A method for estimating the flow rate of liquid nitrogen in a cryogenic wind tunnel test condition

Abstract

The application discloses a method for estimating liquid nitrogen flow of a low-temperature wind tunnel test state, belongs to the field of experimental aerodynamics, and aims to solve the problem that the proportional-integral-derivative closed loop control is adopted to adjust system output in the current low-temperature wind tunnel operation, the space difference between the total temperature measurement position and the liquid nitrogen injection position is limited, and the mixing heat transfer process leads to serious hysteresis of the total temperature control, greatly increases the liquid nitrogen consumption, and reduces the test efficiency. In combination with the high-speed airflow convection heat exchange and gas dynamics, the application aims at the liquid nitrogen flow estimation problem of the low-temperature wind tunnel, proposes a calculation method of the liquid nitrogen flow based on the target values of the total pressure, the total temperature and the Mach number, and can calculate the required liquid nitrogen flow according to the test state before the test, greatly improves the low-temperature wind tunnel test efficiency, and reduces the operation cost. The application can be quickly applied to other similar wind tunnels, has good engineering applicability, high application value and good application prospect.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of experimental aerodynamics, in particular to a method for estimating liquid nitrogen flow in a low-temperature wind tunnel test state. BACKGROUND

[0002] Compared with a conventional wind tunnel, in addition to Mach number and total pressure closed-loop control, a low-temperature wind tunnel can also achieve accurate control of operating total temperature, which plays an irreplaceable role in obtaining the influence of the Reynolds number effect of an aircraft, evaluating the boundary layer transition, and aerodynamic stability characteristics. The low-temperature wind tunnel usually uses nitrogen as the operating medium, and injects liquid nitrogen with controllable mass into the airflow to balance the heat generated by the wind tunnel compressor, the heat generated by the friction of the operating loop, and the heat conduction between the wind tunnel and the environment, thereby achieving accurate control of the operating total temperature. In this process, the liquid nitrogen flow injected into the tunnel is related to the accuracy of the total temperature control, the closed-loop time, and the supply demand, and is one of the most critical factors of the operating cost and test efficiency of the low-temperature wind tunnel.

[0003] At present, the "proportional-integral-derivative" closed-loop control is used to adjust the system output in the operation of the low-temperature wind tunnel, that is, the desired set point is reached or maintained according to the control target and the measured feedback value of the operating total temperature of the wind tunnel. This method can provide good system response characteristics, but the spatial difference between the total temperature measurement position and the liquid nitrogen injection position, as well as the mixing heat transfer process, result in serious hysteresis in the total temperature control, which brings severe challenges to the controller design and parameter optimization analysis. The reason is that the existing method lacks the initial value of the liquid nitrogen injection flow, and gradually approaches the target value of the total temperature balance through closed-loop control. Using this method, not only the liquid nitrogen consumption is greatly increased, but also the test efficiency is significantly reduced.

[0004] Therefore, there is an urgent need for a new method to solve the above problems. SUMMARY

[0005] The present application aims to solve the problem that, in the operation of the low-temperature wind tunnel, the "proportional-integral-derivative" closed-loop control is used to adjust the system output, which is limited by the spatial difference between the total temperature measurement position and the liquid nitrogen injection position, as well as the mixing heat transfer process, resulting in serious hysteresis in the total temperature control, greatly increasing the liquid nitrogen consumption, and reducing the test efficiency, by providing a method for estimating the liquid nitrogen flow in a low-temperature wind tunnel test state. The purpose of the present application is to calculate the liquid nitrogen flow demand for the total temperature closed-loop control in the operation of the low-temperature wind tunnel, to calculate the compressor inlet flow, pressure ratio, and power by using test target parameters such as total pressure, total temperature, and Mach number, and to calculate the liquid nitrogen flow by using the latent heat of vaporization of liquid nitrogen, thereby providing protection for reducing the operating cost of the low-temperature wind tunnel and improving the operating efficiency.

[0006] In order to achieve the above-mentioned purpose, the technical scheme adopted by the present application is as follows:

[0007] A method for estimating the flow of liquid nitrogen in a low-temperature wind tunnel test state, comprising the following steps:

[0008] S1, according to the wind tunnel target parameters planned in the test scheme, calculating the flow of the test section of the wind tunnel , the calculation formula is as follows:

[0009] (1) ;

[0010] In the formula, is the mass flow of the test section gas in the target state, with the unit of kg / s; is the density of the test section gas, with the unit of kg / m 3 ; is the cross-sectional area of the test section, with the unit of m 2 ; is the velocity of the test section gas, with the unit of m / s;

[0011] Combined with the ideal gas state equation, the calculation formula of the test section flow is rewritten as:

[0012] (2) ;

[0013] In the formula, is the static pressure of the test section gas, with the unit of Pa; is the test section gas constant; is the test section gas static temperature, with the unit of K; is the test section gas specific heat ratio; is the test section gas Mach number;

[0014] Using the ideal gas isentropic relationship, the test section gas static temperature and the test section gas static pressure are converted into the stagnation parameters of the stable section, and the calculation formula is as follows:

[0015] (3) ;

[0016] The formula (3) can be obtained by arranging:

[0017] (4) ;

[0018] In the formula, is the target total pressure, with the unit of Pa; is the target total temperature, with the unit of K;

[0019] S2, according to the compressor operating parameters and the wind tunnel operating parameters, calculating the corrected gas temperature rise ;

[0020] For an isentropic compression process, the temperature rise of the gas before and after the compressor is:

[0021] (5);

[0022] wherein, T1 is the total temperature of the gas upstream of the compressor, in K; T2 is the total temperature of the gas downstream of the compressor, in K; wherein, the total temperature of the gas upstream of the compressor is the total temperature of the gas downstream of the compressor ;

[0023] By using the ideal gas isentropic relationship, the total temperature ratio is converted into the total pressure ratio, and substituted into formula (5), the following formula is obtained:

[0024] (6);

[0025] wherein, P1 is the total pressure of the gas upstream of the compressor, in Pa; P2 is the total pressure of the gas downstream of the compressor, in Pa; P2 is the total pressure of the gas downstream of the compressor P2 is the total pressure of the gas downstream of the compressor P2 is the total pressure of the gas downstream of the compressor

[0026] After the temperature rise of the gas flow is corrected, the corrected temperature rise of the gas flow is obtained, and the calculation formula is as follows:

[0027] (7);

[0028] wherein, η is the compressor efficiency factor, ranging from 0 to 1;

[0029] S3, combined with the ideal gas property parameters, the compressor power is calculated, and the calculation formula is as follows:

[0030] (8);

[0031] wherein, W is the compressor power, in MW; Cp is the specific heat capacity of the gas at constant pressure, in kJ / (kg.K);

[0032] S4, assuming that the liquid nitrogen is fully vaporized after being injected into the tunnel circuit, and is uniformly mixed with the operating medium, the heat absorption amount is equal to the power of the compressor; according to the latent heat of vaporization of the gas, the liquid nitrogen flow is calculated, and the calculation formula is as follows:

[0033] (9);

[0034] After formula (9) is arranged, the following formula is obtained:

[0035] (10);

[0036] wherein, is the injected liquid nitrogen flow rate, in kg / s; is the latent heat of liquid nitrogen, in kJ / kg.

[0037] In the step S1, the nitrogen gas is injected into the wind tunnel circuit at a temperature of - 196℃. .

[0038] In the step S2, the total pressure of the compressor is measured. The definition of the total pressure ratio is the ratio of the total pressure at the inlet to the total pressure at the outlet of the compressor.

[0039] In the step S2, the compressor efficiency factor is calculated. The measured value is obtained by adjusting the wind tunnel performance.

[0040] In the step S2, it is assumed that the liquid nitrogen injected into the wind tunnel circuit is vaporized and mixed with the circuit gas to maintain temperature balance, that is, the heat generated by the work of the compressor is equal to the heat absorbed by the vaporization of liquid nitrogen.

[0041] The isentropic relationship refers to an adiabatic reversible process in thermodynamics, in which the entropy remains unchanged.

[0042] The static temperature of the test section gas refers to the temperature measured when the thermometer is relatively stationary with the airflow; the static pressure of the test section gas refers to the pressure component perpendicular to the direction of the airflow.

[0043] Currently, the low-temperature wind tunnel is operated in a constant total temperature mode, and the constant total temperature is achieved by injecting liquid nitrogen; when the test parameters are changed, the temperature imbalance is caused by changes in the compressor power, friction, heat conduction and other factors, and the liquid nitrogen flow rate needs to be quickly adjusted to meet the constant total temperature operation requirement. Therefore, the liquid nitrogen flow rate needs to be calculated in advance to reduce the closed-loop control time and reduce the operating cost.

[0044] Therefore, the present application provides a fast and reliable liquid nitrogen flow rate estimation method for a low-temperature wind tunnel, which calculates the liquid nitrogen flow rate requirement using the operating parameters of the wind tunnel. In combination with the convective heat transfer of high-speed airflow and gas dynamics, the present application proposes a calculation method for the liquid nitrogen flow rate based on the target values of total pressure, total temperature and Mach number, which can calculate the required liquid nitrogen flow rate according to the test state before the test, greatly improving the test efficiency of the low-temperature wind tunnel and reducing the operating cost.

[0045] The present application calculates the compressor power using the total temperature, total pressure and Mach number of the low-temperature wind tunnel, and combines the operating pressure ratio of the wind tunnel, the heat conduction coefficient of the tunnel wall and the structural parameters of the tunnel body to quickly determine the liquid nitrogen flow rate of the wind tunnel, which is used for total temperature control and energy consumption prediction.

[0046] The method quantitatively models the wind tunnel operation pressure ratio, thermal conductivity, latent heat of vaporization and the like, can be quickly popularized and applied to other similar wind tunnels, has good engineering applicability, and has high application value and good application prospect. BRIEF DESCRIPTION OF DRAWINGS

[0047] The application will be described by way of example and with reference to the accompanying drawings, in which:

[0048] Figure 1 is a curve graph of the compressor operating pressure ratio of a certain low-temperature wind tunnel with Mach number.

[0049] Figure 2 is a curve graph of the liquid nitrogen flow and the air temperature rise with the test Mach number. DETAILED DESCRIPTION

[0050] All features disclosed in this specification, or all steps of any methods or processes disclosed in this specification, can be combined in any manner, except where features and / or steps are mutually exclusive.

[0051] Any feature disclosed in this specification, unless specifically stated otherwise, can be replaced by an alternative feature or a feature with a similar purpose. That is, unless specifically stated otherwise, each feature is one example only of a number of equivalent or similar features.

[0052] Example 1

[0053] (I) Estimation method

[0054] The low-temperature wind tunnel utilizes the heat absorption of liquid nitrogen vaporization to balance the heat generated by the compressor, the heat generated by the friction of the running circuit, and the heat conduction between the wind tunnel and the environment; wherein the heat generated by the compressor is the main part of the heat balance. The present application predicts the liquid nitrogen injection amount in the running range of the wind tunnel under the assumptions that the running medium is an ideal gas, the pressure increasing process of the gas flow in the compressor is an isentropic process, and the liquid nitrogen vaporization is fully mixed with the gas in the wind tunnel circuit. The power generated by the compressor is related to the gas flow rate, specific heat capacity and temperature rise of the wind tunnel circuit, so it can be estimated by the operating parameters; wherein the gas flow rate of the wind tunnel circuit is calculated using the cross-sectional area, density and velocity of the test section, and the physical property parameters of the running medium are queried and exported using the data set provided by the National Institute of Standards and Technology. The relevant operations are as follows.

[0055] S1, according to the target parameters of the wind tunnel planned by the test scheme, calculate the flow rate of the test section of the wind tunnel , the calculation formula is as follows:

[0056] (1) ;

[0057] In the formula, is the mass flow rate of the test section gas under the target state, with the unit of kg / s; is the density of the test section gas, unit: kg / m 3 ; is the cross-sectional area of the test section, unit: m 2 ; is the velocity of the test section gas, unit: m / s.

[0058] Combined with the ideal gas state equation, the calculation formula of the test section flow is rewritten as:

[0059] (2);

[0060] In the formula, is the static pressure of the test section gas, unit: Pa; is the gas constant of the test section, the nitrogen gas ; is the static temperature of the test section gas, unit: K; is the specific heat ratio of the test section gas; is the Mach number of the test section gas.

[0061] Using the ideal gas isentropic relationship, the test section gas static temperature and test section gas static pressure are converted into stable section stagnation parameters, and the calculation formula is as follows:

[0062] (3);

[0063] The formula (3) can be obtained by arranging:

[0064] (4);

[0065] In the formula, is the target total pressure, unit: Pa; is the target total temperature, unit: K.

[0066] S2, according to the compressor operating parameters, wind tunnel operating parameters, calculate the corrected air temperature rise .

[0067] For isentropic compression process, the temperature rise of the gas before and after the compressor is:

[0068] (5);

[0069] In the formula, is the total temperature of the gas upstream of the compressor, unit: K; is the total temperature of the gas downstream of the compressor, unit: K; wherein, the total temperature of the gas upstream of the compressor is the total temperature of the wind tunnel ;

[0070] The total temperature ratio of the gas is converted into the total pressure ratio by using the isentropic relationship of ideal gas, and substituted into the above formula (5) to obtain the following formula:

[0071] (6);

[0072] In the formula, is the total pressure of the gas upstream of the compressor, in Pa; is the total pressure of the gas downstream of the compressor, in Pa; is the total pressure of the gas downstream of the compressor is the ratio of the total pressure of the gas downstream of the compressor to the total pressure of the gas upstream of the compressor, and is defined as the ratio of the total pressure of the compressor inlet to the total pressure of the compressor outlet.

[0073] In actual operation, since the flow in the compressor cannot reach the isentropic compression degree, the temperature rise of the gas flow needs to be corrected to obtain the corrected temperature rise of the gas flow , and the calculation formula is as follows:

[0074] (7);

[0075] In the formula, is the compressor efficiency factor, ranging from 0 to 1.

[0076] S3, the compressor power is calculated in combination with the ideal gas property parameters.

[0077] The compressor power is converted into the internal energy of the gas, and the calculation formula is as follows:

[0078] (8);

[0079] In the formula, is the compressor power, in MW; is the specific heat capacity of the gas at constant pressure, in kJ / (kg.K).

[0080] S4, the liquid nitrogen flow rate is calculated according to the latent heat of vaporization of the gas.

[0081] The liquid nitrogen injected into the wind tunnel circuit is vaporized and mixed with the circuit gas to maintain temperature balance, i.e. the heat generated by the compressor work is equal to the heat absorbed by the vaporization of liquid nitrogen: it is assumed that the liquid nitrogen is completely vaporized after being injected into the tunnel circuit, and is uniformly mixed with the operating medium, and the heat absorption is equal to the power of the compressor; the calculation formula is as follows:

[0082] (9);

[0083] After sorting, we get:

[0084] (10);

[0085] In the formula,​ is the injected liquid nitrogen flow rate, in kg / s; is the latent heat of liquid nitrogen, in kJ / kg.

[0086] The ideal gas refers to a hypothetical gas model, in which the volume of molecules and the interaction force between molecules can be ignored, and the physical property parameters meet the ideal gas state equation. The gas in the wind tunnel operating range can be regarded as an ideal gas.

[0087] The isentropic relationship refers to an adiabatic reversible process in thermodynamics, in which the entropy remains unchanged. For an ideal gas, the flow parameters in the isentropic process can be accurately calculated by combining the specific heat ratio.

[0088] The test section static temperature refers to the temperature measured when the thermometer is relatively stationary with the airflow. The test section static pressure refers to the pressure component perpendicular to the direction of airflow velocity. Both the test section static temperature and the test section static pressure can be accurately calculated by combining the total temperature and the total pressure through the isentropic relationship.

[0089] The stagnation parameter in the stable section, also known as the total parameter, refers to the thermodynamic parameters of the airflow when it is isentropically decelerated to zero velocity, including total pressure, total temperature, and total density. These parameters are crucial for wind tunnel operation and test data analysis.

[0090] The isentropic compression refers to the ideal reversible adiabatic compression process of the compressor, in which the entropy remains unchanged, representing the theoretical best compression process. In practice, due to factors such as flow separation, boundary layer friction, shock loss, leakage flow, and secondary flow, the actual compression process deviates from the isentropic process under the same pressure ratio. The compressor efficiency factor indicates the closeness, and the higher the efficiency, the closer the actual process to the isentropic process.

[0091] In order to achieve better technical effects, the Mach number, total temperature, and total pressure values of all test states should be listed in sequence during the test design process. After completing the current state test, the required liquid nitrogen flow rate is calculated according to the next target parameter, improving the efficiency of wind tunnel state conversion and shortening the time of closed-loop control and adjustment.

[0092] In order to achieve better technical effects, the estimated liquid nitrogen demand flow in this scheme is the initial value for target state adjustment control, avoiding regulation oscillation and divergence caused by large differences in target values. The latent heat of vaporization, compressor efficiency factor, and pressure ratio parameters in this scheme are measured by the low-temperature wind tunnel to improve the accuracy of liquid nitrogen flow estimation.

[0093] (II) Estimation Example

[0094] In a certain low-temperature wind tunnel, 8 tests with different operating parameters need to be carried out. The corresponding wind tunnel operating total temperature, total pressure, and Mach number for each test are shown in Table 1.

[0095] Table 1 The corresponding wind tunnel operating total temperature, total pressure and Mach number table under 8 different operating parameter conditions

[0096]

[0097] The size of the low-temperature wind tunnel is =2.2m (high) x 2.6m (wide) =5.72m 2 The wind tunnel compressor efficiency factor obtained after the wind tunnel performance debugging is =85%, the pressure ratio Changes with the test Mach number as shown in Table 2, Figure 1

[0098] Table 2 The pressure ratio Changes with the test Mach number

[0099]

[0100] According to the above Table 2, the compressor pressure ratio under the test Mach number is obtained by interpolation.

[0101] The wind tunnel operating medium is nitrogen, and the gas constant is The specific heat ratio , the constant pressure specific heat capacity , and the liquid nitrogen latent heat of vaporization corresponding to each test state are obtained by using the data set provided by the National Institute of Standards and Technology, and the results are shown in Table 3.

[0102] Table 3 The specific heat ratio , the constant pressure specific heat capacity , and the liquid nitrogen latent heat of vaporization corresponding to each test state are obtained by using the data set provided by the National Institute of Standards and Technology, and the results are shown in Table 3.

[0103]

[0104] Using the above data, the liquid nitrogen flow rate under each state is estimated according to the method proposed in the present application.

[0105] First, according to the target parameters of the wind tunnel planned in the test scheme, the wind tunnel test section flow rate is calculated, and the calculation formula is shown in formula (4), and the calculation results are shown in Table 4.

[0106] Table 4 The test section flow rate calculation results under different test conditions

[0107]

[0108] ​​​​Second step, according to the compressor operating parameters, wind tunnel operating parameters to calculate the temperature rise of airflow, the formula is shown in formula (7), the calculation results are shown in the following table 5.

[0109] Table 5 Airflow temperature rise calculation results

[0110]

[0111] Third step, combined with the ideal gas property parameters to calculate the compressor power , the formula is shown in formula (8), the calculation results are shown in the following table 6.

[0112] Table 6 Compressor power P f Calculation results

[0113]

[0114] Fourth step, according to the latent heat of gas vaporization to calculate the liquid nitrogen flow , the formula is shown in formula (10), the calculation results are shown in the following table 7.

[0115] Table 7 Liquid nitrogen flow calculation results

[0116]

[0117] According to the above steps, the wind tunnel operating parameters corresponding to the test state can be estimated, and the liquid nitrogen flow under the target operating condition is obtained. According to the calculation results of this example, with the increase of test Mach number and the decrease of operating total pressure, the required liquid nitrogen flow will increase, and the maximum flow is 100.599kg / s, corresponding to the test Mach number of 0.9, the total pressure is 214604Pa, the liquid nitrogen flow and the temperature rise of airflow change with the test Mach number as shown in Figure 2 .

[0118] According to the estimation results, the liquid nitrogen flow can be determined before each adjustment of the test state, and the flow field regulation efficiency and closed-loop control accuracy are improved.

[0119] The method of the application is simple and fast, and can estimate the liquid nitrogen flow demand through test parameters and operating medium property parameters, which can provide a powerful means for wind tunnel control operation and test efficiency improvement.

[0120] The present application is not limited to the foregoing specific embodiments. The present application extends to any novel one, or any new combination, of the characteristics disclosed in this specification, as well as to any novel method or process steps disclosed, or any new combination thereof.

[0121] It should be pointed out finally that the above embodiments are only used to illustrate the technical solutions of the present application but not to limit. Although the present application is described in detail with reference to the embodiments, it should be understood by those skilled in the art that the technical solutions of the present application are modified or equivalently replaced without departing from the spirit and scope of the present application, and they should be covered in the scope of the claims of the present application.

Claims

1. A method of estimating the flow rate of liquid nitrogen for cryogenic wind tunnel test conditions, characterized in that, Comprise the following steps: S1, according to the test plan of the wind tunnel target parameters, the calculation of wind tunnel test section flow , the calculation formula is as follows: （1）； wherein is the mass flow of the test section gas in the target state, in kg / s; is the density of the test section gas, in kg / m 3 ; is the cross-sectional area of the test section, in m 2 ; is the velocity of the test section gas, in m / s; Based on the ideal gas law, the flow rate of the test section is... The calculation formula can be rewritten as follows: （2）； wherein is the gas static pressure in the test section, in Pa; is the gas constant in the test section; is the gas static temperature in the test section, in K; is the gas ratio of specific heat in the test section; is the Mach number of the gas in the test section; The test section gas static temperature, test section gas static pressure is converted into stable section stagnation parameter by using ideal gas isentropic relation, the calculation formula is as follows: （3）； The formula (3) is arranged as follows: （4）； In the formula, Ptot is the target total pressure, in Pa; Ttot is the target total temperature, in K; S2, according to the compressor operating parameters, wind tunnel operating parameters, calculate the corrected airflow temperature rise ; For isentropic compression process, the temperature rise of gas before and after the compressor is: （5）； In the formula, is the total temperature of the gas upstream of the compressor, in K; is the total temperature of the gas downstream of the compressor, in K; wherein the total temperature of the gas upstream of the compressor is the total temperature of the wind tunnel in operation ; The total temperature ratio is converted into total pressure ratio by using ideal gas isentropic relation, and is substituted into formula (5), to obtain the following formula: （6）； wherein Ptot,up is the total pressure of the gas upstream of the compressor, in Pa; Ptot,down is the total pressure of the gas downstream of the compressor, in Pa; Ptot,down is the total pressure of the gas downstream of the compressor Ptot,up is the total pressure of the gas upstream of the compressor, in Pa; Ptot,up is the total pressure of the gas upstream of the compressor, in Pa; The air flow temperature rise is corrected to obtain a corrected air flow temperature rise The calculation formula is as follows: （7）； In the formula, is a compressor efficiency factor, ranging from 0 to 1; S3, combined with ideal gas property parameters, the compressor power is calculated, the calculation formula is as follows: （8）； wherein P is the compressor power in MW; Cp is the specific heat capacity of the gas at constant pressure in kJ / (kg.K); S4, it is assumed that the liquid nitrogen is completely vaporized after being injected into the hole body circuit, and is uniformly mixed with the operating medium, the heat absorption is equal to the power of the compressor; according to the gas latent heat of vaporization, the liquid nitrogen flow is calculated, the calculation formula is as follows: （9）； The formula (9) is arranged as follows: （10）； wherein is the flow rate of the injected liquid nitrogen in kg / s; is the latent heat of vaporization of liquid nitrogen in kJ / kg.

2. The method of claim 1, wherein, In the step S2, the compressor efficiency factor is a measured value, obtained by means of the wind performance commissioning.

3. The method of claim 1, wherein, In the step S2, the liquid nitrogen injected into the wind tunnel circuit is vaporized and mixed with the circuit gas to maintain temperature balance, that is, the heat generated by the compressor to the gas is equal to the heat absorption of the liquid nitrogen vaporization.

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