Method for measuring local forced convection heat transfer coefficient on surface of an object

Abstract

The application relates to a kind of object surface local forced convection heat transfer coefficient measurement methods, the core thought is to utilize flexible thermal film shear stress sensor to the local forced convection heat transfer coefficient h of the surface of measured object for measurement.The application not only can be used for the surface local forced convection heat transfer coefficient measurement of conventional plane, pipeline, but also can realize the direct measurement of the local forced convection heat transfer coefficient of complex surface such as curved surface, simple operation, avoids the complex temperature field measurement problem in conventional convection heat transfer coefficient measurement.

Description

Technical fields:

[0001] This invention belongs to the field of heat transfer, specifically relating to a method for measuring the local forced convection heat transfer coefficient of an object surface. Background technology:

[0002] Forced convection heat transfer is the heat transfer phenomenon that occurs when a fluid flows over the surface of an object. Newton's law of cooling provides the basic formula for calculating convective heat transfer and is also the direct definition of the convective heat transfer coefficient h. It states that the convective heat transfer is directly proportional to the heat transfer area, the convective heat transfer coefficient h, and the temperature difference between the fluid and the object surface. Newton's law of cooling reduces the complex heat transfer process to the surface convective heat transfer coefficient h, making the formula concise and clear, but it also illustrates that the core of studying heat transfer problems lies in solving for the surface heat transfer coefficient h. However, convective heat transfer is a complex process. Factors such as fluid density, viscosity, thermal conductivity, specific heat capacity, flow velocity, fluid temperature, the size and morphology of the solid wall, its relative position, and surface temperature distribution all affect the magnitude of the heat transfer coefficient h. Accurately obtaining the local surface convective heat transfer coefficient h is a major challenge in engineering. Summary of the Invention:

[0003] The present invention aims to provide a method for measuring the local forced convection heat transfer coefficient of an object surface, which can directly obtain the local forced convection heat transfer coefficient h of the object surface through a flexible hot film shear stress sensor.

[0004] The key feature of the method for measuring the local forced convection heat transfer coefficient of an object surface described in this invention is that the measuring unit is a flexible hot-film shear stress sensor, which is fabricated using microelectromechanical systems (MEMS) technology and includes: a thermistor unit 1; a lead wire unit 2; and a PI flexible substrate 3.

[0005] The length of the thermal element 1 of the flexible hot-film shear stress sensor along the x-axis (flow direction) is set to L, the width along the z-axis (stretcher direction) is set to W, and the height along the y-axis (wall normal direction) is set to d. The operating temperature of the thermal element 1 is set to T. w Assuming the fluid medium has constant properties and the temperature is T f And there is T w >T f .

[0006] The process of establishing the constitutive equation for the flexible hot-film shear stress sensor described in this invention requires solving the three-dimensional steady-state heat transfer energy equation of the fluid:

[0007]

[0008] Where T(x,y,z,t) is the fluid temperature field, u, v, w are the velocity field components in the x, y, and z directions, respectively, and α is the velocity field component in the z direction. fdenoted as the thermal diffusivity of the fluid.

[0009] The ratio of the spanwise to the flowwise length of the thermal element 1 in the flexible thermal film shear stress sensor described in this invention is 60. In this case, the solution to the three-dimensional steady-state heat transfer energy equation of the fluid can be treated as a two-dimensional heat transfer problem, i.e., the velocity field only considers the x-direction, neglecting heat dissipation in the y and z directions. Since the thermal conductivity of the PI flexible substrate 3 described in this paper is relatively small, to further simplify the above steady-state heat transfer energy equation, the following derivation process neglects the heat conduction from the thermal element 1 to the PI flexible substrate 3.

[0010] At this point, the fluid three-dimensional steady-state heat transfer energy equation described in this invention is simplified to:

[0011]

[0012] Assuming the near-wall velocity boundary layer distribution is linear, i.e., defining u = s x y, where s x This represents the velocity gradient.

[0013] Assuming the near-wall temperature boundary layer distribution is also linear, and defining dimensionless temperature:

[0014] θ=(T w –T(y)) / (T w -T f )

[0015] Furthermore, the steady-state heat transfer energy equation described in this invention can be simplified again to:

[0016]

[0017] And it has boundary conditions:

[0018] θ(0,y)=1,θ(x,∞)=1,θ(x,0)=0

[0019] Introduce similarity variable η = y(s) x / 9α f x) 1 / 3 This is used to characterize the proportional relationship between the normal height y of the thermistor surface and the thickness of the temperature boundary layer. At this point, the steady-state heat transfer energy equation can be further transformed into a nonlinear ordinary differential equation:

[0020]

[0021] It has the following boundary conditions: θ(1)=1,θ(0)=0.

[0022] Solving this nonlinear ordinary differential equation, the solution is:

[0023]

[0024] Therefore, the convective heat transfer from the thermal element 1 of the flexible hot-film shear stress sensor to the fluid can be obtained by integrating along the length of the thermal element:

[0025]

[0026] Where, λ f denoted as , where is the thermal conductivity of the fluid medium.

[0027] Because, α f =λ f / (ρc p ), c p Let ρ be the specific heat capacity at constant pressure of the fluid medium; ρ be the density of the fluid medium; and τ be the definition of fluid wall shear stress, τ = μ(du / dy). y＝0 =μs x The convective heat transfer from the flexible hot-film shear stress sensor's thermistor unit 1 to the fluid can be further described as follows:

[0028]

[0029] Where v is the kinematic viscosity of the fluid medium, v = μ / ρ. Considering that the thermal radiation loss and free convection heat transfer loss of the thermistor unit 1 can be ignored during steady-state operation of a typical flexible hot-film shear stress sensor, the Joule heat power (Q) generated by the thermistor unit 1 under the excitation of the driving circuit 4 is... J =EI) and the forced convection heat transfer loss Q between the heat-sensitive element 1 and the flow field f Thermal conduction loss from the thermally sensitive unit 1 to the PI flexible substrate 3 Phase balance. Where E is the output voltage across the thermistor unit 1; I is the driving current of thermistor unit 1; λ s The thermal conductivity of the PI flexible substrate 3 is ΔT. w-s The temperature difference between the thermal unit 1 and the PI flexible substrate 3.

[0030] At this point, the constitutive equation of the flexible hot-film shear stress sensor under the operating conditions of measuring the local forced convection heat transfer coefficient of the object surface can be written as:

[0031]

[0032] The constitutive equation of the flexible thermal film shear stress microsensor reveals the convective heat transfer between the thermal element 1 and the flow field, as well as the shear stress on the fluid wall. τ Along with the relationship between the two, the relationship between the output voltage E across the thermistor unit 1 and the fluid wall shear stress τ is also given. Therefore, when the calibration equation between the output voltage E of the flexible hot-film shear stress sensor and the fluid wall shear stress τ is known, the convective heat transfer power Q between the thermistor unit 1 and the flow field can be realized. fBy reverse reasoning, the local forced convection heat transfer coefficient h of the surface can be solved.

[0033] Based on the above theoretical analysis, this invention proposes a method for measuring the local forced convection heat transfer coefficient of an object surface, characterized by comprising the following five steps:

[0034] Step 1: Perform temperature-resistivity (TCR) calibration on the flexible hot-film shear stress sensor to obtain the temperature-resistivity α of thermistor unit 1 at 20℃. 20 and resistance value R 20 The working resistance R of the flexible hot film sensor thermistor unit 1 is established. w With operating temperature T w Relationship between them:

[0035] R w =E / I=R 20 [1+R 20 α 20 (T w -T 20 )]

[0036] Among them, T 20 =20℃, I is the driving current of thermistor unit 1;

[0037] Step 2: Perform static calibration on the flexible hot-film shear stress sensor to obtain the relationship between the output voltage E across the thermistor unit 1 and the fluid wall shear stress τ: E 2 / R w =Aτ 1 / 3 +B, where A and B are parameters to be determined, which are related to the convective heat transfer between the thermal unit 1 and the flow field and the heat conduction to the substrate, respectively.

[0038] Step 3: Attach the flexible hot-film shear stress sensor flush with the surface of the object being tested;

[0039] Step 4: Measure the output voltage E and flow field temperature T across the thermistor unit 1 of the flexible hot-film shear stress sensor. f ;

[0040] Step 5: Based on the local fluid wall shear stress measured by the flexible hot-film shear stress sensor, and combined with Newton's cooling formula, calculate the local forced convection heat transfer coefficient h according to the following formula:

[0041]

[0042] Among them, c p λ is the isobaric specific heat capacity of the fluid medium; v is the kinematic viscosity of the fluid medium; λ f L is the thermal conductivity of the fluid medium. eff The effective flow direction working length of thermal unit 1 is calculated using the following formula:

[0043]

[0044] Where W is the span of thermal unit 1.

[0045] Beneficial effects:

[0046] The method for measuring the local forced convection heat transfer coefficient of an object surface described in this invention is applicable to measurements of complex surfaces such as curved surfaces. It can directly obtain the local convection heat transfer coefficient of the object surface by means of wall shear stress data measured by a flexible hot film shear stress sensor, avoiding the complex temperature field measurement problem in conventional convection heat transfer coefficient measurements, and has the outstanding advantage of simple operation. Attached Figure Description

[0047] Figure 1 A schematic diagram illustrating the working principle of a flexible hot-film shear stress sensor for measuring the convective heat transfer coefficient of an object's surface.

[0048] Figure 2 This is a schematic diagram of the structure of a flexible hot-film shear stress sensor.

[0049] Figure 3 This is a cross-sectional view of the AA section of a flexible hot-film shear stress sensor.

[0050] Figure 4 This is a schematic diagram of a measurement system for measuring the convective heat transfer coefficient of an object's surface based on a flexible hot-film shear stress sensor.

[0051] Marker explanation:

[0052] Thermosensitive Unit 1 of Flexible Hot Film Shear Stress Sensor

[0053] Lead unit 2 of flexible hot film shear stress sensor

[0054] PI flexible substrate for flexible hot-film shear stress sensor 3

[0055] The outer sloping plate 4 used in the embodiment Detailed implementation method:

[0056] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0057] One embodiment of this invention involves measuring the forced convection heat transfer coefficient h of a local surface under flow around an externally swept flat plate using a flexible hot-film sensor, as illustrated in the schematic diagram. Figure 4As shown. The flexible thermal film sensor is fabricated using microelectromechanical systems (MEMS) technology and includes: a thermistor unit 1; a lead wire unit 2; and a PI flexible substrate 3. The effective working length of the thermistor unit 1 along the flow direction of the flexible thermal film shear stress sensor is set to L. eff The length along the spanning direction is W.

[0058] The steps in this embodiment are as follows:

[0059] Step 1: Perform temperature-resistivity (TCR) calibration on the flexible hot-film shear stress sensor to obtain the temperature-resistivity α of thermistor unit 1 at 20℃. 20 In this embodiment, the temperature-resistivity coefficient α 20 = 4312.56ppm / ℃, operating temperature T of the flexible thermal film sensor thermistor unit 1 w It can be derived from the following formula:

[0060] R w =E / I=R 20 [1+R 20 α 20 (T w -T 20 )]

[0061] Among them, R 20 R20 represents the resistance value of the thermistor unit 1 of the flexible hot-film sensor at 20℃. In this embodiment, R20 = 7.515Ω; T 20 =20℃;

[0062] Step 2: Perform static calibration on the flexible hot-film shear stress sensor to obtain the relationship between the output voltage E across the thermistor unit 1 and the fluid wall shear stress τ: E 2 / R w =Aτ 1 / 3 +B, where A and B are parameters to be determined, and are related to the convective heat transfer between the thermistor unit 1 and the flow field, and the heat conduction to the substrate, respectively. In this embodiment, the operating resistance of the thermistor unit 1 is maintained at T under constant temperature drive. w =55℃, corresponding to R w =8.65Ω, the calibration parameters obtained after static calibration are A = 0.005823 and B = 0.052846, the output voltage E across the thermistor unit 1 is related to the fluid wall shear stress. τ The relationship between E 2 / 8.65=0.005823τ 1 / 3 +0.052846;

[0063] Step 3: Attach the flexible hot film sensor flush with the plate being measured 4 at a distance of x = 0.1m from the front edge of the plate;

[0064] Step 4: Measure the output voltage E and flow field temperature T across the thermistor unit 1 of the flexible hot-film shear stress sensor. f Flow velocity U;

[0065] Step 5: The local surface forced convection heat transfer coefficient under flow around an outer flat plate is calculated using the following formula:

[0066]

[0067] Among them, c p The isobaric specific heat capacity of the fluid medium is taken as c in this embodiment. p =1006 J / (kg·K); v is the kinematic viscosity of the fluid medium, which is taken as v = 0.0000148 m in this embodiment. 2 / s;λ f The thermal conductivity of the fluid medium is λ, which is taken as λ in this embodiment. f =0.0242W / (m·K); Effective flow direction working length L of thermistor unit 1 eff The calculation formula is:

[0068]

[0069] Where W is the span of thermal element 1, W = 0.003 m.

[0070] In this embodiment, local convective heat transfer coefficients were measured under a series of experimental conditions at different Reynolds numbers (Re). The corresponding parameters and measurement results at different Reynolds numbers are listed below:

[0071]

[0072] As shown in the table, the Reynolds number in this embodiment is less than 500,000, therefore it belongs to the laminar flow heat transfer problem. In this embodiment, the dimensionless surface convective heat transfer coefficient j-factor is used as a comparison standard, and the measured values ​​of this embodiment are compared with the empirical values ​​of classical externally swept flat plate heat transfer laminar flow theory. The definition of the j-factor is as follows:

[0073]

[0074] In the formula, Nu is the Nusselt number, calculated as: Nu = hl / λ f Where l is the characteristic length; Re is the Reynolds number, calculated as Re = Ul / v; and Pr is the Prandtl number. The characteristic length of the measurement value from the flexible hot-film shear stress sensor is taken as L. eff ,Pr 1 / 3 ≈16.

[0075] In this embodiment, the dimensionless surface convection heat transfer coefficient j-factor at the measurement point of the flexible hot-film shear stress sensor is calculated according to the empirical formula of the laminar flow theory of heat transfer over a flat plate:

[0076]

[0077] The characteristic length l of the Reynolds number is taken as the distance x from the leading edge of the plate, and the Pr number is taken as 0.743.

[0078] The comparison list of measured values ​​and theoretical empirical values ​​in this embodiment is as follows:

[0079]

[0080] It can be seen that the measurement error range of the dimensionless heat transfer coefficient of the outer-grazing flat plate surface in this embodiment is within 5%. It can also be seen that the method proposed in this invention provides an effective means for measuring local forced convection heat transfer on the surface of an object.

[0081] The above description is only a preferred embodiment of the present invention and does not limit the present invention. Any modifications, substitutions, or improvements made within the scope of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for measuring the local forced convection heat transfer coefficient of an object surface, characterized in that, It includes the following five steps: Step 1: Perform temperature-resistivity coefficient (TCR) calibration on the flexible hot-film shear stress sensor to obtain the temperature-resistivity coefficient of the thermistor (1) at 20℃. and resistance value The working resistance of the flexible hot film sensor thermistor unit (1) was established. Operating temperature Relationship between them: in, =20℃, I The driving current of the thermal unit (1); Step 2: Perform static calibration on the flexible hot-film shear stress sensor to obtain the output voltage across the thermal unit (1). E With fluid wall shear stress The relationship between them: ,in, A , B All are undetermined parameters, which are related to the convective heat transfer between the thermal element (1) and the flow field and the heat conduction to the substrate, respectively. Step 3: Attach the flexible hot-film shear stress sensor flush with the surface of the object being tested; Step 4: Measure the output voltage across the thermistor unit (1) of the flexible hot-film shear stress sensor. E Flow field temperature ; Step 5: Based on the local fluid wall shear stress measured by the flexible hot-film shear stress sensor, and combined with Newton's cooling formula, calculate the local forced convection heat transfer coefficient according to the following formula. h : in, The convective heat transfer from the thermistor unit of the flexible hot-film shear stress sensor to the fluid. Specific heat capacity at constant pressure of the fluid medium; The kinematic viscosity of the fluid medium; is the thermal conductivity of the fluid medium; L eff The effective flow direction working length of the thermal unit (1) is calculated using the following formula: in, W is the span of the thermal unit (1).

Images