A method for measuring and determining boundary layer transition
By employing the arrangement entropy method and transition identification sensors in fluid mechanics experiments, the problem of poor reliability of traditional discrimination methods in the transition region is solved, and efficient and low-interference measurement of boundary layer flow state is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- BEIHANG UNIV
- Filing Date
- 2025-12-04
- Publication Date
- 2026-06-05
AI Technical Summary
Traditional laminar-turbulent flow discrimination methods have poor reliability when dealing with intermittent flow in the transition zone, and hot-wire anemometer measurement methods are costly and interfere with the flow field.
The method of arrangement entropy based on nonlinear dynamics is adopted. Transition identification sensors are attached to the model surface, and the flow state is calculated by using arrangement entropy. Combined with the intermittent factor, the flow state is quantitatively described, which simplifies the sensor fixing scheme and reduces flow interference.
It achieves reliable and sensitive discrimination of boundary layer flow state, is suitable for complex surface measurement, reduces experimental costs and flow interference, and is suitable for high-precision flow research.
Smart Images
Figure CN122149800A_ABST
Abstract
Description
Technical Field
[0002] This invention relates to the field of fluid mechanics experimental measurement and signal processing technology applications, and is a boundary layer transition measurement and discrimination method, specifically a wall laminar-turbulent flow discrimination method based on information entropy in fluid mechanics experiments. Background Technology
[0004] In fluid mechanics research, the laminar-turbulent transition in boundary layer flow is a core issue. Accurately identifying and distinguishing between laminar, turbulent, and intermittent flow states during the transition process is crucial for understanding transition mechanisms, verifying theoretical models, and for engineering applications (such as drag reduction and thermal control). Traditional laminar-turbulent flow discrimination methods primarily rely on the analysis of the time-domain or frequency-domain characteristics of flow velocity signals.
[0005] Traditional methods for distinguishing between laminar and turbulent flow mainly consist of three types: time-domain methods, frequency-domain methods, and shape factor methods. The time-domain method determines whether the root mean square (RMS) of the velocity fluctuation signal exceeds a certain empirical threshold. This method is prone to misjudgment in strongly intermittent flows and is highly threshold-dependent. The frequency-domain method analyzes the energy spectrum of the velocity signal to observe the presence of broadband turbulent energy spectrum characteristics. This method is sensitive to the signal-to-noise ratio, and in the early stages of transition, the turbulent spot scale is small, and the spectral characteristics are not obvious. The shape factor method calculates the shape factor by measuring the boundary layer velocity profile, which requires complete profile information and is complex to measure. These traditional methods show a significant decrease in reliability when facing the spatiotemporal intermittency (i.e., random alternation of laminar and turbulent sections) in the transition region, making it difficult to accurately capture rapid, localized changes in the flow state.
[0006] In recent years, nonlinear dynamics theory has provided new tools for the analysis of complex time series. Permutation entropy and statistical complexity are two indicators that can effectively characterize the randomness and structural complexity of time series. However, there are currently no publicly available schemes that systematically apply these methods to flat plate boundary layer experiments and successfully achieve highly reliable laminar-turbulent state discrimination, especially for intermittent flows.
[0007] Traditionally, boundary layer flow field signals are acquired using hot-wire anemometers. However, this method has several limitations. First, the measurement probe needs to penetrate deep into the boundary layer, reaching a position very close to the wall. This relies on the displacement adjustment of a high-precision coordinate frame, which not only increases testing costs but also requires mechanical structures to set up the coordinate frame. Second, as a contact-based measurement method, hot-wire measurement interferes with the measured flow field to some extent, affecting the overall experimental results. Summary of the Invention
[0009] To overcome the shortcomings of existing technologies, this invention proposes a method for measuring and identifying boundary layer transition. This method, based on arrangement entropy in nonlinear dynamics, distinguishes between laminar and turbulent flow states. It can more reliably and sensitively identify laminar, turbulent, and intermittent flow states, and is particularly suitable for detailed analysis of transition regions.
[0010] The boundary layer transition measurement device and discrimination method of the present invention comprises the following steps:
[0011] Step 1: Calibrate the transition sensor to obtain the transition sensor voltage signal. With speed signal The relationship is used to establish a calibration curve.
[0012] Step 2: Deploy transition sensors on the target wall of the experimental model; turn on the wind tunnel and set the target operating conditions. Once the target operating conditions are reached, activate the transition sensors to collect the boundary layer velocity time series signal. .
[0013] Step 3: Convert the original velocity time series signal Divided into several time windows; each window contains a fixed number of elements. The original velocity sample; the dimension of the instantaneous velocity sample vector is selected. .
[0014] Step 4: Calculate the normalized permutation entropy within each time window. .
[0015] 401: From the raw velocity time series signal within the window China and Israel Select specified elements for the sampling interval to construct multiple instantaneous velocity sample vectors of dimension D. ; .
[0016] 402: Count the number of vectors in the constructed instantaneous velocity sample that conform to the ascending arrangement π, and calculate the proportion of vectors with this arrangement to the total number of vectors. This is the probability of that arrangement occurring.
[0017] .
[0018] 403: Calculate permutation entropy .
[0019] 404: Maximum value of permutation entropy Normalized permutation entropy, we get .
[0020] Step 5: Select the critical value It is used to determine the flow state; if the result calculated within a certain time window is... > If so, it indicates that the flow within the window is in a laminar state; if < If , it indicates that the flow is in a turbulent state.
[0021] Step 6: Count the number of windows identified as turbulent across all time windows. Calculate the intermittent factor : = ;in The total number of windows quantitatively describes the transition process; when At that time, the flow is laminar. At that time, the flow is turbulent. At that point, the flow is in a critical state.
[0022] The present invention has the following beneficial effects:
[0023] 1. The transition identification sensor proposed in this invention can be attached to any model surface that requires measurement and identification of boundary layer transition states, facilitating measurements on surfaces with a certain degree of complexity (such as wing surfaces). Furthermore, the method involved in this invention requires no additional fixing structures or displacement mechanisms after calibration, greatly simplifying the design of sensor fixing schemes in experiments and minimizing the interference of contact measurements on the flow field, making it suitable for high-precision flow research scenarios.
[0024] 2. This invention identifies flow states based on information entropy technology. It analyzes velocity time-series signals measured by sensors, calculates the dimensionless permutation entropy of the signal and statistically analyzes the intermittency factor, thereby distinguishing the laminar-turbulent state of the boundary layer and providing a quantitative description of the critical flow state, effectively reflecting the intermittency of the turbulent structure during the transition process. Attached Figure Description
[0026] Figure 1 This is an overall flowchart of the boundary layer transition measurement and discrimination method of the present invention.
[0027] Figure 2 This diagram illustrates the installation method and calibration scenario of the transition recognition sensor on the model surface. Detailed Implementation
[0029] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.
[0030] This invention relates to a boundary layer transition measurement and discrimination method based on information entropy, such as... Figure 1 As shown, the specific steps are as follows:
[0031] Step 1: Transition identification sensor calibration.
[0032] Transition detection sensors (such as hot-film sensors) need to be calibrated beforehand. The calibration process is performed in a wind tunnel, such as... Figure 2 As shown, specifically:
[0033] The transition recognition sensor to be used is attached to the surface of a smooth flat plate model, positioned at a spanwise center distance from the leading edge of the model. This flat plate model is horizontally set in the core area of the wind tunnel center and supported on the bottom tunnel wall by a metal workpiece with a shaped flow-rectified profile.
[0034] During the installation of the transition sensor, it is important to ensure that the transition sensor does not protrude excessively from the smooth flat plate surface. This can be achieved by slotting the transition sensor on the surface of the flat plate model. Furthermore, by laying gaskets or putty material at the junction of the transition sensor and the flat plate model, the transition sensor and the surface of the flat plate model can be smoothly transitioned, minimizing the interference of the sensor itself on the flow and thus reducing flow interference.
[0035] Near the transition sensor location (3 mm vertically from the top surface of the flat plate model), the flow field information at that location was measured using a hot-wire anemometer to determine the average wind speed during a single calibration sampling period. This serves as a reference speed. Simultaneously, the transition sensor voltage signal output is recorded to determine the average value of the transition sensor output voltage within the sampling time of a single calibration condition. .
[0036] The wind tunnel inflow velocity was then varied (e.g., from 5 m / s to 50 m / s in 5 m / s increments), and multiple sets of data (at least 10 sets) were measured using the aforementioned method, including the reference velocity and the average sensor voltage.
[0037] Finally, the transition sensor voltage signal was obtained through fourth-order polynomial fitting. With speed signal Relationship Establish calibration curves:
[0038]
[0039] in, arrive The fitting coefficients are denoted as .
[0040] The calibration curve is used to convert the sensor voltage into a velocity value in subsequent experiments. The calibration process should ensure that the gas parameters (such as gas composition, temperature, pressure, etc.) are consistent with the experimental conditions to reduce errors.
[0041] Step 2: Experimental model setup and data acquisition.
[0042] Transition sensors are deployed at the target wall (the wall surface requiring laminar-turbulent flow analysis) of the experimental model (e.g., the surface of an aircraft wing). The wind tunnel is turned on and target conditions are set (e.g., specific angle of attack, Reynolds number). Once the target conditions are reached, the transition sensors are activated to begin data acquisition. Boundary layer velocity time-series signals are acquired using the transition sensors. The sampling frequency should be high enough (typically no less than 10 kHz) to capture high-frequency turbulent fluctuations. The signal length should contain at least 10,000 data points to ensure statistical reliability.
[0043] Step 3: Time window division and in-window entropy calculation
[0044] To better describe the intermittency of the boundary layer transition process, the original velocity time series signal was... It is divided into several time windows. Each window contains a fixed number of elements. The original velocity sample. Selecting an appropriate dimension for the instantaneous velocity sample vector. For example, consider In this case, set , That is, the velocity time series signal in the selected k-th window. There are a total of 200 original velocity samples.
[0045] Step 4: Calculate the normalized permutation entropy within each time window using the following method. .
[0046] 401: Construction of instantaneous velocity sample vectors.
[0047] Raw velocity time series signal from the window China and Israel Select specified elements for the sampling interval to construct multiple instantaneous velocity sample vectors of dimension D. You can select up to [number] The instantaneous velocity sample vector is composed of several elements. The sampling interval between adjacent sample points. The time scale is selected based on the flow field characteristics and sampling conditions, and is usually... Estimation based on the average flow timescale. , This represents the dimension of the original velocity time series signal within the window, i.e., the number of elements. For example, in step 401 above, the velocity time series signal of the k-th window... It can be divided into 197 instantaneous velocity sample vectors ,in Through each By selecting one at a time, the dimension of the original velocity time series signal can be reduced. reduce times.
[0048] 402: Permutation probability calculation.
[0049] For each instantaneous velocity sample vector There must exist a way to arrange the elements in a vector such that the elements in the vector are arranged in ascending order, that is... , for The 0th, 1st, ..., 2nd elements in the permutation correspond to A certain arrangement obtained through permutation and combination satisfies For example, if the instantaneous velocity sample vector is {6, 7, 4} and the elements are arranged in ascending order according to {2, 0, 1}... Sort, then ,in =2, =0, =1, substitute each element with its index to get .
[0050] When the elements of the instantaneous velocity sample vectors constructed based on the original velocity time series signal are arranged in ascending order, the number of various permutations that conform to each pattern is counted, and the proportion of vectors with that permutation out of the total number of vectors is calculated, which is the probability of that permutation occurring.
[0051] .
[0052] This uses the original velocity time series signal ( =9) is {3, 6, 7, 4, 8, 9, 1, 2, 3}, the dimension D of all instantaneous velocity sample vectors is 3, and the step size is... Taking step 3 as an example, a total of [number] steps can be constructed. -(D-1) = 7 instantaneous velocity sample vectors, namely: {3, 6, 7}, {6, 7, 4}, {7, 4, 8}, {4, 8, 9}, {8, 9, 1}, {9, 1, 2}, {1, 2, 3}. Then, the vectors satisfying {0, 1, 2} are counted. Sort the data so that {3, 6, 7} satisfies {0, 1, 2}. Sort the following: {6, 7, 4} satisfies {2, 0, 1}. Sort the data. Then, count the number of instantaneous velocity sample vectors that satisfy the above ascending arrangement of elements and calculate the probability. Then examine each... How many instantaneous velocity sample vectors satisfy the sorting condition? For example, how many instantaneous velocity sample vectors satisfy {0, 1, 2} are there in {3, 6, 7}, {1, 2, 3}, and {4, 8, 9}? Sort, then p( ={0, 1, 2}) = 3 / 7.
[0053] In addition to the p calculated above ( In addition to 3 / 7 (={0, 1, 2}), we also need to calculate... ={1, 2, 0}、 The proportion of instantaneous velocity sample vectors p in the arrangement of elements in ascending order, such as {2, 0, 1}. ={1, 2, 0}), p( ={2, 0, 1}), We need to calculate the probability of each possibility (6 possibilities when D=3) before proceeding to the next step of calculating the permutation entropy.
[0054] 403. Calculation of permutation entropy.
[0055] Based on all probability distributions determined in sub-step 402 Calculate the permutation entropy Permutation entropy reflects the degree of randomness in a time series: in laminar flow, velocity fluctuations are small but almost completely random, and permutation entropy... The permutation entropy is relatively high; however, in turbulent flow, due to the presence of quasi-ordered structures, although the fluctuations are higher, they possess a certain degree of repeatability and regularity, thus the permutation entropy is relatively high. Lower.
[0056] 404. Permutation Entropy Normalization
[0057] For the sample under consideration (all instantaneous velocity sample vectors) For a dimensional vector, the total number of possible permutations is Therefore, the maximum value of the permutation entropy is... ,pass Normalized permutation entropy is obtained Normalized permutation entropy The value range is [0,1], which facilitates subsequent comparison and threshold setting.
[0058] Step 5: Flow state determination
[0059] Selecting critical values Used to determine flow state; critical value This can be determined through prior experiments or theoretical analysis, such as calibration under known laminar and turbulent flow conditions, or based on relevant theories and experience. If calculated within a certain time window... > If so, the flow within that window is considered to be laminar. < If the flow rate is high, it is considered to be in a turbulent state.
[0060] Step 6: Calculation of Intermittent Factor
[0061] Count the number of windows identified as turbulent across all time windows. Calculate the intermittent factor : = .in, This represents the total number of windows. This factor can quantitatively describe the transition process, that is, the laminar-turbulent transition process at this location of the wall; and when At that time, the flow is laminar. At that time, the flow is turbulent. At that point, the flow is in a critical state.
Claims
1. A method for measuring and determining boundary layer transition, characterized in that: The specific steps are as follows: Step 1: Calibrate the transition sensor to obtain the transition sensor voltage signal. With speed signal Establish calibration curves based on the relationship between the two: Step 2: Deploy transition sensors on the target wall of the experimental model; turn on the wind tunnel and set the target operating conditions. Once the target operating conditions are reached, activate the transition sensors to collect the boundary layer velocity time series signal. ; Step 3: Convert the original velocity time series signal Divided into several time windows; each window contains a fixed number of elements. The original velocity sample; the dimension of the instantaneous velocity sample vector is selected. ; Step 4: Calculate the normalized permutation entropy within each time window. ; 401: From the raw velocity time series signal within the window China and Israel Select specified elements for the sampling interval to construct multiple instantaneous velocity sample vectors of dimension D. ; ; 402: Count the number of vectors in the constructed instantaneous velocity sample that conform to the ascending arrangement π, and calculate the proportion of vectors with this arrangement to the total number of vectors. This is the probability of that arrangement occurring. ； 403: Calculate permutation entropy ; 404: Maximum value of permutation entropy Normalized permutation entropy, we get ; Step 5: Select the critical value It is used to determine the flow state; if the result calculated within a certain time window is... > If so, it indicates that the flow within the window is in a laminar state; if < This indicates that the flow is in a turbulent state. Step 6: Count the number of windows identified as turbulent across all time windows. Calculate the intermittent factor : = ;in The total number of windows quantitatively describes the transition process; when At that time, the flow is laminar. At that time, the flow is turbulent. At that point, the flow is in a critical state.
2. The boundary layer transition measurement and discrimination method as described in claim 1, characterized in that: The calibration of the dedicated transition identification sensor in step 1 is carried out in a wind tunnel, specifically as follows: First, the transition recognition sensor to be used is attached to the surface of a smooth flat plate model, located at the spanwise center of the leading edge of the model; the flat plate model is placed in the core area of the wind tunnel; the flow field information at the location of the transition sensor is measured using a hot-wire anemometer to determine the average wind speed during a single calibration sampling time. The reference speed is recorded; simultaneously, the transition sensor voltage signal output is recorded to determine the average value of the transition sensor output voltage within the sampling time of a single calibration condition. ; Subsequently, the wind tunnel inflow velocity was changed, and multiple sets of data were measured using the aforementioned method, including the reference velocity and the average value of the sensor voltage. Finally, the transition sensor voltage signal was obtained by fourth-order polynomial fitting. With speed signal Relationship Establish calibration curves.
3. The boundary layer transition measurement and discrimination method as described in claim 1, characterized in that: The transition sensor is placed in a slot on the surface of the flat plate model, and a smooth transition is achieved at the point where the transition sensor meets the flat plate model.
4. The boundary layer transition measurement and discrimination method as described in claim 1, characterized in that: The flat plate model is supported on the bottom cavity wall by a metal workpiece with a shaped and streamlined design.
5. The boundary layer transition measurement and discrimination method as described in claim 1, characterized in that: In step 2, the sampling frequency is no less than 10 kHz, and the signal length contains at least 10,000 data points.
6. The boundary layer transition measurement and discrimination method as described in claim 1, characterized in that: Normalized permutation entropy The value range is [0,1].