Method for calculating temperature of rarefied flow field from convective heat flux and gordon's surface temperature

Abstract

The present invention discloses a method for calculating the temperature of a rarefied flow field from convective heat flux and the surface temperature of a Gordon meter. The method is used for measuring the incoming flow temperature in a rarefied fluid wind tunnel, comprising: installing a Gordon meter and a radiation heat flux meter on a mobile motor at a certain distance, controlling a measurement point by the mobile motor, and the measurement point being the area covered in the incoming flow direction; after selecting a measurement point, under the same working conditions, the mobile motor sequentially measures the total heat flux Q (average value) and the pure radiation heat flux q at the measurement point. r , we get the average heat flux Q of convective heat transfer c =Q‑q r and use an infrared pyrometer to measure the Gordon meter center temperature T r＝0 ; Through convection heat flow Q c Gordon-Gecko copper foil center temperature T r＝0 , calculate the incoming flow temperature T at the current measuring point f The present invention replaces the complex measurement system of the conventional rarefied wind tunnel temperature measurement method with a simple structure, solving the problem that the spectrum temperature measurement method has weak signal in highly rarefied wind tunnels and the temperature measured by thermocouples is difficult to reflect the actual temperature of the flow field.

Description

Technical Field

[0001] The invention belongs to the technical field of rarefied fluid wind tunnel testing, and in particular relates to a method for calculating rarefied flow field temperature based on convective heat flux and Gordon meter surface temperature. Background Art

[0002] Rarefied-flow wind tunnels can be used to simulate and measure environments in near-space and even very low orbit, providing critical data for aircraft design and performance evaluation, and are widely used in aerospace and other fields. Measuring the temperature of the rarefied flow is essential to accurately reflect parameters such as heat flow and drag in a real-world aircraft environment. Conventional rarefied-flow wind tunnel temperature measurement methods are complex, have weak signals, and are costly. Summary of the Invention

[0003] In view of the problems existing in the prior art, the present invention proposes a method for calculating the temperature of a rarefied flow field from the convective heat flux and the surface temperature of a Gordon meter, aiming to solve the problems of complex measurement system, weak signal and high cost in conventional wind tunnel temperature measurement methods.

[0004] The present invention adopts the following technical solutions to solve the technical problems:

[0005] A method for calculating the temperature of a rarefied flow field from convective heat flux and Gordon meter surface temperature, the method being used for measuring the incoming flow temperature in a rarefied fluid wind tunnel, is characterized by comprising the following steps:

[0006] Step 1: Install the Gordon meter and the radiation heat flux meter on a mobile motor at a certain distance, and control the measurement point by the mobile motor. The measurement point is the area covered by the incoming flow direction;

[0007] Step 2: After selecting the measurement point, under the same working conditions, move the motor to measure the total heat flux Q (average value) and pure radiation heat flux q of the measurement point in turn. r , we get the heat flux (average value) Q of convective heat transfer c =Qq r and use an infrared pyrometer to measure the Gordon meter center temperature T r＝0 ;

[0008] Step 3: Heat flow Q through convection c Gordon-Gecko copper foil center temperature T r＝0 , calculate the incoming flow temperature T at the current measuring point f The convective heat transfer coefficient h is assumed to be uniform along the radial direction of the copper foil.

[0009] Furthermore, the step 3 is to heat the product Q by convection. c Gordon-Gecko copper foil center temperature T r＝0 , calculate the incoming flow temperature T at the current measuring pointf And the convection heat transfer coefficient h, the specific process is as follows:

[0010] 1) By solving the steady-state heat transfer equation, we can obtain the inflow temperature T f Theoretical expression of the surface temperature of the Constantan foil T(r) with the convection heat transfer coefficient h

[0011] 2) Using the theoretical expression of the circular foil surface temperature T(r), by integrating the single-point convection heat flow on the surface of the copper foil, the incoming flow temperature T f Theoretical expression of the average convective heat flux Q with the convective heat transfer coefficient h c ;

[0012] 3) The center temperature of copper foil T is measured by Gordon-Germany r＝0 Get the incoming flow temperature T f Theoretical expression of the surface temperature of the deformed circular foil △T with the convection heat transfer coefficient h;

[0013] 4) Solving the above two equations 2) and 3) can obtain the convection heat transfer coefficient h and the flow field temperature T near the wall surface. f .

[0014] Furthermore, the step 3 process 1) is to solve the steady-state heat transfer equation to obtain the temperature T f The theoretical expression of the surface temperature of the copper foil T(r) with the convection heat transfer coefficient h is as follows:

[0015] A. According to the steady-state heat conduction equation and the boundary conditions of the Gordon meter, the steady-state heat conduction equation of the Gordon meter is obtained:

[0016]

[0017] Among them, r, T(r), and q are all unknown quantities, and T0, δ, R, and λ are all known quantities;

[0018] Among the unknown quantities, r is the independent variable, which is the distance measured from the center of the foil in the radial direction; T(r) is the temperature at position r on the surface of the foil; q is the total heat at a single point;

[0019] Among the known quantities, T0 is the temperature at the edge of the Constantan foil on the Gordon meter, δ is the thickness of the Constantan foil, R is the radius of the Constantan foil, and the thermal conductivity λ of the Constantan foil is a linear function of temperature;

[0020] λ is the thermal conductivity, and assuming that the thermal conductivity λ is uniform at different radial positions on the foil surface, the average temperature on the radius of the circular foil is used. describe: When T1 = 0°C, λ0 = 20.9W / (m°C), b = 0.00231°C -1 , is a known quantity, and defines

[0021] B. Obtain the total heat flow q value of formula (1)

[0022] ① Total heat flux at a single point on the circular foil surface due to convection and radiation heat transfer:

[0023] q=q c +q r ; (2)

[0024] q r The radiation heat flux is known;

[0025] ② The single point convection heat flux q c Use the other three variables and h, T f , T(r) represents

[0026] q c =h(T f -T(r)) (3)

[0027] T f is the incoming flow temperature T f , h is the convective heat transfer coefficient, T(r) is the temperature at position r on the foil surface; q c is an unknown quantity;

[0028] C. The theoretical expression of the circular foil surface temperature T(r) is obtained by using equations (1), (2) and (3):

[0029]

[0030] Among them, I0(m ξ r) is about m ξ r's zeroth-order modified Bessel function of the first kind, m ξ =(h / ξλ0δ) 1 / 2 is a function of h, which is an unknown variable; T(r) is the temperature of the Gordon meter at r as the dependent variable, r is the distance to the center of the Gordon meter as the independent variable, T f The incoming flow temperature is unknown, h is the convective heat transfer coefficient is unknown, and q r is the radiation heat flux which is known, T0 is the edge temperature of the Gordon-German copper foil which can be obtained by formula (6), and R is the radius of the Gordon-German copper foil which is known.

[0031] In the process 2) of step 3, the theoretical expression of the circular foil surface temperature T(r) is used to integrate the single-point convection heat flow on the surface of the copper foil to obtain the incoming flow temperature T f Theoretical expression of the average convective heat flux Q with the convective heat transfer coefficient h c ; The details are as follows:

[0032] A. Obtain ΔT in equation (5) by measuring the voltage output E: The voltage output E of the thermoelectromotive force of the copper-constantan thermocouple formed by the Gordon heat flow meter is a function of the temperature difference ΔT:

[0033] E=kΔT(1+gΔT) (5)

[0034] Where, k = 0.0381mV / °C, g = 0.0012°C -1 , the voltage output E can be obtained through experiments;

[0035] B. Substituting T(r) from equation (4) into equation (6) yields the average heat flux density Q for convective heat transfer. c :

[0036] The average value of the heat flux density Q of convective heat transfer c It can be obtained by the following integral:

[0037]

[0038] Among them, T in formula (4) f It can be eliminated in formula (6); I1(m ξ r) is m ξ The first-order modified Bessel function of the first kind, I0(m ξ r) is about m ξ r's zeroth-order modified Bessel function of the first kind, m ξ =(h / ξλ0δ) 1 / 2 is an unknown number, and the temperature difference between the edge and center of the copper foil is ΔT=T r＝0 -T0 is a known quantity, T f is the incoming flow temperature which is unknown, h is the convective heat transfer coefficient which is unknown, T(r) is the temperature at position r on the foil surface which is the dependent variable of the independent variable r;

[0039] Furthermore, the center temperature of the copper foil T r＝0 Get the incoming flow temperature T f Theoretical expression of the surface temperature of the deformed circular foil △T with the convection heat transfer coefficient h;

[0040] 1) The ΔT obtained by formula (6) and the known center temperature T of the copper foil on the Gordon meter surface r＝0 , we get the edge temperature of the copper foil T0 = T r＝0 -ΔT;

[0041] 2) Transform Equation (4) to obtain Equation (7), set r = 0 in Equation (4), and move the first T0 on the right side of Equation (4) to the left, and we can get:

[0042]

[0043] Due to m ξ is a function of h, so Equation (6) and Equation (7) only contain two unknowns T f and h; The above two equations can be used to obtain the convective heat transfer coefficient h and the flow field temperature T near the wall surface. f .

[0044] Advantages and effects of the present invention

[0045] 1. Compared with conventional rarefied wind tunnel temperature measurement methods, the present invention replaces the complex measurement system of conventional rarefied wind tunnel temperature measurement methods with a simple structure (radiation heat flux meter, Gordon meter, infrared pyrometer, bidirectional movable motor, and related algorithms). This solves the problem that in highly rarefied wind tunnels, the spectral temperature measurement method has a weak signal and the temperature measured by thermocouples cannot reflect the actual temperature of the flow field.

[0046] 2. Compared with conventional rarefied fluid wind tunnel temperature measurement methods, the present invention uses the average total heat flux measured by the Gordon meter minus the radiation heat flux measured by the radiation heat flux meter, thereby eliminating the radiation interference generated by the rarefied fluid wind tunnel generator. Conventional rarefied fluid wind tunnel temperature measurement methods do not consider the interference of radiation heating, so the present invention provides more accurate flow field temperature measurement results. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is a schematic diagram of the rarefied wind tunnel temperature measurement system;

[0048] Figure 2 This is the temperature distribution diagram of the Gordon meter structure on the surface;

[0049] Figure 3 Flowchart of the method for calculating rarefied flow field temperature from convective heat flux and Gordon gauge surface temperature. DETAILED DESCRIPTION

[0050] Design principle of the present invention

[0051] 1. Innovation of the present invention: The innovation lies in using a relatively simple method to measure the flow field temperature T f Specifically, the method of calculating the temperature of the rarefied flow field is organically combined with the radiation heat flux meter, Gordon meter, infrared pyrometer, and bidirectional moving motor, and the radiation heat flux q of the radiation heat flux meter is obtained. r and Gordon-Jiang Kang copper foil center temperature T r＝0 The average convective heat flux Q is obtained by measuring c (heat flux (average value) of convection heat transfer Q c =Qq r ), and the center temperature of the Gordon-Jackson copper foil T r＝0, and then calculate the incoming flow temperature T at the current measuring point using these two known numbers f The convection heat transfer coefficient h solves the problems of the conventional rarefied wind tunnel temperature measurement method, such as complex measurement system, weak signal and high cost. c , which comes from the total heat flux Q minus the radiation heat flux q r , the total heat flux Q is obtained by measurement; the radiation heat flux q in the two known numbers r From a radiation heat flux meter.

[0052] 2. Design principle of the present invention: The present invention is realized by establishing two equations to obtain two parameters: the incoming flow temperature T f and the convection heat transfer coefficient h, these two equations are formula (6) and formula (7);

[0053] Formula (6) is the average heat flux Q of the known parameters of convective heat transfer obtained by combining formulas (1)-(5) with the measured heat flux. c get;

[0054] Formula (7) is established on the basis of formula (4) and uses the known parameter Gordon-Gecko copper foil center temperature T r＝0 , and finally get the modified formula (4), which is formula (7). The specific steps to get formula (7) are: First, substitute T(r) in formula (4) into formula (6) to get the average heat flux density Q of convective heat transfer c , which is formula (6). The unknown number of formula (6) is h. Second, △T of formula (6) is obtained by formula (5). At this time, formula (6) only has one unknown number h. Third, since △T is obtained by formula (5), T r＝0 It is also measured, so T0 on the right side of the equal sign in formula (4) can be moved to the left side of formula (4) to form △T, that is, △T=T r＝0 -T0, thus completing the transformation of formula (4) to obtain formula (7). Since both formula (6) and formula (7) contain only two unknowns: the incoming flow temperature T f and the convection heat transfer coefficient h, so solving these two equations can yield two unknowns: the incoming flow temperature T f And the convection heat transfer coefficient h.

[0055] Based on the above principles, the present invention designs a method for calculating the temperature of a rarefied flow field from the convective heat flux and the surface temperature of the Gordon meter, such as Figure 1-3 As shown, the method is used for measuring the incoming flow temperature in a rarefied fluid wind tunnel, and is characterized by comprising the following steps:

[0056] Step 1: Install the Gordon meter and the radiation heat flux meter on a mobile motor at a certain distance, and control the measurement point by the mobile motor. The measurement point is the area covered by the incoming flow direction;

[0057] Step 2: After selecting the measurement point, under the same working conditions, move the motor to measure the total heat flux Q (average value) and pure radiation heat flux q of the measurement point in turn. r , we get the heat flux (average value) Q of convective heat transfer c =Qq r and use an infrared pyrometer to measure the Gordon meter center temperature T r＝0 ;

[0058] Step 3: Heat flow Q through convection c Gordon-Gecko copper foil center temperature T r＝0 , calculate the incoming flow temperature T at the current measuring point f and the convection heat transfer coefficient h, assuming that the convection heat transfer coefficient h is uniform along the radial direction of the Constantan foil.

[0059] Furthermore, the step 3 is to heat the product Q by convection. c Gordon-Gecko copper foil center temperature T r＝0 , calculate the incoming flow temperature T at the current measuring point f And the convection heat transfer coefficient h, the specific process is as follows:

[0060] 1) By solving the steady-state heat transfer equation, we can obtain the inflow temperature T f Theoretical expression of the surface temperature of the Constantan foil T(r) with the convection heat transfer coefficient h

[0061] 2) Using the theoretical expression of the circular foil surface temperature T(r), by integrating the single-point convection heat flow on the surface of the copper foil, the incoming flow temperature T f Theoretical expression of the average convective heat flux Q with the convective heat transfer coefficient h c ;

[0062] 3) The center temperature of copper foil T is measured by Gordon-Germany r＝0 Get the incoming flow temperature T f Theoretical expression of the surface temperature of the deformed circular foil △T with the convection heat transfer coefficient h;

[0063] 4) Solving the above two equations 2) and 3) can obtain the convection heat transfer coefficient h and the flow field temperature T near the wall surface. f .

[0064] Furthermore, the step 3 process 1) is to solve the steady-state heat transfer equation to obtain the temperature T f The theoretical expression of the surface temperature of the copper foil T(r) with the convection heat transfer coefficient h is as follows:

[0065] A. According to the steady-state heat conduction equation and the boundary conditions of the Gordon meter, the steady-state heat conduction equation of the Gordon meter is obtained:

[0066]

[0067] Among them, r, T(r), and q are all unknown quantities, and T0, δ, R, and λ are all known quantities;

[0068] Among the unknown quantities, r is the independent variable, which is the distance measured from the center of the foil in the radial direction; T(r) is the temperature at position r on the surface of the foil; q is the total heat at a single point;

[0069] Among the known quantities, T0 is the temperature at the edge of the Constantan foil on the Gordon meter, δ is the thickness of the Constantan foil, R is the radius of the Constantan foil, and the thermal conductivity λ of the Constantan foil is a linear function of temperature;

[0070] λ is the thermal conductivity, and assuming that the thermal conductivity λ is uniform at different radial positions on the foil surface, the average temperature on the radius of the circular foil is used. describe: When T1 = 0°C, λ0 = 20.9W / (m°C), b = 0.00231°C -1 , is a known quantity, and defines

[0071] Additional notes:

[0072] This example assumes that the convective heat transfer coefficient h and thermal conductivity λ are uniform across the foil surface at different radial locations. This assumption is based on the fact that the temperature difference between the center and edge of the circular foil is small due to the low heat flux in a rarefied wind tunnel. Therefore, the assumption that the convective heat transfer coefficient h and thermal conductivity λ are undetermined constants is feasible.

[0073] B. Obtain the total heat flow q value of formula (1)

[0074] ① Total heat flux at a single point on the circular foil surface due to convection and radiation heat transfer:

[0075] q=q c +q r ; (2)

[0076] q r The radiation heat flux is known;

[0077] ② The single point convection heat flux q c Use the other three variables and h, T f , T(r) represents

[0078] q c =h(T f -T(r)) (3)

[0079] T f is the free stream temperature T f , h is the convective heat transfer coefficient, T(r) is the temperature of the foil surface at position r; q c is the unknown;

[0080] C, the theoretical expression of the circular foil surface temperature T(r) is obtained by formula (1) formula (2) and formula (3)

[0081]

[0082] wherein I0(m ξ r) is the zeroth order first kind modified Bessel function about m ξ r, m ξ =(h / ξλ0δ) 1 / 2 is a function about h, is an unknown; T(r) is the temperature of the gordon meter at r as the dependent variable, r is the distance to the center of the gordon meter as the independent variable, T f is the free stream temperature as the unknown, h is the convective heat transfer coefficient as the unknown, q r is the radiant heat flow as the known, T0 is the edge temperature of the gordon meter can be obtained by formula (6), R is the radius of the gordon meter can be obtained by formula (6).

[0083] Further, the step three process 2) uses the theoretical expression of the circular foil surface temperature T(r), and the average convective heat flow Q c containing the free stream temperature T f and the convective heat transfer coefficient h is obtained by integrating the convective heat flow of a single point on the constantan foil; Specifically as follows:

[0084] A, the ΔT in formula (5) is obtained by measuring the voltage output E: the voltage output E of the thermoelectric power of the copper-constantan thermocouple formed by the gordon heat flow meter is a function of the temperature difference ΔT:

[0085] E=kΔT(1+gΔT) (5)

[0086] wherein k=0.0381 mV / ℃, g=0.0012℃ -1 , the voltage output E can be obtained by experiment;

[0087] B, the T(r) of formula (4) is substituted into formula (6) to obtain the average value Q c of the heat flow density of convective heat transfer:

[0088] The average value Q c of the heat flow density of convective heat transfer can be obtained by the following integral:

[0089]

[0090] wherein T f in formula (4) can be eliminated in formula (6); I1(m ξ r) is the first order first kind modified Bessel function of m ξ r, I0(m ξ r) is the zero order first kind modified Bessel function of m ξ r, m ξ =(h / ξλ0δ) 1 / 2 is an unknown number, while the temperature difference ΔT=T r＝0 -T0 between the edge and the center of the Gortatian copper foil is known, and the temperature of the incoming flow T f is unknown, h is the unknown convective heat transfer coefficient, and T(r) is the temperature of the foil surface at position r which is the dependent variable of the independent variable r;

[0091] Further, the step three process 3) obtains the theoretical expression of the surface temperature of the deformed circular foil containing the incoming flow temperature T r＝0 and the convective heat transfer coefficient h through the Gortatian copper foil center temperature T f ;

[0092] 1) ΔT obtained according to formula (6) and the known Gortatian copper foil surface center temperature T r＝0 , the Gortatian copper foil edge temperature T0=T r＝0 -ΔT is obtained;

[0093] 2) formula (7) is obtained by deforming formula (4), letting r=0 in formula (4), and moving the first T0 on the right side of formula (4) to the left side, and obtaining:

[0094]

[0095] Since m ξ is a function of h, formula (6) and formula (7) constitute an equation group containing only two unknown numbers T f and h; through the above two equations, the convective heat transfer coefficient h and the flow field temperature T f near the wall can be obtained.

[0096] It should be emphasized that the above specific embodiments are only an explanation of the present application, and are not a limitation of the present application, and those skilled in the art can make modifications to the above embodiments without creative contribution according to the needs after reading the present specification, but as long as it is within the scope of the claims of the present application, it is protected by the patent law.

Claims

1. A method for calculating the temperature of a rarefied flow field from convective heat flux and Gordon meter surface temperature, the method being used for measuring the incoming flow temperature in a rarefied fluid wind tunnel, characterized in that: The following steps are involved: Step 1: Install the Gordon meter and the radiation heat flux meter on a mobile motor at a certain distance, and control the measurement point by the mobile motor. The measurement point is the area covered by the incoming flow direction; Step 2: After selecting the measurement point, under the same working conditions, move the motor to measure the total heat flux average value Q and the pure radiation heat flux q of the measurement point in turn. r , we get the average heat flux Q of convective heat transfer c =Qq r and use an infrared pyrometer to measure the Gordon meter center temperature T r＝0 ; Step 3: Heat flow Q through convection c Gordon-Gecko copper foil center temperature T r＝0 , calculate the incoming flow temperature T at the current measuring point f and the convection heat transfer coefficient h, assuming that the convection heat transfer coefficient h is uniform along the radial direction of the Constantan foil; The step three is to pass the convection heat flow Q c Gordon-Gecko copper foil center temperature T r＝0 , calculate the incoming flow temperature T at the current measuring point f And the convection heat transfer coefficient h, the specific process is as follows: 1) By solving the steady-state heat transfer equation, we can obtain the inflow temperature T f Theoretical expression of the surface temperature of the Constantan foil T(r) with the convection heat transfer coefficient h; 2) Using the theoretical expression of the circular foil surface temperature T(r), by integrating the single-point convection heat flow on the surface of the copper foil, the incoming flow temperature T f Theoretical expression of the average convective heat flux Q with the convective heat transfer coefficient h c ; 3) The center temperature of copper foil T is measured by Gordon-Germany r＝0 Get the incoming flow temperature T f Theoretical expression of the surface temperature of the deformed circular foil △T with the convection heat transfer coefficient h; 4) Solving the above two equations 2) and 3) can obtain the convection heat transfer coefficient h and the flow field temperature T near the wall surface. f ; In step 3, process 1) the steady-state heat transfer equation is solved to obtain the inflow temperature T f The theoretical expression of the surface temperature of the copper foil T(r) with the convection heat transfer coefficient h is as follows: A. Based on the steady-state heat conduction equation and the boundary conditions of the Gordon meter, the steady-state heat conduction equation of the Gordon meter is obtained: Among them, r, T(r), and q are all unknown quantities, and T0, δ, R, and λ are all known quantities; Among the unknown quantities, r is the independent variable, which is the distance measured from the center of the foil in the radial direction; T(r) is the temperature at position r on the surface of the foil; q is the total heat at a single point; Among the known quantities, T0 is the temperature at the edge of the Constantan foil on the Gordon meter, δ is the thickness of the Constantan foil, R is the radius of the Constantan foil, and the thermal conductivity λ of the Constantan foil is a linear function of temperature; λ is the thermal conductivity, and assuming that the thermal conductivity λ is uniform at different radial positions on the foil surface, the average temperature on the radius of the circular foil is used. describe: When T1 = 0°C, λ0 = 20.9W / (m°C), b = 0.00231°C -1 , is a known quantity, and defines B. Obtain the total heat flow q value of formula (1) ① Total heat flux at a single point on the circular foil surface due to convection and radiation heat transfer: q=q c +q r ; (2) q r The radiation heat flux is known; ② The single point convection heat flux q c Use the other three variables and h, T f , T(r) represents q c =h(T f -T(r)) (3) T f is the incoming flow temperature T f , h is the convective heat transfer coefficient, T(r) is the temperature at position r on the foil surface; q c is an unknown quantity; C. The theoretical expression of the circular foil surface temperature T(r) is obtained by using equations (1), (2) and (3): Among them, I0(m ξ r) is about m ξ r's zeroth-order modified Bessel function of the first kind, m ξ =(h / ξλ0δ) 1 / 2 is a function of h, which is an unknown variable; T(r) is the temperature of the Gordon meter at r as the dependent variable, r is the distance to the center of the Gordon meter as the independent variable, T f The incoming flow temperature is unknown, h is the convective heat transfer coefficient is unknown, and q r is the radiation heat flux is known, T0 is the edge temperature of the Gordon-German copper foil which can be obtained by formula (6), R is the radius of the Gordon-German copper foil which is known; In the process 2) of step 3, the theoretical expression of the circular foil surface temperature T(r) is used to integrate the single-point convection heat flow on the surface of the copper foil to obtain the incoming flow temperature T f Theoretical expression of the average convective heat flux Q with the convective heat transfer coefficient h c ; The details are as follows: A. Obtain ΔT in equation (5) by measuring the voltage output E: The voltage output E of the thermoelectromotive force of the copper-constantan thermocouple formed by the Gordon heat flow meter is a function of the temperature difference ΔT: E=kΔT(1+gΔT) (5) Where, k = 0.0381mV / °C, g = 0.0012°C -1 , the voltage output E can be obtained through experiments; B. Substituting T(r) from equation (4) into equation (6) yields the average heat flux density Q for convective heat transfer. c : The average value of the heat flux density Q of convective heat transfer c It can be obtained by the following integral: Among them, T in formula (4) f It can be eliminated in formula (6); I1(m ξ R) is m ξ The first-order first-kind modified Bessel function of R, I0(m ξ R) is about m ξ R's zeroth-order modified Bessel function of the first kind, m ξ =(h / ξλ0δ) 1 / 2 is an unknown number, and the temperature difference between the edge and center of the copper foil is ΔT=T r＝0 -T0 is a known quantity, T f is the incoming flow temperature which is unknown, h is the convective heat transfer coefficient which is unknown, T(r) is the temperature at position r on the foil surface which is the dependent variable of the independent variable r; The center temperature T of the copper foil is measured by Gordon-Germany. r＝0 Get the incoming flow temperature T f Theoretical expression of the surface temperature of the deformed circular foil △T with the convection heat transfer coefficient h; 1) The ΔT calculated according to formula (5) is compared with the known center temperature T of the copper foil on the Gordon meter surface. r＝0 , we get the edge temperature of the copper foil T0 = T r＝0 -ΔT; 2) Transform Equation (4) to obtain Equation (7), set r = 0 in Equation (4), and move the first T0 on the right side of Equation (4) to the left, and we can get: Due to m ξ is a function of h, so Equation (6) and Equation (7) only contain two unknowns T f and h; The above two equations can be used to obtain the convective heat transfer coefficient h and the flow field temperature T near the wall surface. f .

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