continuous gradient porous structure along a flow direction in some embodiments of the present application, in step S1, the single porosity porous structure is selected from one of a Weaire-Phelan lattice structure, a Kelvin lattice structure and a BCC lattice structure.

[0006] According to a method for predicting the pressure drop of a continuous gradient porous structure along a flow direction in some embodiments of the present application, in step S1, the porosity range of the single porosity porous structure is: 0.7~0.95.

[0007] According to a method for predicting the pressure drop of a continuous gradient porous structure along the flow direction in some embodiments of the present application, in step S1, the correlation between the inlet fluid velocity and the pressure drop of the single porosity porous structure is as shown in formula (1): (1) in, is the pressure drop per unit length, represents the dynamic viscosity of the fluid, represents the permeability coefficient, is the inlet fluid velocity, represents the density of the fluid, represents the coefficient of inertia.

[0008] According to some embodiments of the present application, a method for predicting the pressure drop of a continuous gradient porous structure along the flow direction, in step S2, the calculation of the inertia coefficient and permeability coefficient of each of the single porosity porous structures includes plotting the pressure drop and inlet fluid velocity data of each specification of the single porosity porous structure in a pressure drop-velocity diagram, fitting the data in the pressure drop-velocity diagram to obtain the pressure drop-velocity curve of each specification of the single porosity porous structure, and interpreting the linear coefficient and quadratic coefficient of each pressure drop-velocity curve through the correlation between the inlet fluid velocity and the pressure drop of the single porosity porous structure to obtain the inertia coefficient and permeability coefficient of the single porosity porous structure.

[0009] According to a method for predicting the pressure drop of a continuous gradient porous structure along a flow direction in some embodiments of the present application, in step S3, the fitting determination coefficient of the linear fitting is greater than 0.999.

[0010] According to a method for predicting the pressure drop of a continuous gradient porous structure along the flow direction in some embodiments of the present application, in step S4, the average permeability coefficient of the single porosity porous structure is as shown in formula (2): (2) in, represents the average permeability coefficient, represents the end porosity along the flow direction, represents the initial porosity along the flow direction, represents the permeability coefficient, Function expression representing the permeability-porosity fitting curve.

[0011] According to a method for predicting the pressure drop of a continuous gradient porous structure along the flow direction in some embodiments of the present application, in step S4, the average inertia coefficient of the single porosity porous structure is as shown in formula (3): (3) in, represents the average inertia coefficient, represents the end porosity along the flow direction, represents the initial porosity along the flow direction, represents the inertia coefficient, Function expression representing the inertia coefficient-porosity fitting curve.

[0012] According to a method for predicting a pressure drop of a continuous gradient porous structure along a flow direction in some embodiments of the present application, in step S5, the porosity of the continuous gradient porous structure along the flow direction changes continuously according to a linear function.

[0013] According to a method for predicting the pressure drop of a continuous gradient porous structure along the flow direction in some embodiments of the present application, in step S5, the continuous gradient porous structure prediction model is shown in formula (4): (4) in, represents the predicted pressure drop per unit length, represents the dynamic viscosity of the fluid, represents the average permeability coefficient, is the inlet fluid velocity, represents the density of the fluid, represents the mean inertia coefficient.

[0014] The present invention proposes a method for predicting the pressure drop of a continuous gradient porous structure along the flow direction. When the pressure drop parameters of a single porosity porous structure are determined, the pressure drop parameters of the continuous gradient porous structure can be obtained without other simulation or experimental means, and the pressure drop in any gradient range can be obtained. The present invention also proves that for a continuous gradient structure, as long as the average inertia coefficient and the average permeability coefficient of its variable characteristic parameters in the interval are determined, the macroscopic characteristics of the continuous gradient structure can be obtained, which provides ideas for research other than the flow resistance characteristics of the continuous gradient structure. In addition, the pressure drop prediction data obtained by the prediction method of the present invention is accurate and has great application potential, and can effectively guide the design of porous structure flow components, such as the design of porous medium heat exchangers and porous medium cold plates. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a schematic flow chart of a method for predicting pressure drop of a continuous gradient porous structure along the flow direction of the present invention; Figure 2 This is a schematic diagram of the structure of the continuous gradient porous structure in Example 1 of the present invention; Figure 3 It is a schematic diagram of the pressure drop-velocity curve of the porous structure with a single porosity of each specification fitted in Example 2 of the present invention; Figure 4 It is a schematic diagram of the inertia coefficient-porosity fitting curve of the single porosity porous structure of each specification fitted in Example 2 of the present invention; Figure 5 It is a schematic diagram of the permeability coefficient-porosity fitting curve of the single porosity porous structure of each specification fitted in Example 2 of the present invention; Figure 6 This is a comparison diagram of the predicted pressure drop and the actual simulated pressure drop of the first continuous gradient porous structure model in Example 2 of the present invention; Figure 7 This is a comparison diagram of the predicted pressure drop and the actual simulated pressure drop of the second continuous gradient porous structure model in Example 2 of the present invention; Figure 8 This is a comparison diagram of the predicted pressure drop and the actual simulated pressure drop of the third continuous gradient porous structure model in Example 2 of the present invention; Fig. 9 This is a comparison chart of the predicted pressure drop and the actual simulated pressure drop of the fourth continuous gradient porous structure model in Example 2 of the present invention. DETAILED DESCRIPTION

[0016] The following embodiments of the present invention are described in further detail in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0017] Example 1: This example provides a method for predicting the pressure drop of a continuous gradient porous structure along the flow direction. Figure 1 As shown, the following steps are included: S1. Establish physical models of porous structures with single porosity of different specifications, calculate the pressure drop of each porous structure with single porosity at different inlet fluid velocities, and establish the correlation between the inlet fluid velocity and the pressure drop of each porous structure with single porosity; As a preferred embodiment of the present invention, specifically, the pressure drop of each single porosity porous structure at different inlet fluid velocities can be obtained by experiments, simulations, literature data or theoretical formulas. The single porosity porous structure is selected from one of a Weaire-Phelan lattice structure, a Kelvin lattice structure and a BCC lattice structure. The porosity range of the single porosity porous structure is 0.7-0.95. The correlation between the inlet fluid velocity and the pressure drop of the single porosity porous structure is a quadratic function with a constant term of 0, as shown in formula (1): (1) in, is the pressure drop per unit length, represents the dynamic viscosity of the fluid, represents the permeability coefficient, is the inlet fluid velocity, represents the density of the fluid, represents the coefficient of inertia.

[0018] S2. Obtaining the inertia coefficient and permeability coefficient of each single porosity porous structure according to the correlation between the inlet fluid velocity and the pressure drop of each single porosity porous structure obtained in step S1; As a preferred embodiment of the present invention, specifically, the calculation of the inertia coefficient and permeability coefficient of each single porosity porous structure includes plotting the pressure drop and inlet fluid velocity data of each specification of the single porosity porous structure in a pressure drop-velocity diagram, fitting the data in the pressure drop-velocity diagram, respectively obtaining the pressure drop-velocity curve of each specification of the single porosity porous structure, interpreting the first-order coefficient and the second-order coefficient of each pressure drop-velocity curve through the correlation between the inlet fluid velocity and the pressure drop of the single porosity porous structure, and obtaining the inertia coefficient and permeability coefficient of the single porosity porous structure. As can be seen from formula (1), the dynamic viscosity of the fluid is It is known that the permeability coefficient can be obtained by the linear coefficient of the correlation between the inlet fluid velocity and the pressure drop of a single porosity porous structure. , the density of the fluid It is known that the inertia coefficient can be obtained by the quadratic coefficient of the correlation between the inlet fluid velocity and the pressure drop of a single porosity porous structure. .

[0019] S3. According to the inertia coefficient and permeability coefficient obtained in step S2, a coefficient of inertia-porosity diagram and a permeability-porosity diagram are drawn respectively. After the drawing is completed, the data in the coefficient of inertia-porosity diagram and the permeability-porosity diagram are linearly fitted to obtain a coefficient of inertia-porosity fitting curve and a permeability-porosity fitting curve; As a preference of this embodiment, specifically, the fitting determination coefficient of the linear fitting is greater than 0.999.

[0020] S4. Calculate the average inertia coefficient and average permeability coefficient of all specifications of the single porosity porous structure established in step S1 according to the inertia coefficient-porosity fitting curve and the permeability coefficient-porosity fitting curve obtained in step S3; As a preferred embodiment of this invention, specifically, the average permeability coefficient of the porous structure with a single porosity is as shown in formula (2): (2) in, represents the average permeability coefficient, represents the end porosity along the flow direction, represents the initial porosity along the flow direction, represents the permeability coefficient, Function expression representing the permeability coefficient-porosity fitting curve; The average inertia coefficient of a single porosity porous structure is shown in formula (3): (3) in, represents the average inertia coefficient, represents the end porosity along the flow direction, represents the initial porosity along the flow direction, represents the inertia coefficient, Function expression representing the inertia coefficient-porosity fitting curve.

[0021] S5. Constructing a continuous gradient porous structure model, inputting the average inertia coefficient and the average permeability coefficient obtained in step S4 into the continuous gradient porous structure model to obtain a continuous gradient porous structure prediction model, and predicting the pressure drop of the continuous gradient porous structure by the continuous gradient porous structure prediction model; As a preferred embodiment of this embodiment, specifically, Figure 2 As shown, the porosity of the continuous gradient porous structure along the flow direction changes continuously according to a linear function; The continuous gradient porous structure prediction model is shown in formula (4): (4) in, represents the predicted pressure drop per unit length, represents the dynamic viscosity of the fluid, represents the average permeability coefficient, is the inlet fluid velocity, represents the density of the fluid, represents the mean inertia coefficient.

[0022] Example 2: This example provides a method for predicting the pressure drop of a continuous gradient porous structure along the flow direction, comprising the following steps: Physical models of porous structures with single porosity of different specifications were established respectively, with the cell size of 5 mm and the porosities of 0.7, 0.75, 0.8, 0.85, 0.9 and 0.95 respectively. ANSYS Fluent software was used to simulate and calculate the pressure drop of each porous structure with single porosity in the inlet fluid velocity range of 10-25 m / s, and establish a correlation between the inlet fluid velocity and the pressure drop of the porous structure with single porosity, such as formula (1) in Example 1. The pressure drop and inlet fluid velocity data of the porous structure with single porosity of each specification were plotted in a pressure drop-velocity diagram, and the data in the pressure drop-velocity diagram were fitted, such as Figure 3 As shown, the pressure drop-velocity curves of the single porosity porous structure of each specification are obtained respectively, and the linear coefficient and the quadratic coefficient of each pressure drop-velocity curve are interpreted by the correlation between the inlet fluid velocity and the pressure drop of the single porosity porous structure, so as to obtain the inertia coefficient and the permeability coefficient of the single porosity porous structure.

[0023] According to the inertia coefficient and permeability coefficient obtained in step S2, an inertia coefficient-porosity diagram and a permeability coefficient-porosity diagram are drawn respectively. After the drawing is completed, the data in the inertia coefficient-porosity diagram and the permeability coefficient-porosity diagram are linearly fitted respectively. The fitting determination coefficient of the linear fitting is greater than 0.999, and the inertia coefficient-porosity fitting curve and the permeability coefficient-porosity fitting curve are obtained. The inertia coefficient-porosity fitting curve is as follows: Figure 4 As shown in Figure 2, the permeability coefficient-porosity fitting curve is as follows: Figure 5 As shown, the average inertia coefficient and average permeability coefficient of the single porosity porous structure of all specifications are calculated by implementing formula (2) and formula (3) in 1.

[0024] In this embodiment, four continuous gradient porous structure models are constructed, and the gradient porosity ranges of the four continuous gradient porous structure models are respectively: 0.8~0.9, 0.75~0.95, 0.7~0.9 and 0.85~0.95.

[0025] The first continuous gradient porous structure model: the initial porosity along the flow direction is 0.9, the terminal porosity along the flow direction is 0.8, and the porosity gradient along the flow direction changes uniformly. The average inertia coefficient and average permeability coefficient are calculated for the inertia coefficient-porosity fitting curve and the permeability coefficient-porosity fitting curve in the porosity range of 0.8~0.9, respectively. The average inertia coefficient and average permeability coefficient are added to the formula (4) of the continuous gradient porous structure prediction model in Example 1 to obtain the predicted pressure drop under different inlet fluid velocities. In addition, in this implementation, a three-dimensional gradient model of a continuous gradient porous structure with an actual gradient porosity range of 0.8~0.9 is established and a simulation is performed to obtain pressure drop data. Figure 6 As shown, in this embodiment, the maximum error between the predicted pressure drop and the actual simulated pressure drop is 1.8%.

[0026] The second continuous gradient porous structure model: the initial porosity along the flow direction is 0.95, the terminal porosity along the flow direction is 0.75, and the porosity gradient along the flow direction changes uniformly. The average inertia coefficient and average permeability coefficient are calculated for the inertia coefficient-porosity fitting curve and the permeability coefficient-porosity fitting curve in the porosity range of 0.75~0.95, respectively. The average inertia coefficient and average permeability coefficient are added to the formula (4) of the continuous gradient porous structure prediction model in Example 1 to obtain the predicted pressure drop under different inlet fluid velocities. In addition, in this implementation, a three-dimensional gradient model of a continuous gradient porous structure with an actual gradient porosity range of 0.75~0.95 is established and a simulation is performed to obtain pressure drop data. Figure 7 As shown, in this embodiment, the maximum error between the predicted pressure drop and the actual simulated pressure drop is 3.0%.

[0027] The third continuous gradient porous structure model: the initial porosity along the flow direction is 0.9, the terminal porosity along the flow direction is 0.7, and the porosity gradient along the flow direction changes uniformly. The average inertia coefficient and average permeability coefficient are calculated for the inertia coefficient-porosity fitting curve and the permeability coefficient-porosity fitting curve in the porosity range of 0.7~0.9, respectively. The average inertia coefficient and average permeability coefficient are added to the formula (4) of the continuous gradient porous structure prediction model in Example 1 to obtain the predicted pressure drop under different inlet fluid velocities. In addition, in this implementation, a three-dimensional gradient model of a continuous gradient porous structure with an actual gradient porosity range of 0.7~0.9 is established and a simulation is performed to obtain pressure drop data. Figure 8 As shown, in this embodiment, the maximum error between the predicted pressure drop and the actual simulated pressure drop is 1.7%.

[0028] The fourth continuous gradient porous structure model: the initial porosity along the flow direction is 0.95, the terminal porosity along the flow direction is 0.85, and the porosity gradient along the flow direction changes uniformly. The average inertia coefficient and average permeability coefficient are calculated for the inertia coefficient-porosity fitting curve and the permeability coefficient-porosity fitting curve in the porosity range of 0.85~0.95, respectively. The average inertia coefficient and average permeability coefficient are added to the formula (4) of the continuous gradient porous structure prediction model in Example 1 to obtain the predicted pressure drop under different inlet fluid velocities. In addition, in this implementation, a three-dimensional gradient model of a continuous gradient porous structure with an actual gradient porosity range of 0.85~0.95 is established and a simulation is performed to obtain pressure drop data. Fig. 9 As shown, in this embodiment, the maximum error between the predicted pressure drop value and the actual simulated pressure drop value is 1.4%.

[0029] The embodiments of the present invention are given for the purpose of illustration and description, and are not intended to be exhaustive or to limit the invention to the disclosed forms. Many modifications and variations will be apparent to those of ordinary skill in the art. The embodiments are selected and described in order to better illustrate the principles and practical applications of the present invention and to enable those of ordinary skill in the art to understand the present invention and thereby design various embodiments with various modifications suitable for specific uses.

Claims

1. A method for predicting the pressure drop of a continuous gradient porous structure along the flow direction, characterized in that: The steps include: S1. establishing physical models of single porosity porous structures of different specifications, calculating the pressure drop of each single porosity porous structure at different inlet fluid velocities, and establishing a correlation between the inlet fluid velocity and the pressure drop of the single porosity porous structure; S2. calculating the inertia coefficient and permeability coefficient of each single porosity porous structure according to the correlation between the inlet fluid velocity and the pressure drop of the single porosity porous structure obtained in step S1; S3. According to the inertia coefficient and permeability coefficient obtained in step S2, a coefficient of inertia-porosity diagram and a permeability-porosity diagram are drawn respectively. After the drawing is completed, the data in the coefficient of inertia-porosity diagram and the permeability-porosity diagram are linearly fitted to obtain a coefficient of inertia-porosity fitting curve and a permeability-porosity fitting curve; S4. Calculate the average inertia coefficient and average permeability coefficient of the single porosity porous structure of all specifications established in step S1 according to the inertia coefficient-porosity fitting curve and permeability coefficient-porosity fitting curve obtained in step S3; S5. Construct a continuous gradient porous structure model, input the average inertia coefficient and average permeability coefficient obtained in step S4 into the continuous gradient porous structure model to obtain a continuous gradient porous structure prediction model, and predict the pressure drop of the continuous gradient porous structure by using the continuous gradient porous structure prediction model.

2. The method for predicting the pressure drop of a continuous gradient porous structure along the flow direction according to claim 1, characterized in that: In the step S1, the single porosity porous structure is selected from one of a Weaire-Phelan lattice structure, a Kelvin lattice structure and a BCC lattice structure.

3. The method for predicting the pressure drop of a continuous gradient porous structure along the flow direction according to claim 1, characterized in that: In the step S1, the porosity range of the single porosity porous structure is: 0.7~0.

95.

4. The method for predicting the pressure drop of a continuous gradient porous structure along the flow direction according to claim 1, characterized in that: In step S1, the correlation between the inlet fluid velocity and the pressure drop of the single porosity porous structure is shown in formula (1): （1） in, is the pressure drop per unit length, represents the dynamic viscosity of the fluid, represents the permeability coefficient, is the inlet fluid velocity, represents the density of the fluid, represents the coefficient of inertia.

5. The method for predicting the pressure drop of a continuous gradient porous structure along the flow direction according to claim 4, characterized in that: In step S2, the calculation of the coefficient of inertia and the coefficient of permeability of each single porosity porous structure includes plotting the pressure drop and inlet fluid velocity data of each specification of the single porosity porous structure in a pressure drop-velocity diagram, fitting the data in the pressure drop-velocity diagram to obtain the pressure drop-velocity curve of each specification of the single porosity porous structure, and interpreting the linear coefficient and the quadratic coefficient of each pressure drop-velocity curve through the correlation between the inlet fluid velocity and the pressure drop of the single porosity porous structure to obtain the coefficient of inertia and the permeability of the single porosity porous structure.

6. The method for predicting the pressure drop of a continuous gradient porous structure along the flow direction according to claim 1, characterized in that: In step S3, the fitting determination coefficient of the linear fitting is greater than 0.

999.

7. The method for predicting the pressure drop of a continuous gradient porous structure along the flow direction according to claim 1, characterized in that: In step S4, the average permeability coefficient of the single porosity porous structure is as shown in formula (2): （2） in, represents the average permeability coefficient, represents the end porosity along the flow direction, represents the initial porosity along the flow direction, represents the permeability coefficient, Function expression representing the permeability-porosity fitting curve.

8. The method for predicting the pressure drop of a continuous gradient porous structure along the flow direction according to claim 1, characterized in that: In step S4, the average inertia coefficient of the single porosity porous structure is as shown in formula (3): （3） in, represents the average inertia coefficient, represents the end porosity along the flow direction, represents the initial porosity along the flow direction, represents the inertia coefficient, Function expression representing the inertia coefficient-porosity fitting curve.

9. The method for predicting the pressure drop of a continuous gradient porous structure along the flow direction according to claim 1, characterized in that: In the step S5, the porosity of the continuous gradient porous structure along the flow direction changes continuously according to a linear function.

10. The method for predicting the pressure drop of a continuous gradient porous structure along the flow direction according to claim 1, characterized in that: In step S5, the continuous gradient porous structure prediction model is shown in formula (4): （4） in, represents the predicted pressure drop per unit length, represents the dynamic viscosity of the fluid, represents the average permeability coefficient, is the inlet fluid velocity, represents the density of the fluid, represents the mean inertia coefficient.

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