Measurement method of displacement thickness and momentum loss thickness of strongly compressible turbulent boundary layer

Abstract

A method for measuring the displacement thickness and momentum loss thickness of a highly compressible turbulent boundary layer belongs to the field of aerospace testing technology. The method comprises: obtaining the boundary layer velocity field distribution for the boundary layer flow field at a specific position of a flat plate model in a continuously operating hypersonic wind tunnel; obtaining the wall temperature distribution after the model reaches thermal equilibrium at a specific position of the flat plate model; utilizing the boundary layer velocity field distribution and wall temperature distribution at a specific flow direction station, obtaining the temperature and density distribution along the normal direction of the flow in the boundary layer by introducing relevant assumptions, and then calculating the displacement thickness and momentum loss thickness based on the temperature and density distributions. The present invention solves the problem of measuring and obtaining the boundary layer displacement thickness and momentum loss thickness in a wind tunnel environment from an experimental perspective.

Description

Technical Field

[0001] The invention relates to a method for measuring displacement thickness and momentum loss thickness of a highly compressible turbulent boundary layer, and belongs to the technical field of aerospace testing. Background Art

[0002] For high-speed aircraft, measuring boundary layer parameters is crucial, as they are crucial for flow transition, wall friction, and thermal protection. However, non-intrusive quantitative measurement of boundary layer parameters is difficult at high Mach numbers, especially under turbulent conditions, where obtaining high-resolution boundary layer flow field parameters is crucial. After decades of development, particle image velocimetry (PIV), with its advantages of combining flow visualization and measurement, has achieved rapid progress. With the introduction of dual-exposure lasers, digital cross-frame cameras, and high-precision time-delay signal generators, coupled with the continuous advancement and refinement of image processing techniques such as cross-correlation and fast Fourier transforms, PIV has significantly improved image quality, velocity measurement range, and accuracy. It is now being applied in a growing number of fields, and aerodynamic research institutes in major aerodynamic countries worldwide have adopted PIV for aerodynamic research. For PIV, the presence of tracer particles in the fluid under investigation is essential. By capturing particle images with a cross-frame camera and calculating the velocity field, flow field characteristics such as isovelocity lines, streamlines, and vorticity can be calculated using appropriate mathematical software.

[0003] At present, a large number of boundary layer research fields in domestic high-speed wind tunnels lack accurate quantitative measurement and analysis of boundary layer velocity types. The displacement thickness and momentum loss thickness in the boundary layer are determined by theoretical methods and numerical simulation methods. Affected by the model boundary and temperature effects, many test results do not match expectations and cannot provide data reference for transition research and heat reduction and drag reduction research. Summary of the Invention

[0004] The technical problem solved by the present invention is: to overcome the shortcomings of the existing technology, provide a method for measuring the displacement thickness and momentum loss thickness of the highly compressible turbulent boundary layer, and solve the problem of measuring the boundary layer displacement thickness and momentum loss thickness in a wind tunnel environment from an experimental perspective.

[0005] The technical solution of the present invention is: a method for measuring the displacement thickness and momentum loss thickness of a highly compressible turbulent boundary layer, comprising:

[0006] In a continuously operating hypersonic wind tunnel, the boundary layer velocity field distribution is obtained for the boundary layer flow field at a specific position of a flat plate model.

[0007] For a specific position of the flat plate model, obtain the wall temperature distribution after the model is thermally balanced;

[0008] By using the boundary layer velocity field distribution and wall temperature distribution at a specific flow direction station, the temperature distribution and density distribution along the normal direction of the flow in the boundary layer are obtained by introducing relevant assumptions, and then the displacement thickness and momentum loss thickness are calculated based on the temperature distribution and density distribution.

[0009] Furthermore, obtaining the boundary layer velocity field distribution includes:

[0010] (1) Using a particle generator to inject tracer particles of a specific size into the wind tunnel flow field;

[0011] (2) Select a dual-pulse laser light source and a high-resolution cross-frame camera for flow field illumination and image acquisition;

[0012] (3) Using the acquired particle images to analyze the instantaneous velocity field of the boundary layer (u x,y ,v x,y ) calculation to obtain the boundary layer velocity field distribution.

[0013] Furthermore, the TiO2 particles in the boundary layer flow field meet a delay time of better than 1 microsecond.

[0014] Furthermore, the number of velocity vectors in the normal direction of the inner wall surface of the boundary layer thickness is not less than 20.

[0015] Furthermore, the selected cross-frame CCD camera meets the requirements of a resolution of not less than 2000 pixels in the normal direction of the wall surface and a lens focal length of f=200 mm, and in the normal direction, the optical axis of the camera and lens optical system is parallel to the surface of the flat plate model and just passes through the surface of the flat plate model, so that the particle image only occupies 1 / 2 of the CCD camera frame height.

[0016] Furthermore, the temperature distribution is achieved by Calculate; where, is the time-averaged velocity in the boundary layer The time-averaged temperature at the location, is the time-averaged wall temperature, is the time-averaged temperature at the boundary layer thickness δ, To restore the temperature, is the time average of the streamwise velocity at a specific streamwise position in the boundary layer, is the time-averaged velocity of the stream at the boundary layer thickness δ.

[0017] Furthermore, the density distribution is achieved by Calculate; where, is the time-averaged velocity of the boundary layer The time-averaged density at the location, ρ ∞ is the static density of the incoming flow, is the time-averaged velocity in the boundary layer Time-averaged temperature at location, T∞ For the incoming flow, quiet and warm.

[0018] Furthermore, the displacement thickness and momentum loss thickness are respectively

[0019]

[0020] Among them, δ * is the displacement thickness of the compressible boundary layer, θ is the momentum loss thickness of the compressible boundary layer, δ is the boundary layer thickness, is the time-averaged velocity of the boundary layer The time-averaged density at the location, ρ ∞ is the static density of the incoming flow, is the time average of the streamwise velocity at a specific streamwise position in the boundary layer, is the time-averaged velocity of the stream at the boundary layer thickness δ.

[0021] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of a method for measuring displacement thickness and momentum loss thickness of a strongly compressible turbulent boundary layer.

[0022] A device for measuring the displacement thickness and momentum loss thickness of a highly compressible turbulent boundary layer comprises a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of a method for measuring the displacement thickness and momentum loss thickness of a highly compressible turbulent boundary layer are implemented.

[0023] The advantages of the present invention compared with the prior art are:

[0024] (1) The present invention obtains a boundary layer velocity field with high vector resolution through an optical system of a high-resolution cross-frame CCD camera and a telephoto macro lens;

[0025] (2) The present invention obtains the model wall temperature through infrared thermal imaging technology, introduces the Walz equation combined with the velocity distribution, and obtains the boundary layer temperature distribution. Furthermore, the complete gas equation and the assumption that the pressure in the boundary layer is approximately constant are introduced to obtain the density distribution in the boundary layer. Finally, the displacement thickness and momentum loss thickness of the compressible flow turbulent boundary layer are obtained by integration. DETAILED DESCRIPTION

[0026] In order to better understand the above technical solution, the technical solution of the present invention is described in detail below through specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations on the technical solution of the present invention. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0027] The following is a further detailed description of a method for measuring displacement thickness and momentum loss thickness of a highly compressible turbulent boundary layer provided by an embodiment of the present invention. Specific implementation methods may include:

[0028] In a continuously operating hypersonic wind tunnel, the boundary layer velocity field distribution is obtained for the boundary layer flow field at a specific position of a flat plate model.

[0029] For a specific position of the flat plate model, obtain the wall temperature distribution after the model is thermally balanced;

[0030] By using the boundary layer velocity field distribution and wall temperature distribution at a specific flow direction station, the temperature distribution and density distribution along the normal direction of the flow in the boundary layer are obtained by introducing relevant assumptions, and then the displacement thickness and momentum loss thickness are calculated based on the temperature distribution and density distribution.

[0031] The solution provided in the embodiment of the present invention specifically includes:

[0032] 1. Step 1: In a continuously operating hypersonic wind tunnel, use PIV technology to obtain discrete high-resolution boundary layer instantaneous velocity field (u x,y ,v x,y ), where the subscripts x and y represent different flow direction positions and wall normal positions. The specific requirements for velocity field acquisition are as follows:

[0033] (1) Use a particle generator to inject tracer particles of a specific size into the wind tunnel flow field

[0034] Tracer particles with larger diameters have difficulty entering the hypersonic boundary layer or cannot represent the actual boundary layer airflow velocity. Therefore, the diameter of the tracer particles needs to be limited. Generally speaking, for TiO2 particles, the delay time should be better than 1 microsecond. The delay time τ is calculated as follows:

[0035]

[0036] The density of the particle is ρ p , with a diameter of d p , the density of the fluid is ρ f , the dynamic viscosity coefficient is υ f .

[0037] (2) Select dual-pulse laser light source and high-resolution cross-frame camera for flow field illumination and image acquisition

[0038] The illumination laser light source is the Nd:YAG high-energy double-pulse laser commonly used in PIV technology, with a single pulse energy of no less than 300mJ.

[0039] In order to obtain high-resolution boundary layer space velocity patterns, the more velocity vectors along the wall normal in the boundary layer, the better. The vector resolution R of the velocity vector along the wall normal in the boundary layer is defined as v-δ as follows:

[0040] R v-δ =δ / r v

[0041] Among them, r v is the number of velocity vectors in the normal direction of the wall surface within the boundary layer thickness, δ is the boundary layer thickness obtained by velocity field evaluation, and for the PIV velocity field, the boundary layer thickness δ is defined by the normal coordinate of the position close to 99% of the mainstream velocity value.

[0042] Optimize r v ≥20, so that the vector resolution R v-δ To achieve a small value and fully resolve the boundary layer velocity pattern, the selected cross-frame CCD camera should have high resolution, preferably with a resolution of at least 2000 pixels in the direction normal to the wall. The optical system should also have a high magnification factor, and preferably a telephoto macro lens with a focal length of f = 200 mm should be used for imaging. In the normal direction, the optical axis of the camera and lens optical system should be parallel to and just pass through the surface of the flat plate model, ensuring that the particle image only occupies approximately 1 / 2 of the CCD camera frame height to avoid the influence of wall reflections. A PIV system composed of these cameras was used to collect particle images during wind tunnel operation, and the PIV system cross-frame time Δt was recorded.

[0043] (3) Using the acquired particle images to analyze the instantaneous velocity field of the boundary layer (u x,y ,v x,y )calculate

[0044] According to the principle of PIV technology, the displacement field (du x,y ,dv x,y ), combined with the cross-frame time Δt, the boundary layer instantaneous velocity field (u x,y ,v x,y )=(du x,y / Δt,dv x,y Because the cross-correlation algorithm requires a certain interpretation range, the pixel resolution of the vector is much larger than 1 pixel. Although the pixel resolution of the vector can be improved by increasing the overlap rate of the interpretation area, the improvement effect is limited.

[0045] 2. Step 2: In a continuously operating hypersonic wind tunnel, use infrared thermal imaging technology to obtain the wall temperature distribution T w (x,z), z represents the spanwise coordinate of the plate model. The specific requirements for obtaining the surface temperature of the plate are as follows:

[0046] The model recommends using an approximate insulating material such as PEEK. In a continuously operating hypersonic wind tunnel, infrared thermal image data is selected after the wind tunnel has been running for a period of time and the model has reached temperature equilibrium, and temperature correction is performed considering the model surface reflectivity. For environments where the model predicts low temperatures (within 100°C), the insulating tape method can be used. That is, under a calibration environment, a piece of insulating tape with a known emissivity is attached to the model surface for a certain period of time. Then, by adjusting the emissivity of the infrared thermal imager, the surface temperature of the model being tested is made the same or similar to the surface temperature of the surface with the insulating tape. At this time, the thermal imager emissivity is considered to be the correct emissivity of the model being tested. Under this parameter, the surface temperature distribution T of the test model is measured. w (x,z) are considered to be measured values ​​within the allowable error range.

[0047] 3. Step 3: Calculate the displacement thickness and momentum loss thickness using the velocity data and wall temperature data at a specific flow direction station. The specific implementation is as follows:

[0048] (1) Calculate the temperature distribution in the turbulent boundary layer using the velocity profile and wall temperature.

[0049] The high-resolution boundary layer space velocity field has been obtained above, but since the velocity field measured by PIV cannot reach the time resolution, the stream velocity u at a specific stream position x0 is selected here. y x=x0 performs sample averaging of a large number of time series As an approximation of the time average The time-averaged velocity of the stream at the boundary layer thickness δ is definition is the time-averaged velocity in the boundary layer The time-averaged temperature at the location, is the time-averaged temperature at the boundary layer thickness δ, is the time-averaged wall temperature, The velocity field can be used to measure T at the cross section (z = z0) w (x,z) are obtained, is the recovery temperature, r is the rewarming factor, which is 0.89 for the compressible turbulent boundary layer. The boundary layer temperature distribution is estimated using the Walz equation:

[0050]

[0051] in,

[0052]

[0053] T0 is the total temperature of the incoming flow, which is obtained by measuring the total temperature in the wind tunnel test. Ma is the Mach number of the incoming flow. ∞ is the static temperature of the incoming flow, it can be approximately considered γ is the specific heat ratio of air, generally taken as γ = 1.4.

[0054] (2) Obtaining density distribution using the assumption of perfect gas and the assumption of stable pressure in the boundary layer

[0055] After obtaining the boundary layer temperature distribution, through the complete gas equation and the assumption of pressure approximation invariance, it can be considered that the pressure p is independent of y, so the boundary layer time-averaged velocity is Time-averaged density at location Given by:

[0056]

[0057] Among them, ρ ∞ is the static density of the incoming flow, which is given by

[0058]

[0059] Among them, ρ0 is the total density of the incoming flow, P0 is the total pressure of the incoming flow, which is obtained by measuring the total pressure in the wind tunnel test, and R is the perfect gas constant, which is R = 287.06 J / (kg.K).

[0060] (3) Calculate the displacement thickness and momentum loss thickness using the calculation formula for compressible flow displacement thickness and momentum loss thickness.

[0061] All the necessary parameters are available, and the displacement thickness and momentum loss thickness in the boundary layer are calculated using the following integral formula:

[0062]

[0063] where δ * is the displacement thickness of the compressible boundary layer, θ is the momentum loss thickness of the compressible boundary layer, and the discreteness of the data needs to be considered during integration.

[0064] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such changes and modifications fall within the scope of the claims and their equivalents, the present invention is intended to include such changes and modifications.

[0065] The contents not described in detail in the specification of the present invention belong to the common knowledge of those skilled in the art.

Claims

1. A method for measuring displacement thickness and momentum loss thickness of a strongly compressible turbulent boundary layer, characterized in that: include: In a continuously operating hypersonic wind tunnel, the boundary layer velocity field distribution is obtained for the boundary layer flow field at a specific position of a flat plate model. For a specific position of the flat plate model, obtain the wall temperature distribution after the model is thermally balanced; Using the boundary layer velocity field distribution and wall temperature distribution at a specific flow direction station, the temperature distribution and density distribution along the normal direction of the flow in the boundary layer are obtained by introducing relevant assumptions, and then the displacement thickness and momentum loss thickness are calculated based on the temperature distribution and density distribution; The temperature distribution is achieved by Calculate; where, is the time-averaged velocity in the boundary layer The time-averaged temperature at the location, is the time-averaged wall temperature, is the time-averaged temperature at the boundary layer thickness δ, To restore the temperature, is the time average of the streamwise velocity at a specific streamwise position in the boundary layer, is the streamwise time-averaged velocity at the boundary layer thickness δ; The density distribution is obtained by Calculate; where, is the time-averaged velocity of the boundary layer The time-averaged density at the location, ρ ∞ is the static density of the incoming flow, is the time-averaged velocity in the boundary layer Time-averaged temperature at location, T ∞ For the incoming flow, quiet and warm; The displacement thickness and momentum loss thickness are Among them, δ * is the displacement thickness of the compressible boundary layer, θ is the momentum loss thickness of the compressible boundary layer, δ is the boundary layer thickness, is the time-averaged velocity of the boundary layer The time-averaged density at the location, ρ ∞ is the static density of the incoming flow, is the time average of the streamwise velocity at a specific streamwise position in the boundary layer, is the time-averaged velocity of the stream at the boundary layer thickness δ.

2. The method for measuring displacement thickness and momentum loss thickness of a highly compressible turbulent boundary layer according to claim 1, characterized in that: The obtaining of the boundary layer velocity field distribution comprises: (1) Using a particle generator to inject tracer particles of a specific size into the wind tunnel flow field; (2) Select a dual-pulse laser light source and a high-resolution cross-frame camera for flow field illumination and image acquisition; (3) Using the acquired particle images to analyze the instantaneous velocity field of the boundary layer (u x,y ,v x,y ) calculation to obtain the boundary layer velocity field distribution.

3. The method for measuring displacement thickness and momentum loss thickness of a highly compressible turbulent boundary layer according to claim 2, characterized in that: The TiO2 particles in the boundary layer flow field meet a delay time of less than 1 microsecond.

4. The method for measuring displacement thickness and momentum loss thickness of a highly compressible turbulent boundary layer according to claim 2, characterized in that: The number of velocity vectors in the normal direction of the inner wall surface of the boundary layer thickness is not less than 20.

5. The method for measuring displacement thickness and momentum loss thickness of a highly compressible turbulent boundary layer according to claim 4, characterized in that: The selected cross-frame CCD camera meets the requirements of a resolution of not less than 2000 pixels in the normal direction of the wall and a lens focal length of f = 200 mm. In the normal direction, the optical axis of the camera and lens optical system is parallel to the surface of the flat plate model and just passes through the surface of the flat plate model, so that the particle image only occupies 1 / 2 of the CCD camera frame height.

6. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

7. A device for measuring displacement thickness and momentum loss thickness of a highly compressible turbulent boundary layer, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 5 are implemented.

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