Method for determining empirical formula of convective heat transfer coefficient in storage tank in hydrogen filling process

Abstract

The invention discloses a method for determining a convective heat transfer coefficient empirical formula in a storage tank in a hydrogen filling process, and the method comprises the following steps: S1, determining a heat transfer coefficient theoretical formula, and obtaining a heat transfer coefficient theoretical formula between hydrogen in the storage tank and a tank wall according to the energy conservation of the hydrogen in the storage tank, the method comprises the following steps: # imgabs0 # S2, determining numerical values of correction parameters in a heat exchange coefficient empirical formula, taking a heat exchange coefficient calculated by adopting a heat exchange coefficient theoretical formula (2) provided by the invention as a standard value, and then fitting heat exchange coefficient empirical formulas (3), (4) and (5) so as to determine numerical values of the parameters in the heat exchange coefficient empirical formula (3), the heat exchange coefficient empirical formula (4) and the heat exchange coefficient empirical formula (5); and S3, result verification: the empirical formula heat exchange coefficient of which the parameters are determined is adopted to simulate the temperature and pressure in the hydrogen storage tank in the hydrogen filling process, the simulation result and the experiment result are good in consistency, and the effectiveness of the empirical formula heat exchange coefficient determination method provided by the invention is explained.

Description

Technical Field

[0001] The present invention relates to the field of determining the convective heat transfer coefficient in a storage tank during hydrogen filling, and more specifically, to a method for determining an empirical formula for the convective heat transfer coefficient in a storage tank during hydrogen filling. Background Art

[0002] At present, the compressed hydrogen storage tanks of fuel cell vehicles usually store hydrogen at a pressure of 35 or 70MPa. Due to the compression effect and Joule-Thomson effect during the hydrogenation process, the temperature inside the hydrogen storage tank will increase. The Society of Automotive Engineers of the United States stipulates that during the filling process, the maximum pressure and temperature inside the hydrogen storage tank should not exceed 125% of the nominal working pressure and 85°C. Therefore, heat transfer analysis of the hydrogen storage tank charging and discharging cycle is conducive to a more comprehensive understanding of the thermal effects in the tank and the formulation of a safe and effective filling strategy. The heat transfer in the hydrogen storage tank directly determines the heat loss during the filling and discharging process, among which the heat transfer coefficient is the key to heat transfer analysis. Some studies regard it as a constant. However, sometimes a more accurate heat transfer coefficient is needed to simulate a more accurate actual hydrogen filling process. Ignoring the accuracy of the heat transfer coefficient calculation may lead to inaccurate predicted temperature of hydrogen in the tank, which will have an adverse effect on the safety of the hydrogen storage tank. However, at present, experimental research is generally used to calculate the heat transfer coefficient, with experimental measurement as the premise, complex experimental equipment, and time-consuming and laborious experimental process. Summary of the invention

[0003] In order to achieve these purposes and other advantages according to the present invention, a preferred embodiment of the present invention provides a method for determining an empirical formula for the convective heat transfer coefficient in a storage tank during hydrogen filling, comprising the following steps:

[0004] S1. Determine the heat transfer coefficient calculation formula

[0005] In the actual hydrogen filling process, both hydrogen and air will exchange heat with the tank wall through thermal convection. Assuming that there is no temperature gradient inside the hydrogen storage tank wall, that is, the tank wall temperature is uniform, the hydrogen storage tank model includes a hydrogen zone and a tank wall zone. There are two temperatures, hydrogen temperature and tank wall temperature, which is defined as a dual-zone dual-temperature model.

[0006] At this time, the hydrogen will exchange heat with the inner wall of the storage tank by thermal convection, and the energy conservation of hydrogen can be expressed as:

[0007]

[0008] Wherein, m represents the mass of hydrogen, in kg; u represents the specific internal energy of hydrogen, in J / kg; d(mu) / dt represents the change of the internal energy of hydrogen in the storage tank over time; Indicates the hydrogen inlet flow rate, in kg / s; h inrepresents the specific enthalpy of hydrogen inflow, in J / kg; T and T w Respectively represent the temperature of hydrogen and the temperature of the hydrogen storage tank wall, the unit is K; A in Represents the surface area of ​​the inner wall of the tank, in m 2 ; α in Indicates the heat transfer coefficient between hydrogen and the inner wall of the tank, in W / m 2 / K;

[0009] According to formula (1), the theoretical formula of the heat transfer coefficient between the hydrogen in the storage tank and the tank wall is obtained as follows:

[0010]

[0011] S2. Determine the value of the correction parameter in the empirical formula

[0012] The heat transfer coefficient between hydrogen and the tank wall is calculated using the heat transfer coefficient theoretical formula (2), and then the calculated heat transfer coefficient between hydrogen and the tank wall is used as a standard value to determine the correction parameters a, b and c in the heat transfer coefficient empirical formulas (3), (4) and (5);

[0013] Among them, the empirical formula of heat transfer coefficient (3) is as follows:

[0014]

[0015] Among them, α in Indicates the heat transfer coefficient between hydrogen and tank wall, in W / m 2 / K;D in Represents the inner diameter of the tank, in m; λ represents the thermal conductivity of hydrogen, in W / m / K; Re represents the Reynolds number at the inlet of the tank, ρ represents the density of hydrogen, in kg / m 3 , v represents the kinematic viscosity of hydrogen, the unit is m 2 / s, represents the mass flow rate of hydrogen in kg / s, μ represents the dynamic viscosity of hydrogen in Pa·s, d in represents the ejector diameter at the tank inlet, in meters; Pr is the Prandtl number; L in It indicates the internal length of the hydrogen storage tank, in meters; SOC indicates the filling state in the tank. and It represents the hydrogen density at rated working pressure and 15℃ and the real-time hydrogen density during filling, in kg / m 3 ; a represents the correction parameter;

[0016] The empirical formula of heat transfer coefficient (4) is as follows:

[0017]

[0018] Among them, α in Indicates the heat transfer coefficient between hydrogen and tank wall, in W / m 2 / K; Indicates the mass flow rate of hydrogen, in kg / s; p N Indicates the rated working pressure of the vehicle tank, in Pa; p on Indicates the real-time pressure in the vehicle tank, in Pa; a indicates the correction parameter;

[0019] The empirical formula for heat transfer coefficient (5) is as follows:

[0020] α in =ae -bt +c (5)

[0021] Among them, α in Indicates the heat transfer coefficient between hydrogen and tank wall, in W / m 2 / K; t represents the filling time in seconds; a, b and c are correction parameters.

[0022] Preferably, the method further comprises the following steps:

[0023] S3. Result verification

[0024] The heat transfer coefficient calculated by formula (2) is used as the standard value to fit formula (3), formula (4) and formula (5) to determine whether the results of formula (3), formula (4) and formula (5) are consistent with the result of formula (2).

[0025] Preferably, the method further comprises the following steps:

[0026] S4. If there is consistency, substitute the values ​​of correction parameters a, b and c into formula (2), formula (3) and formula (4) respectively to obtain accurate formula (3), formula (4) and formula (5).

[0027] The present invention includes at least the following beneficial effects: the heat transfer coefficient calculated by the heat transfer coefficient theoretical formula (2) proposed in the present invention is used as a standard value, which is then used to fit the empirical heat transfer coefficient formulas (3), (4) and (5) to determine the values ​​of the parameters therein, and finally the empirical heat transfer coefficient with the determined parameters is used to simulate the temperature and pressure in the hydrogen storage tank during the hydrogen filling process. The simulation results are in good agreement with the experimental results, which illustrates the effectiveness of the method for determining the empirical heat transfer coefficient proposed by us.

[0028] Other advantages, objectives and features of the present invention will be embodied in part through the following description, and in part will be understood by those skilled in the art through study and practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 In order to use the heat transfer coefficient calculated by formula (2) as the standard value, the results of fitting the empirical heat transfer coefficient formulas (3), (4) and (5) (using the data of type IV 19L tank);

[0030] Figure 2 To apply the heat transfer coefficient formulas (3), (4) and (5) with determined parameters in Table 3 to the heat transfer coefficient simulation results of a type IV 29L tank;

[0031] Figure 3 In order to apply the heat transfer coefficient formula (3) with the determined parameters in Table 3 to the hydrogen temperature simulation results of the IV type 19L tank and compare them with the experimental results;

[0032] Figure 4 In order to apply the heat transfer coefficient formula (3) with the determined parameters in Table 3 to the hydrogen temperature simulation results of the IV type 29L tank and compare them with the experimental results;

[0033] Figure 5 In order to apply the heat transfer coefficient formula (3) with the determined parameters in Table 3 to the hydrogen pressure simulation results of the IV type 19L tank and compare them with the experimental results;

[0034] Figure 6 In order to apply the heat transfer coefficient formula (3) with the determined parameters in Table 3 to the hydrogen pressure simulation results of a type IV 29L storage tank and compare them with the experimental results. DETAILED DESCRIPTION

[0035] The present invention is further described in detail below in conjunction with the accompanying drawings so that those skilled in the art can implement the invention with reference to the description.

[0036] The following description is used to disclose the present invention so that those skilled in the art can implement the present invention. The preferred embodiments described below are only examples, and those skilled in the art can think of other obvious variations. The basic principles of the present invention defined in the following description can be applied to other embodiments, variations, improvements, equivalents, and other technical solutions that do not deviate from the spirit and scope of the present invention.

[0037] Those skilled in the art should understand that, in the disclosure of the present invention, the orientation or position relationship indicated by the terms "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc. are based on the orientation or position relationship shown in the drawings, which are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation. Therefore, the above terms should not be understood as limiting the present invention.

[0038] It is to be understood that the term "one" should be understood as "at least one" or "one or more", that is, in one embodiment, the number of an element may be one, while in another embodiment, the number of the element may be multiple, and the term "one" should not be understood as a limitation on the quantity.

[0039] like Figure 1 As shown, a preferred embodiment of the present invention provides a method for determining an empirical formula for the convective heat transfer coefficient in a storage tank during hydrogen filling, comprising the following steps:

[0040] S1. Determine the theoretical formula for heat transfer coefficient

[0041] In the actual hydrogen filling process, both hydrogen and air will exchange heat with the tank wall through thermal convection. Assuming that there is no temperature gradient inside the hydrogen storage tank wall, that is, the tank wall temperature is uniform, the hydrogen storage tank model includes a hydrogen zone and a tank wall zone. There are two temperatures, hydrogen temperature and tank wall temperature, which is defined as a dual-zone dual-temperature model.

[0042] At this time, the hydrogen will exchange heat with the inner wall of the storage tank by thermal convection, and the energy conservation of hydrogen can be expressed as:

[0043]

[0044] Wherein, m represents the mass of hydrogen, in kg; u represents the specific internal energy of hydrogen, in J / kg; d(mu) / dt represents the change of the internal energy of hydrogen in the storage tank over time; Indicates the hydrogen inlet flow rate, in kg / s; h in represents the specific enthalpy of hydrogen inflow, in J / kg; T and T w Respectively represent the temperature of hydrogen and the temperature of the hydrogen storage tank wall, the unit is K; A in Represents the surface area of ​​the inner wall of the tank, in m 2 ; α in Indicates the heat transfer coefficient between hydrogen and the inner wall of the tank, in W / m 2 / K;

[0045] According to formula (1), the theoretical formula of the heat transfer coefficient between the hydrogen in the storage tank and the tank wall is obtained as follows:

[0046]

[0047] The above formula (1) can accurately calculate the heat transfer coefficient between hydrogen and the tank wall, and the calculation result can be used as a standard value to determine the parameters in the empirical formula for the heat transfer coefficient.

[0048] S2. Determine the value of the correction parameter in the empirical formula of the heat transfer coefficient

[0049] The heat transfer coefficient between hydrogen and the tank wall is calculated using the heat transfer coefficient formula (2), and then the calculated heat transfer coefficient between hydrogen and the tank wall is used as a standard value to determine the correction parameters a, b and c in the heat transfer coefficient empirical formula formula (3), formula (4) and formula (5);

[0050] Among them, the empirical formula of heat transfer coefficient (3) is as follows:

[0051]

[0052] Among them, α in Indicates the heat transfer coefficient between hydrogen and tank wall, in W / m 2 / K;D in Represents the inner diameter of the tank, in m; λ represents the thermal conductivity of hydrogen, in W / m / K; Re represents the Reynolds number at the inlet of the tank, ρ represents the density of hydrogen, in kg / m 3 , v represents the kinematic viscosity of hydrogen, the unit is m 2 / s, represents the mass flow rate of hydrogen in kg / s, μ represents the dynamic viscosity of hydrogen in Pa·s, d in represents the ejector diameter at the tank inlet, in meters; Pr is the Prandtl number; L in It indicates the internal length of the hydrogen storage tank, in meters; SOC indicates the filling state in the tank. and It represents the hydrogen density at rated working pressure and 15℃ and the real-time hydrogen density during filling, in kg / m 3 ; a represents the correction parameter;

[0053] The empirical formula of heat transfer coefficient (4) is as follows:

[0054]

[0055] Among them, α inIndicates the heat transfer coefficient between hydrogen and tank wall, in W / m 2 / K; Indicates the mass flow rate of hydrogen, in kg / s; p N Indicates the rated working pressure of the vehicle tank, in Pa; p on Indicates the real-time pressure in the vehicle tank, in Pa; a indicates the correction parameter;

[0056] The empirical formula for heat transfer coefficient (5) is as follows:

[0057] α in =ae -bt +c (5)

[0058] Among them, α in Indicates the heat transfer coefficient between hydrogen and tank wall, in W / m 2 / K; t represents the filling time in seconds; a, b and c are correction parameters.

[0059] Specifically,

[0060] The study was conducted using two types of IV hydrogen storage tanks, 19L and 29L, and their corresponding experimental data from the reference. The 19L tank was used as the experimental group to determine the correction parameters in the empirical heat transfer coefficient formulas (3), (4), and (5). The 29L tank was used as the control group to verify the applicability of the determined parameters. The initial conditions and boundary conditions of the hydrogen filling process in the reference are shown in Table 1, and the geometric parameters and physical parameters of the hydrogen storage tank are shown in Table 2.

[0061] Table 1 Initial conditions and boundary conditions of hydrogen filling process

[0062]

[0063] Table 2 Geometric parameters and physical parameters of hydrogen storage tank

[0064]

[0065]

[0066] The heat transfer coefficient formula (2) is used to calculate the heat transfer coefficient between hydrogen and the tank wall, and then it is used as the standard value to determine the parameters in formulas (3), (4) and (5) of the empirical formula heat transfer coefficient. Finally, the parameter values ​​in various empirical formula heat transfer coefficient formulas can be determined as shown in Table 3.

[0067] Table 3 takes the heat transfer coefficient calculated by formula (2) as the standard value, and fits the parameter values ​​obtained by the heat transfer coefficient of different forms of empirical formulas (using the data of IV type 19L storage tank)

[0068]

[0069] S3. Result verification

[0070] The heat transfer coefficient value calculated by formula (2) is used as the standard fitting formula (3), formula (4) and formula (5) to determine whether the results of formula (3), formula (4) and formula (5) are consistent with the result of formula (2).

[0071] Another technical solution also includes the following steps:

[0072] S4. If there is consistency, substitute the values ​​of correction parameters a, b and c into formula (3), formula (4) and formula (5) respectively to obtain accurate formula (3), formula (4) and formula (5).

[0073] Figure 1 The heat transfer coefficient value calculated by formula (2) is shown as the result of the standard fitting heat transfer coefficient formulas (3), (4) and (5). Intuitively, during the entire filling process, the results of the empirical formula heat transfer coefficients (3), (4) and (5) are consistent with the results of formula (2), among which the results of formula (3) are most consistent with formula (2).

[0074] In order to further verify the accuracy of various heat transfer coefficient formulas, we applied the heat transfer coefficient formulas (3), (4) and (5) to the 29L tank after fitting the 19L tank data to determine the specific parameters. Figure 2 It shows that during the whole filling process, the results of the empirical formulas for heat transfer coefficient (3), (4) and (5) are still consistent with the result of formula (2), among which the result of formula (3) is the most consistent with formula (2), which shows the accuracy of the parameters obtained by fitting in Table 3. Next, we use the empirical formulas for heat transfer coefficient (3), (4) and (5), which has the best effect, for further verification.

[0075] Figure 3 and Figure 4 The simulated hydrogen temperature using the empirical heat transfer coefficient formula (3) with parameter values ​​determined in Table 3 was compared with the experimental value in the reference. In general, at other filling times except the end of the filling period, there is a certain error between the simulated value and the experimental value, with the maximum error of about 10°C for the 19L tank and about 5°C for the 29L tank. However, at the end of the filling period, the simulated value of the final hydrogen temperature is in good agreement with the experimental value, and the final value of the hydrogen temperature is exactly what we need to focus on.

[0076] Figure 5 and Figure 6The hydrogen pressure simulated by the empirical heat transfer coefficient formula (3) with parameter values ​​determined in Table 3 was compared with the experimental value of the reference. In general, at other filling times except the end of the filling period, the maximum error between the simulation value and the experimental value is only about 1 MPa, and at the end of the filling period, the simulation value is very consistent with the experimental value.

[0077] Although the embodiments of the present invention have been disclosed as above, they are not limited to the applications listed in the specification and the implementation modes, and they can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily implemented. Therefore, without departing from the general concept defined by the claims and the scope of equivalents, the present invention is not limited to the specific details and the illustrations shown and described herein.

Claims

1. A method for determining an empirical formula for the convective heat transfer coefficient in a storage tank during hydrogen filling, characterized in that: The following steps are involved: S1. Determine the theoretical formula for heat transfer coefficient In the actual hydrogen filling process, both hydrogen and air will exchange heat with the tank wall through thermal convection. Assuming that there is no temperature gradient inside the hydrogen storage tank wall, that is, the tank wall temperature is uniform, the hydrogen storage tank model includes the hydrogen area and the tank wall area, and there are two temperatures: hydrogen temperature and tank wall temperature. At this time, the hydrogen will exchange heat with the inner wall of the storage tank by thermal convection, and the energy conservation of hydrogen can be expressed as: Wherein, m represents the mass of hydrogen, in kg; u represents the specific internal energy of hydrogen, in J / kg; d(mu) / dt represents the change of the internal energy of hydrogen in the storage tank over time; Indicates the hydrogen inlet flow rate, in kg / s; h in represents the specific enthalpy of hydrogen inflow, in J / kg; T and T w Respectively represent the temperature of hydrogen and the temperature of the hydrogen storage tank wall, the unit is K; A in Represents the surface area of ​​the inner wall of the tank, in m 2 ; α in Indicates the heat transfer coefficient between hydrogen and the inner wall of the tank, in W / m 2 / K; According to formula (1), the theoretical formula of the heat transfer coefficient between the hydrogen in the storage tank and the tank wall is obtained as follows: S2. Determine the value of the correction parameter in the empirical formula of the heat transfer coefficient The heat transfer coefficient between hydrogen and the tank wall is calculated using the heat transfer coefficient theoretical formula (2), and then the calculated heat transfer coefficient between hydrogen and the tank wall is used as a standard value to determine the correction parameters a, b and c in the heat transfer coefficient empirical formulas (3), (4) and (5); Among them, the empirical formula of heat transfer coefficient (3) is as follows: Among them, α in Indicates the heat transfer coefficient between hydrogen and tank wall, in W / m 2 / K;D in Represents the inner diameter of the storage tank, in m; λ represents the thermal conductivity of hydrogen, in W / m / K; Re represents the Reynolds number at the inlet of the storage tank, ρ represents the density of hydrogen, in kg / m 3 , v represents the kinematic viscosity of hydrogen, the unit is m 2 / s, represents the mass flow rate of hydrogen in kg / s, μ represents the dynamic viscosity of hydrogen in Pa·s, d in represents the ejector diameter at the tank inlet, in meters; Pr is the Prandtl number; L in It indicates the internal length of the hydrogen storage tank, in meters; SOC indicates the filling state in the tank. and Respectively represent the hydrogen density at rated working pressure and 15°C and the real-time hydrogen density during filling, in kg / m 3 ; a represents the correction parameter; The empirical formula of heat transfer coefficient (4) is as follows: Among them, α in Indicates the heat transfer coefficient between hydrogen and tank wall, in W / m 2 / K; Indicates the mass flow rate of hydrogen, in kg / s; p N Indicates the rated working pressure of the vehicle tank, in Pa; p on Indicates the real-time pressure in the vehicle tank, in Pa; a indicates the correction parameter; The empirical formula for heat transfer coefficient is as follows: α in =ae -bt +c (5) Among them, α in Indicates the heat transfer coefficient between hydrogen and tank wall, in W / m 2 / K; t represents the filling time in seconds; a, b and c are correction parameters.

2. The method for determining the empirical formula of the convection heat transfer coefficient in the storage tank during hydrogen filling according to claim 1, characterized in that: The following steps are also included: S3. Result verification The heat transfer coefficient calculated by formula (2) is used as the standard value to fit formula (3), formula (4) and formula (5) to determine whether the results of formula (3), formula (4) and formula (5) are consistent with the result of formula (2).

3. The method for determining the empirical formula of the convection heat transfer coefficient in the storage tank during hydrogen filling according to claim 2, characterized in that: The following steps are also included: S4. If there is consistency, substitute the values ​​of correction parameters a, b and c into formula (3), formula (4) and formula (5) respectively to obtain accurate formula (3), formula (4) and formula (5).

Images