A high-efficiency and high-precision numerical simulation method for propeller slipstream

Abstract

The present application proposes a high-efficiency and high-precision propeller slipstream numerical simulation method: firstly, the isolated propeller under actual working conditions is numerically simulated by using the frozen rotor method, the axial force and the circumferential force of the blade element are extracted by integrating the blade surface pressure and friction force at different radial positions, and the size and phase of the blade load are corrected by a semi-empirical method; then, the axial force and the circumferential force of the blade at the same radial position and different phases are taken as a group of fitting points, the fitting parameters based on the blade element momentum theory are obtained, and the non-uniform load distribution of the disc is predicted; next, the disc load is time-averaged, and the work of the propeller is converted into the axial and circumferential pressure increments of the excitation disc; finally, the pressure increments of the excitation disc are added to the momentum equation in the form of volume force source term, and then the slipstream effect is simulated. The method has both the calculation accuracy of the unsteady method and the calculation efficiency of the quasi-steady method, and has good engineering practicability.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of propeller slipstream numerical simulation, in particular to a high-efficiency and high-precision propeller slipstream numerical simulation method. BACKGROUND

[0002] At present, the propeller slipstream simulation methods based on quasi-steady and unsteady have been applied in engineering, the simulation accuracy of these methods is high, the main characteristics of propeller slipstream can be simulated, but there are certain limitations. The quasi-steady method uses the rotation of the coordinate system instead of the rotation of the real propeller, the slipstream characteristics are affected by the phase of the propeller, and the unsteady method has high requirements for computing resources and long computing time, which is difficult to be used for rapid iterative design of aircraft.

[0003] In view of the above shortcomings of quasi-steady and unsteady methods, the momentum source method attracts people's attention, especially with the emergence of distributed propeller propulsion aircraft. The momentum source method is to replace the real propeller geometry with a disc (excitation disc) with a certain thickness, and to realize the simulation of the axial acceleration effect and the circumferential rotation effect of the propeller by adding a source term to the momentum equation, which not only considers the time-averaged effect of the slipstream influence of the blades at different phases, but also converts the unsteady flow calculation of the propeller into the steady flow calculation of the excitation disc, shortening the research period of predicting the aerodynamic interference effect of propeller slipstream.

[0004] However, the traditional momentum source method has a contradiction between precision and efficiency when establishing the excitation disc load, the high-precision unsteady method is time-consuming, and the low-precision method is not accurate enough for the disc load. SUMMARY

[0005] In order to solve the problems in the prior art, the present application provides a high-efficiency and high-precision propeller slipstream numerical simulation method, which uses a new excitation disc load prediction model based on the combination of the frozen rotor method and the blade element momentum theory to improve the traditional momentum source method, so as to have the calculation precision of the unsteady method and the calculation efficiency of the quasi-steady method, and has good engineering practicability.

[0006] The technical scheme of the present application is as follows:

[0007] A high-efficiency and high-precision propeller slipstream numerical simulation method, comprising the following steps:

[0008] Step 1: using the frozen rotor method to perform numerical simulation on the isolated propeller under actual working conditions, extracting the blade element axial force and circumferential force by integrating the blade surface pressure and friction force at different radial positions, and correcting the blade element axial force and circumferential force;

[0009] Step 2: Using the axial and circumferential forces of the blade element at different phases at the same radial position as a set of fitting points, the fitting parameters based on the blade element momentum theory are obtained; while for different radial positions, fitting is performed separately to obtain the excitation disk load prediction model, which predicts the non-uniform load distribution of the propeller disk.

[0010] Step 3: Average the load on the propeller disk over time and convert the propeller work into axial and circumferential pressure increments on the excitation disk;

[0011] Step 4: Add the pressure increment of the excitation disk to the momentum equation in the form of a volumetric force source term to simulate the slip flow effect through the momentum source method.

[0012] Furthermore, in step 1, according to the formula

[0013]

[0014]

[0015] The axial force T′ and circumferential force F′ of the blade element calculated by the frozen rotor method are corrected. and To correct for the axial and circumferential forces on the rear blade element, r i and ψ i These represent the radial and circumferential positions of the leaf element, respectively; λ is the blade load correction factor; and ψ0 is the blade phase correction factor. It is the phase after the blade is corrected.

[0016] Furthermore, in step 2, based on the blade element momentum theory, the axial and circumferential forces of the blade element are expressed as follows:

[0017]

[0018]

[0019] in dL is the angle between the free flow velocity component and the resultant rotational speed, β is the induction angle, and dL and dD are the lift and drag of the leaf element.

[0020]

[0021]

[0022]

[0023] V0 is the free-flow velocity, α0 is the free-flow angle of attack, and n s ρ is the propeller rotational speed, r is the radial position of the blade element, ψ is the blade phase; ρ is the density, C L and C Dis the lift and drag coefficient of the blade element, b is the chord length of the blade element, dr is the infinitesimal element, and W is the geometric composite velocity of the airflow relative to the blade element.

[0024]

[0025] C L =k L α+C L0

[0026] C D =k D (C L -C LD0 ) 2 +C D0

[0027] V a k is the axial induced velocity. L It is the slope of the lift curve, C L0 The lift coefficient k is the lift coefficient at a 0-degree angle of attack. D C is the quadratic coefficient of the parabola in the riser-drag curve. D0 It is the minimum drag coefficient in the riser-drag curve, C LD0 Is with C D0 The corresponding lift coefficient, α is the angle of attack of the flow relative to the blade element;

[0028]

[0029] θ is the installation angle of the leaf element;

[0030] The parameter to be fitted is k L C L0 ,k D C D0 C LD0 V a and β.

[0031] Furthermore, in step 2, the objective function R is solved using the nonlinear least squares method. obj Minimize it to obtain the fitting parameters; the objective function R obj for:

[0032]

[0033] Where ψ i It is the phase of the i-th leaf element, and m is the total number of phases. and For a certain radial position, the phase ψ obtained through step 1 i The corresponding corrected axial and circumferential forces of the blade element, σ is the set of parameters to be fitted, f(ψ) i ,σ) and g(ψ) i,σ) are the expressions for the axial and circumferential forces of the leaf element as a function of the phase angle, obtained based on the leaf element momentum theory.

[0034] Furthermore, in step 2, for the blade separation region, the propeller disk load distribution is obtained using a linear interpolation method.

[0035] Further, in step 3, according to the formula...

[0036]

[0037]

[0038] The axial pressure increment Δp and circumferential pressure increment Δv of the excitation disk are obtained. ψ ·(ρu); where rdψdr is the area swept by the infinitesimal segment dr within time dψ / ω, N is the number of blades, and T′ and F′ are the axial and circumferential forces of the blades determined based on the disk load distribution predicted in step 2.

[0039] Furthermore, in step 4, the momentum equation is:

[0040]

[0041] In the formula, ρ is the density. Let t be the velocity and t be the time. For pressure, For mass force, The source term is: The volumetric force source term is:

[0042]

[0043] Where Δs is the thickness of the excitation disk. and The directions of the axial force T′ and the circumferential force F′ are Δp and Δv, respectively. ψ ·(ρu) represents the axial pressure increment and circumferential pressure increment of the excitation disk.

[0044] Furthermore, the present invention also proposes a computer-readable storage medium storing computer-executable instructions, which, when executed, are used to implement the above-described method.

[0045] And a computer system is proposed, comprising: one or more processors, and a computer-readable storage medium for storing one or more programs, which, when executed by the one or more processors, cause the one or more processors to implement the above method.

[0046] Beneficial effects

[0047] This invention proposes a highly efficient and accurate numerical simulation method for propeller slipflow. First, a frozen rotor method is used to numerically simulate an isolated propeller under actual operating conditions. The axial and circumferential forces of the blade elements are extracted by integrating the surface pressure and friction at different radial positions of the blades, and the magnitude and phase of the blade load are corrected using a semi-empirical method. Then, the axial and circumferential forces of the blades at different phases at the same radial position are used as a set of fitting points to obtain fitting parameters based on blade element momentum theory, thereby predicting the non-uniform load distribution on the propeller disk. Next, the propeller disk load is time-averaged, and the propeller work is converted into the axial and circumferential pressure increments of the excitation disk. Finally, the pressure increments of the excitation disk are added to the momentum equation in the form of a volumetric force source term to simulate the slipflow effect. This method combines the computational accuracy of unsteady methods with the computational efficiency of quasi-steady methods, exhibiting good engineering applicability.

[0048] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0049] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0050] Figure 1 : Schematic diagram of the rotating propeller element and the fixed excitation disk element; (a) rotating propeller element; (b) fixed excitation disk element;

[0051] Figure 2 : The velocity polygon of the propeller blade element;

[0052] Figure 3 Flowchart of the momentum source method;

[0053] Figure 4 : Geometric model of a turboprop aircraft;

[0054] Figure 5 Definitions of the positions of each section of the left wing and the propeller phase angle;

[0055] Figure 6 Comparison of pressure distribution across different sections of the left wing; a) y = -0.240m, b) y = -0.408m, c) y = -0.642m, d) y = -0.810m, e) y = -1.075m, f) y = -1.392m;

[0056] Figure 7Comparison of total pressure cloud maps at position y = -0.468m; a) Sliding mesh method (ψ = 0°), b) Sliding mesh method (ψ = 30°), c) Frozen rotor method (ψ = 0°), d) Frozen rotor method (ψ = 30°), e) Hybrid plane method (ψ = 0°), f) High-efficiency and high-precision momentum source method;

[0057] Figure 8 Comparison of total pressure cloud maps at position y = -0.984m; a) Sliding mesh method (ψ = 0°), b) Sliding mesh method (ψ = 30°), c) Frozen rotor method (ψ = 0°), d) Frozen rotor method (ψ = 30°), e) Hybrid plane method (ψ = 0°), f) High-efficiency and high-precision momentum source method;

[0058] Figure 9 Comparison of propeller slipstream wakes: a) Slip mesh method (ψ = 0°), b) Slip mesh method (ψ = 30°), c) Frozen rotor method (ψ = 0°), d) Frozen rotor method (ψ = 30°), e) Hybrid plane method (ψ = 0°), f) High-efficiency and high-precision momentum source method. Detailed Implementation

[0059] This invention addresses the trade-off between accuracy and efficiency in establishing excitation disk loads using traditional momentum source methods. Specifically, high-precision unsteady methods are time-consuming, while low-precision methods result in inaccurate disk load measurements. To address this, a highly efficient and accurate numerical simulation method for propeller slipflow is proposed. This method employs a novel excitation disk load prediction model combining the frozen rotor method and blade element momentum theory to improve upon traditional momentum source methods. This results in a method that combines the computational accuracy of unsteady methods with the computational efficiency of quasi-steady methods, demonstrating good engineering applicability.

[0060] To better illustrate this invention, the basic principle of the momentum source method used in this invention will first be explained:

[0061] 1. Governing equations

[0062] The momentum source method used in this invention involves defining a disk with a certain thickness in the propeller region, and adding a volume force source term within the computational grid enveloped by the disk boundary to simulate the propeller's influence on the axial and circumferential momentum of the flow field. The momentum equation after adding the volume force source term is as follows:

[0063]

[0064] In the formula, ρ is the density. Let t be the velocity and t be the time. For pressure, For mass force, For source terms.

[0065] The volumetric force source term needs to be obtained by conversion based on the actual propeller load. Figure 1 A schematic diagram of a rotating propeller element and a fixed excitation disk element is given. The study focuses on the element segment dr of the propeller and excitation disk. The area swept by the element segment within the time interval dt = dψ / ω is dS = rdψdr. Based on the fact that the change in airflow through the propeller is constant within one rotation period T, the corresponding relationships of the axial and circumferential load distributions of the propeller and excitation disk are as follows:

[0066]

[0067]

[0068] In the formula, Δp and Δv ψ ·(ρu) represents the axial and circumferential pressure increments of the excitation disk, T′ and F′ represent the axial and circumferential forces of the blades, respectively, and N represents the number of blades.

[0069] The volumetric force source term of the momentum source method can be expressed as:

[0070]

[0071] Where Δs is the thickness of the excitation disk. and These are defined as the directions of the axial force T′ and the circumferential force F′ of the propeller, respectively.

[0072] 2. The excitation disk load prediction model proposed in this invention

[0073] The difference in load distribution between the excitation disk and the propeller directly affects the accuracy of slipflow simulation, and efficient evaluation of slipflow effects is required in engineering. Therefore, this invention proposes a novel excitation disk load prediction model by utilizing high-precision loads of different phases obtained through the frozen rotor method and the circumferential blade load variation law given by blade element momentum theory.

[0074] Compared to low-precision blade element momentum theory, the frozen rotor method can calculate blade loads at a fixed phase more accurately, while its computational efficiency is significantly higher than that of unsteady methods. However, due to the size of the rotating domain and the interaction of the blade wake, the magnitude and phase of the blade loads in the frozen rotor method still differ somewhat from the unsteady results. This can be addressed by...

[0075]

[0076] It was corrected using a semi-empirical method, where T′ and F′ are the axial and circumferential forces of the blade element calculated by the frozen rotor method. and Corrected axial and circumferential forces of the blade element, r i and ψ iThese represent the radial and circumferential positions of the leaf element, respectively; λ is the blade load correction factor; and ψ0 is the blade phase correction factor. It is the phase after the blade is corrected.

[0077] In the corresponding embodiment of the present invention, the magnitude and phase correction coefficients for the load are given based on the unsteady junction: λ = 1.07, ψ0 = 20°. These correction coefficients can be applied to the same propeller thrust level at different angles of attack. Correction coefficients for other propeller blades can also be directly given based on the designer's experience.

[0078] The blade element momentum theory can provide the circumferential variation law of blade load in one rotation cycle, thus avoiding time-consuming unsteady-state simulation. Figure 2 The velocity polygon based on the blade element momentum theory is shown. The geometrically synthesized velocity of the airflow relative to the blade element is:

[0079]

[0080]

[0081] Where V0 is the free-flow velocity, α0 is the free-flow angle of attack, and V a The axial induced velocity, The angle between the free flow velocity component and the resultant rotational speed is β, where β is the induced angle and n is n. s denoted as propeller speed, r as radial position of blade element, and ψ as blade phase.

[0082] Given that the installation angle of the blade element is θ, the angle of attack of the airflow relative to the blade element is:

[0083]

[0084] Assuming lift varies linearly with the angle of attack, and drag is a quadratic function of lift, the lift and drag of the blade element can be expressed as:

[0085]

[0086]

[0087] C L =k L α+C L0 (11)

[0088] C D =k D (C L -C LD0 ) 2 +C D0 (12)

[0089] Among them, C L and CD It is the lift and drag coefficient of leaf element, k L It is the slope of the lift curve, C L0 The lift coefficient k is the lift coefficient at a 0-degree angle of attack. D C is the quadratic coefficient of the parabola in the riser-drag curve. D0 It is the minimum drag coefficient in the riser-drag curve, C LD0 Is with C D0 The corresponding lift coefficient, b is the leaf element chord length.

[0090] The axial and circumferential forces of the leaf element can be expressed as:

[0091]

[0092]

[0093] Assuming axial induced velocity V a If the induced angle β is uniformly distributed circumferentially, then the parameter k that needs to be determined in the load model is... L C L0 ,k D C D0 C LD0 V a And β. The optimal estimates of these seven parameters can be obtained using the nonlinear least squares method (making the objective function R... obj (Minimum).

[0094]

[0095] Where, ψ i σ is the leaf element phase, m is the total number of phases, σ is the set of seven parameters to be fitted, and f and g are the theoretical functions of the leaf element axial force and circumferential force as a function of the phase angle, respectively, as shown in equations (13) and (14).

[0096] Based on the above control equations and excitation disk load prediction model, the flowchart of the efficient and high-precision propeller slipflow numerical simulation method proposed in this invention is as follows: Figure 3 As shown, the specific steps are as follows:

[0097] Step 1: The frozen rotor method is used to numerically simulate the isolated propeller under actual working conditions. The axial force and circumferential force of the blade element are extracted by integrating the blade surface pressure and friction at different radial positions. The magnitude and phase of the blade load are corrected by a semi-empirical method, as shown in formula (5).

[0098] Step 2: Take the axial force and circumferential force of the blade element at different phases at the same radial position as a set of fitting points to obtain the fitting parameters based on the blade element momentum theory. For different radial positions, perform fitting respectively to obtain the excitation disk load prediction model and predict the non-uniform load distribution of the propeller disk. The specific form is shown in formulas (6) to (15). Of course, for the blade separation region, the linear interpolation method can be used instead of the fitting method.

[0099] Step 3: Average the load on the propeller disk over time and convert the propeller work into the axial and circumferential pressure increments of the excitation disk, as shown in formulas (2) and (3).

[0100] Step 4: Add the pressure increment of the excitation disk to the momentum equation in the form of a volumetric force source term, as shown in formulas (1) and (4), to simulate the slip flow effect.

[0101] It is worth noting that the non-uniform load on the propeller disk generates lift and pitching torque, while the rotation of the left and right propellers in the same direction also generates yaw and roll torque. In the efficient and high-precision momentum source method, the propeller forces and torques can be obtained by integrating the load on the excitation disk.

[0102] In this embodiment, a turboprop aircraft is used for verification, and its geometry is as follows: Figure 4 As shown, the Mach number of the incoming flow at takeoff is 0.2, and the angle of attack is 12°. To demonstrate the advantages of the High Efficiency and High Precision Momentum Source Method (HPE-MSM) in terms of efficiency and accuracy, its engineering applicability is verified by comparing the results with those of typical propeller slipflow numerical simulation methods such as the Slip Grid Method (SMM), the Frozen Rotor Method (FRM), and the Hybrid Plane Method (MPM).

[0103] The positions of the cross sections of the left wing and the definition of the propeller are as follows: Figure 5 As shown. In the numerical simulation, the typical slip grid method starts outputting results after the unsteady flow field reaches stable fluctuations after the propeller rotates 15 times. The frozen rotor method selects two typical propeller phases, ψ=0° and ψ=30°, for quasi-steady simulation. The hybrid plane method, due to considering the circumferential averaging effect, only selects the ψ=0° phase for quasi-steady simulation. The high-efficiency and high-precision momentum source method uses an excitation disk instead of a real propeller for steady simulation.

[0104] Table 1 compares the computational resource consumption of different numerical simulation methods. Figures 6-9 The pressure distribution of each section of the left wing is compared, as are the total pressure cloud maps of the propeller's upper and lower wash sides and the propeller slipstream wake.

[0105] Table 1 Comparison of computational resource consumption for different numerical simulation methods

[0106]

[0107]

[0108] The time-averaged pressure distribution of the slip grid method is very close to the experimental value. The velocity of the airflow does not change significantly when passing through the interface between the rotating and stationary domains. The slip flow rotates and develops backward over time, which is more in line with the real physical situation. However, the unsteady simulation consumes significantly more computational resources than the other three methods.

[0109] The pressure distribution results of the frozen rotor method are significantly affected by the propeller phase. When the airflow moves from the rotating domain to the stationary domain, the slipstream changes from the direction of the blade chord to the direction of the incoming flow velocity. The slipstream is mainly characterized by a high-energy wake region with a fixed flow direction and a rotational tendency. This phenomenon is obviously a non-physical situation.

[0110] Because the hybrid plane method takes into account the circumferential averaging effect, when the angle of attack of the incoming flow is positive, the vertical velocities on the left and right sides of the propeller will cancel each other out, so the angle of attack of the slipstream region will be significantly reduced and its pressure distribution will deviate significantly from the experimental value. Therefore, this method should be used with caution in slipstream numerical simulation.

[0111] The efficient and high-precision momentum source method simulates the slipstream intensity and location with accuracy comparable to unsteady time-averaged results, effectively simulating the interference between the slipstream and the wing, rear fuselage, horizontal stabilizer, and vertical stabilizer. Because it uses an excitation disk instead of a real propeller, its computational resource consumption is lower than that of quasi-steady methods (frozen rotor method and hybrid plane method). Therefore, the efficient and high-precision momentum source method proposed in this invention combines the computational accuracy of unsteady methods with the computational efficiency of quasi-steady methods, demonstrating good engineering applicability.

[0112] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A highly efficient and high-precision numerical simulation method for propeller slipstream, characterized in that: Includes the following steps: Step 1: Numerical simulation of an isolated propeller under actual operating conditions is performed using the frozen rotor method. Axial and circumferential forces of the blade element are extracted by integrating the surface pressure and friction at different radial positions of the blade, and then corrected for these forces. Specifically, according to the formula... Axial force of blade element calculated using the frozen rotor method and circumferential force Make corrections. and To correct for the axial and circumferential forces on the rear leaf element, and These represent the radial and circumferential positions of the leaf element, respectively. It is the blade load correction factor. It is the blade phase correction factor. It is the phase after the blade is corrected; Step 2: Using the axial and circumferential forces of the blade element at different phases at the same radial position as a set of fitting points, the fitting parameters based on the blade element momentum theory are obtained; for different radial positions, fitting is performed separately to obtain the excitation disk load prediction model, predicting the non-uniform load distribution of the propeller disk; wherein, the objective function is solved by nonlinear least squares method. Minimize the objective function to obtain the fitted parameters; for: in It is the phase of the i-th leaf element, and m is the total number of phases. and For a certain radial position, the phase obtained through step 1 The corresponding corrected axial and circumferential forces of the blade element, It is the set of parameters to be fitted. and The expressions for the axial and circumferential forces of the blade element as a function of the phase angle are derived from the blade element momentum theory. Step 3: Average the load on the propeller disk over time and convert the propeller work into axial and circumferential pressure increments on the excitation disk; Step 4: Add the pressure increment of the excitation disk as a volumetric force source term to the momentum equation to simulate the slipflow effect using the momentum source method; the momentum equation is: In the formula, For density, For speed, For time, For pressure, For mass force, The source term is: The volumetric force source term is: in, For the thickness of the excitation disk, and Axial force He Zhou Xiangli direction, and This refers to the axial pressure increment and circumferential pressure increment of the excitation disk.

2. The efficient and high-precision numerical simulation method for propeller slipstream according to claim 1, characterized in that: In step 1, take =1.07, =20°.

3. The efficient and high-precision numerical simulation method for propeller slipstream according to claim 1, characterized in that: In step 2, based on the blade element momentum theory, the expressions for the axial and circumferential forces of the blade element are as follows: in The angle between the free flow velocity component and the resultant rotational speed. The induced angle, and For the lift and drag of leaf elements; For free flow velocity, For free-flow angle of attack, The propeller speed, The radial position of the leaf element. For the blade phase; For density, and C D 'b' is the lift and drag coefficients of the leaf element, and 'b' is the chord length of the leaf element. It is a micro-element; The geometric composite velocity of the airflow relative to the leaf element; For axial induced velocity, k L It is the slope of the lift curve, C L0 The lift coefficient k is the lift coefficient at a 0-degree angle of attack. D C is the quadratic coefficient of the parabola in the riser-drag curve. D0 It is the minimum drag coefficient in the riser-drag curve, C LD0 Is with C D0 The corresponding lift coefficient, The angle of attack of the flow relative to the leaf element; The installation angle of the leaf element; The parameter to be fitted is k L C L0 , k D C D0 C LD0 V a and β.

4. The efficient and high-precision numerical simulation method for propeller slipstream according to claim 1, characterized in that: In step 2, for the blade separation region, the propeller disk load distribution is obtained using a linear interpolation method.

5. The efficient and high-precision numerical simulation method for propeller slipstream according to claim 1, characterized in that: Step 3, according to the formula Obtain the axial pressure increment of the excitation disk and circumferential pressure increment ;in In time Inner micro segment The area swept The number of blades, and The axial and circumferential forces of the blades are determined based on the propeller disk load distribution predicted in step 2.

6. A computer-readable storage medium storing computer-executable instructions, characterized in that: When executed, the instructions are used to implement the method of any one of claims 1 to 5.

7. A computer system, comprising: One or more processors, the computer-readable storage medium of claim 6, for storing one or more programs, characterized in that: when the one or more programs are executed by the one or more processors, the one or more processors implement the method of any one of claims 1 to 5.

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