A variable-momentum-gradient-based diffuser design method

Abstract

This invention discloses a diffuser design method based on variable variable gradient, relating to the field of diffuser design. The method includes: establishing a one-dimensional flow analysis model containing mass, momentum, and energy conservation equations; specifying a variable variable gradient objective function along the flow direction, defined as the spatial rate of change of fluid momentum along the flow direction; coupling the objective function with the mass conservation equation, and iteratively solving the closed equation set in conjunction with boundary conditions to obtain the variation law of the diffuser cross-sectional area along the flow direction; generating the profile curve accordingly, and iteratively optimizing it through three-dimensional numerical simulation. This invention directly couples the flow field control objective to the geometric profile design process, realizing active control of boundary layer growth and pressure distribution, effectively suppressing flow separation, improving the pressure recovery coefficient and outlet flow field uniformity, and has a short design cycle and wide applicability.

Description

Technical Field

[0001] This invention relates to the field of diffuser design, and more specifically, to a diffuser design method based on variable gradient. Background Technology

[0002] The main function of a diffuser is to effectively decelerate and pressurize incoming airflow, converting some of the airflow's kinetic energy into pressure potential energy. This enables kinetic energy recovery or increases the outlet pressure, and maximizing static pressure recovery is a crucial indicator of the economic efficiency of large wind tunnel operations. Therefore, this equipment is widely used in recirculation wind tunnels, centrifugal compressors, high-latitude atmospheric environment simulation devices, and gas ejectors.

[0003] Currently, the downstream diffuser section of wind tunnel testing equipment generally adopts a square-to-circular diffuser section with an approximately straight surface. The main problems with this are high manufacturing difficulty and high total pressure loss due to viscous friction dissipation after fluid deceleration, posing certain technical challenges to the overall system layout and cost reduction / efficiency improvement. Secondly, in ejector devices widely used in the aerospace field, diffuser design mainly adopts a straight surface, using empirical fitting or empirical formulas. The diffuser's geometric parameters are determined by selecting a suitable diffusion angle based on the upstream cross-section and length. However, the design process does not fully consider the quantitative description of the energy exchange and flow loss processes of the fluid in the diffuser by the actual fluid working fluid properties and flow parameters.

[0004] Suppressing and delaying flow separation and eddies within diffusers, improving the inlet and outlet pressure ratio and diffusion efficiency, and reducing total pressure loss within diffusers are key scientific issues in diffuser design. However, traditional design methods do not provide an operational interface for implementing and optimizing flow separation suppression techniques within diffusers during the design process. Generally, a certain expansion angle is selected, and numerical simulations are used to verify whether the flow separation meets the design requirements. Existing design methods typically consider 7-10° as a safe expansion angle for straight-walled diffuser sections, which can meet most design requirements when there is sufficient layout space. However, it is often difficult to meet design requirements when the overall layout is fixed.

[0005] In traditional diffuser design methods, the diffuser inlet area A1 and outlet area A2 are usually known, and then a suitable equivalent diffusion angle is determined based on the actual layout size constraints. And diffuser length L. When flow separation is unavoidable in confined spaces due to traditional design methods, the existing solution is to use higher-order curves, such as cubic or Vickers curves, to optimize the profile, thereby delaying flow separation within the confined space. This method, which relies on pure geometric parameter optimization, requires multiple iterations to obtain results that meet design requirements, and is usually highly dependent on engineering design experience.

[0006] Existing diffuser design requirements typically necessitate highly efficient energy recovery devices with minimal flow separation, minimal total pressure loss, and a high pressure recovery coefficient within a limited layout space. This necessitates designers balancing flow separation risk assessment with parameter selection, and spatial constraints with optimal performance to find the optimal design outcome. Traditional design methods rely heavily on iterative CFD verification and analysis of design parameters. The calculations are used to identify the causes of flow separation, leading to the selection of new geometric parameters for the next iteration until the design meets the requirements. The primary reason for the long-chain, inefficient nature of this method is its inability to couple flow field parameters to diffuser geometry design, resulting in near-independent flow field analysis and geometry design.

[0007] Therefore, how to design a high-efficiency diffuser with no flow separation, low total pressure loss, and high pressure recovery coefficient within a limited layout space, and shorten the design cycle, is a key technical problem that urgently needs to be solved in this field. Summary of the Invention

[0008] The purpose of this invention is to overcome the shortcomings of the prior art and provide a diffuser design method based on variable gradient, so as to solve the technical problems of long design iteration cycle, single flow field control means, and disconnect between design results and flow physics mechanism in the existing diffuser design methods.

[0009] To achieve the above-mentioned objective, this invention provides a diffuser design method based on a variable gradient, the method comprising:

[0010] A one-dimensional flow analysis model of the fluid inside the diffuser is established, which includes the mass conservation equation, the momentum conservation equation, and the energy conservation equation.

[0011] Specify a variable gradient objective function λ along the fluid flow direction. The variable gradient objective function λ is defined as the spatial rate of change of fluid momentum along the flow direction, and is a function of the coordinate x along the flow direction, or, the variable gradient objective function λ is the ratio of the fluid density to the coordinate x along the flow direction. and fluid velocity The coupling function of at least two of them;

[0012] The variable gradient objective function λ is coupled with the mass conservation equation and attributed to the source term of the equation. Combined with the given inlet and outlet boundary conditions, the closed equation set consisting of the coupled mass conservation equation, momentum conservation equation, energy conservation equation and gas state equation is iteratively solved to update the pressure field and temperature field along the fluid flow direction until the calculation converges, and the variation law A(x) of the diffuser cross-sectional area along the flow direction is obtained.

[0013] The diffuser profile curve is generated based on the cross-sectional area variation law A(x).

[0014] Existing diffuser design methods fail to effectively couple flow field parameters (especially momentum changes directly related to boundary layer development) into the geometric profile solution process, resulting in a lack of active flow field control and long iteration cycles. To address this issue, this method establishes a one-dimensional flow analysis model incorporating mass, momentum, and energy conservation equations, providing a theoretical foundation for profile inversion. A variable momentum gradient objective function λ is defined and specified as the core design variable for actively constraining the internal flow field of the diffuser. λ is coupled with the mass conservation equation, ensuring that changes in geometric area are directly controlled by a pre-defined momentum change law. Combined with boundary conditions, a closed system of equations, including the aforementioned coupled equations, is iteratively solved to invert the cross-sectional area change law A(x) that achieves the pre-defined momentum gradient distribution. This provides a novel diffuser design paradigm that directly uses the flow field control objective (momentum gradient) as input conditions for geometric profile solution, enabling the design of diffusers with specific flow field characteristics and improving design specificity and efficiency.

[0015] Preferably, when the variable gradient objective function changes only with spatial location, a simple representation of the calculation method for λ is as follows:

[0016] ;

[0017] in, Let A be the fluid density and A be the cross-sectional area of ​​the diffuser. Let x be the fluid velocity and x be the coordinate along the flow direction. The velocity can be used to control the rate of change of the reverse pressure gradient along the flow direction to meet the design of diffusers under more demanding conditions.

[0018] Preferably, the iterative solution steps include:

[0019] The coupled mass conservation equation and the variable gradient objective function λ are discretized using the finite difference method based on finite volume or finite difference to obtain a discrete set of equations.

[0020] Based on the inlet boundary conditions and combined with the outlet boundary conditions, the fluid velocity at each discrete node along the fluid flow direction is obtained by iteratively solving the discrete-form equations. And the diffuser cross-sectional area A, and then the variation law A(x) of the diffuser cross-sectional area along the flow direction is obtained.

[0021] The above method provides a specific and operable numerical solution method, namely the finite difference method, which ensures the feasibility of automatically calculating the diffuser profile through a computer program.

[0022] Preferably, the momentum conservation equation includes a frictional resistance source term to characterize wall friction loss. .

[0023] Basic one-dimensional flow models typically neglect wall friction, leading to discrepancies between calculated results and actual flow, particularly inaccurate predictions of total pressure loss. This method introduces an additional frictional drag term into the mathematical expression of the momentum conservation equation. This source term represents the resistance experienced by the fluid element due to wall shear force. By adding a frictional resistance source term to the momentum equation, the one-dimensional design model can account for energy losses caused by viscous effects, thus making the designed diffuser profile curve closer to reality and improving the design fidelity.

[0024] Preferably, the frictional resistance source term The calculations were performed based on an empirical model that considers the fluid Reynolds number and the relative roughness of the diffuser wall.

[0025] Among them, an empirical model based on dimensionless parameters (Reynolds number and relative roughness) is used to calculate frictional resistance, so that the one-dimensional model can accurately reflect the influence of different flow states (laminar flow, turbulent flow) and wall conditions on flow loss.

[0026] Preferably, in the closed system of equations, the energy conservation equation is coupled with the gas equation of state to suit diffuser design for compressible fluids. During the solution process, the energy conservation equation is coupled with the gas equation of state (such as the ideal gas equation of state). The temperature field is solved using the energy equation, and then the density field is updated using the state equation based on temperature and pressure. This makes density a variable rather than a constant, ensuring the closed nature of the solution to the compressible flow equations.

[0027] Preferably, when the variable gradient objective function λ is a position function of the flow direction, it can be expressed as an elementary function, a combination of elementary functions, a transcendental function, or an infinite series.

[0028] Furthermore, when the variable gradient objective function λ depends simultaneously on the coordinate x along the flow direction and the fluid density... and fluid velocity When at least one of them is present, λ can be expressed as The coupling function relationship is obtained by introducing it as a source term into the momentum equation for discrete solution.

[0029] Preferably, the method further includes:

[0030] A three-dimensional geometric model of the diffuser is established based on the generated diffuser profile curve.

[0031] Three-dimensional computational fluid dynamics numerical simulations were performed on the three-dimensional geometric model to verify and evaluate the flow field characteristics and performance indicators inside the diffuser.

[0032] After generating the profile curve, a three-dimensional geometric model of the diffuser is established and a computational mesh is generated. Then, a three-dimensional CFD solver is run for numerical simulation to analyze key performance indicators such as flow field distribution, flow separation location, boundary layer thickness, pressure recovery coefficient, and total pressure loss. By introducing three-dimensional CFD numerical simulation, the one-dimensional design results are verified and evaluated with high fidelity, ensuring that the designed diffuser still exhibits good performance in actual three-dimensional flow, providing a reliable bridge from theoretical design to engineering application.

[0033] Preferably, the method further includes:

[0034] Based on the evaluation results of the three-dimensional computational fluid dynamics numerical simulation, adjust the form of the variable gradient objective function λ or its parameters.

[0035] Repeat the steps of solving the one-dimensional flow analysis model and performing three-dimensional computational fluid dynamics numerical simulation until the diffuser's performance indicators meet the preset design goals, thereby achieving iterative optimization of the diffuser profile curve.

[0036] One-dimensional design may not provide an optimal performance profile, necessitating a systematic optimization process to approximate the design objective. This method employs feedback adjustment: based on the evaluation results of three-dimensional numerical simulation, it determines whether the performance requirements are met; if not, it adjusts the mathematical form of the objective function or its internal constant coefficient parameters. Iterative iteration: the adjusted objective function is re-substituted into the one-dimensional design process, repeatedly executing the solution and three-dimensional verification steps until the diffuser's performance meets the preset design objective. This constructs a complete closed-loop iterative process of one-dimensional inverse design—three-dimensional verification—objective function optimization, enabling the design process to automatically converge towards the optimal solution, ultimately obtaining the diffuser profile with optimal performance.

[0037] Preferably, the diffuser is a wind tunnel diffuser, a compressor diffuser, or a gas ejector diffuser.

[0038] One or more technical solutions provided by this invention have at least the following technical effects or advantages:

[0039] With rich design freedom and high control precision: Because a variable gradient objective function is used as the design input, designers can flexibly select the function form and parameters according to their needs, so as to achieve qualitative and even quantitative control of the velocity field, pressure field and boundary layer growth in the diffuser, breaking through the limitations of traditional methods that only have a few design parameters such as the expansion angle.

[0040] Significantly suppresses flow separation: By optimizing the momentum gradient objective function, the designed curved diffuser can significantly delay or even eliminate flow separation, reduce the boundary layer thickness, thereby reducing kinetic energy loss caused by viscous friction and improving the pressure recovery performance of the diffuser.

[0041] Good uniformity of outlet flow field: Compared with traditional straight wall diffusers, the curved diffuser designed using this method has a more uniform internal velocity distribution, which is beneficial to the efficient and stable operation of downstream components (such as engine combustion chambers).

[0042] Short design cycle and high efficiency: By combining one-dimensional rapid solution with three-dimensional accurate verification, the blind and time-consuming geometric parameter trial and error process in traditional methods is avoided, which greatly shortens the development and iteration cycle of the diffuser.

[0043] Wide applicability: By selecting different gas state equations, this method can be applied to diffuser design in extreme operating environments, from ideal gas to real gas effects, low vacuum, high temperature, rarefied gas, etc. Attached Figure Description

[0044] The accompanying drawings, which are provided to further illustrate embodiments of the invention and constitute a part of this invention, are not intended to limit the scope of the invention.

[0045] Figure 1 This is a flowchart illustrating a diffuser design method based on variable gradient.

[0046] Figure 2 A schematic diagram showing the calculation results of the curved wall diffuser profile curves under different target momentum gradient functions;

[0047] Figure 3 Schematic diagram of velocity distribution along the flow direction for verification of calculation results;

[0048] Figure 4 A schematic diagram showing the comparison of static pressure distribution results to verify the calculation results;

[0049] Figure 5 This is a schematic diagram of the flow field distribution inside a straight-walled diffuser when the momentum gradient is a directly proportional function.

[0050] Figure 6 This is a schematic diagram of the pressure field distribution inside a linear wall diffuser when the momentum gradient is a directly proportional function.

[0051] Figure 7 This diagram illustrates the boundary layer thickness growth pattern within a straight-walled diffuser when the momentum gradient is a directly proportional function. Detailed Implementation

[0052] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, where there is no conflict, the embodiments of the present invention and the features thereof can be combined with each other.

[0053] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0054] Those skilled in the art should understand that, in the disclosure of this invention, the terms "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the above terms should not be construed as limiting this invention.

[0055] It is understood that the term "a" should be understood as "at least one" or "one or more", that is, in one embodiment, the number of an element can be one, while in another embodiment, the number of the element can be multiple, and the term "a" should not be understood as a limitation on the number.

[0056] Example 1;

[0057] Please refer to Figure 1 , Figure 1 This is a flowchart illustrating a diffuser design method based on variable variable gradients. The present invention provides a diffuser design method based on variable variable gradients, the method comprising:

[0058] A one-dimensional flow analysis model of the fluid inside the diffuser is established, which includes the mass conservation equation, the momentum conservation equation, and the energy conservation equation.

[0059] Specify a variable gradient objective function λ along the fluid flow direction. The variable gradient objective function λ is defined as the spatial rate of change of fluid momentum along the flow direction, and is a function of the coordinate x along the flow direction, or, the variable gradient objective function λ is the ratio of the fluid density to the coordinate x along the flow direction. and fluid velocity The coupling function of at least two of them;

[0060] The variable gradient objective function λ is coupled with the mass conservation equation. Combined with the given inlet and outlet boundary conditions, the closed equation set consisting of the coupled mass conservation equation, momentum conservation equation, energy conservation equation and gas state equation is solved iteratively to update the pressure field and temperature field along the fluid flow direction until the calculation converges, and the variation law A(x) of the diffuser cross-sectional area along the flow direction is obtained.

[0061] The diffuser profile curve is generated based on the cross-sectional area variation law A(x).

[0062] This invention adopts the following technical solution: a diffuser design method based on variable gradient, comprising the following steps:

[0063] Step 1: Establish a one-dimensional flow analysis model:

[0064] A one-dimensional flow analysis model of the fluid inside the diffuser is established, including the mass conservation equation, the momentum conservation equation (including the wall friction loss source term), and the energy conservation equation.

[0065] Step 2: Specify the variable gradient objective function:

[0066] Based on design requirements, specify the objective function λ for the variable gradient along the fluid flow direction. This function is defined as the spatial rate of change of fluid momentum along the flow direction, and its specific form can be an elementary function, a combination of elementary functions, a transcendental function, or an infinite series.

[0067] Step 3: Coupled solution of the one-dimensional equation system:

[0068] The variable gradient objective function λ is coupled with the mass conservation equation. Combined with the inlet and outlet boundary conditions, the closed equation set consisting of the coupled mass conservation equation, momentum conservation equation, energy conservation equation and gas state equation is solved iteratively to obtain the pressure field and temperature field along the flow path, and then the variation law A(x) of the diffuser cross-sectional area along the flow direction is determined.

[0069] Step 4: Generate the surface curve:

[0070] The diffuser profile curve is generated based on the cross-sectional area variation law A(x).

[0071] Step 5: 3D Numerical Verification and Iterative Optimization

[0072] A three-dimensional geometric model is established based on the generated profile curve, and CFD numerical simulation is performed to evaluate the flow field characteristics and performance indicators. Based on the evaluation results, the form of the variable gradient objective function λ or its parameters are adjusted, and steps three through five are repeated until the performance indicators meet the design objectives.

[0073] Through the above technical solution, the present invention achieves the following objectives:

[0074] Shorten the design cycle: The initial profile is obtained by quickly solving the one-dimensional flow model, which replaces the traditional method that relies entirely on repeated trial and error of CFD, and significantly improves design efficiency.

[0075] Active flow field control: By directly specifying the variable gradient objective function λ, the flow field control objectives (such as suppressing separation and uniform pressure) are directly used as design inputs, thus realizing active and precise control of boundary layer growth and pressure distribution, solving the problem of the single control means in traditional methods.

[0076] Improve design quality: Introduce a wall friction loss model into the one-dimensional model to make the design results closer to the real flow, and ensure that the final design results meet the performance requirements such as high pressure recovery coefficient and low total pressure loss through three-dimensional CFD iterative optimization.

[0077] The principle of this invention is as follows:

[0078] 1. Boundary layer control principle;

[0079] According to boundary layer theory, increasing the radial and axial velocity gradients near the diffuser wall can effectively reduce the boundary layer thickness. Therefore, the rate of change of momentum of the fluid near the wall along the flow direction (i.e., momentum gradient) is a key parameter for measuring the fluid's ability to resist adverse pressure gradients near the wall. By setting and controlling the momentum gradient variation along the flow path, boundary layer thickening and flow separation can be effectively suppressed.

[0080] 2. Inverse problem design concept:

[0081] This invention adopts an inverse problem design approach: instead of directly giving the geometric profile, it first gives the desired flow field characteristics (i.e., the variable gradient objective function λ), and then derives the diffuser geometry that can achieve the flow field characteristics by solving the flow control equations.

[0082] 3. Coupling one-dimensional and three-dimensional solution strategy:

[0083] First, a one-dimensional flow analysis model incorporating frictional losses is established. The momentum gradient objective function is coupled with the mass, momentum, and energy conservation equations for solution, quickly obtaining the preliminary variation law of the diffuser cross-sectional area. Then, based on this law, a three-dimensional geometric model is generated, and precise verification and iterative optimization are performed through CFD numerical simulation to achieve the design objectives.

[0084] This invention provides a surface diffuser design method, which is an advanced flow control method. The diffuser obtained using this method is suitable for all fluid working media, significantly improving pressure distribution uniformity, suppressing boundary layer growth, inhibiting adverse pressure gradients and flow separation, and significantly improving diffuser pressure recovery performance and operational stability. It can be used as a design method for diffusers in aerospace equipment and diffuser sections in ground wind tunnel testing equipment.

[0085] Example 2:

[0086] The method in this embodiment simplifies the one-dimensional flow pattern within the flow channel by using an optimized momentum distribution function with a specified distribution pattern during the channel geometry design phase. Then, three-dimensional numerical simulation technology is used to accurately analyze the flow state and iteratively optimize the diffuser geometry and internal flow field structure, thereby suppressing or eliminating flow separation and improving the diffuser's pressure recovery performance and operational stability. This type of diffuser profile design method is based on the differential discretization form of the one-dimensional mass, momentum, and energy conservation equations, and represents an advanced flow control method.

[0087] To improve the compactness of diffusers and shorten the design iteration cycle of profile curves, this application provides a diffuser design method based on variable gradient.

[0088] Based on boundary layer theory, increasing the radial and axial velocity gradients near the diffuser wall can effectively reduce the boundary layer thickness. In other words, the momentum gradient variation near the wall can serve as an effective design parameter for the fluid's resistance to adverse pressure gradients. Based on this understanding, this application proposes a design and calculation method that uses the momentum gradient as the objective function and couples it to the diffuser profile curve calculation.

[0089] The main mathematical idea behind this method is to control the separation of airflow by regulating the change in momentum gradient along the flow direction.

[0090] This method is based on the inverse problem design concept and proposes a design method for curved wall diffusers based on the variable gradient of the Navier-Stokes equations. It determines the variation law of the diffuser cross-sectional area with the flow direction through a one-dimensional steady-state design method, and quickly determines the variation law of the diffuser profile curve by comparing and analyzing important data such as the flow field, temperature field, boundary layer thickness and diffusion performance of different curved wall diffusers through numerical simulation.

[0091] The diffuser design scheme and calculation method based on variable gradient are as follows:

[0092] The differential equation for the mass conservation equation of one-dimensional flow within the diffuser is:

[0093] (1)

[0094] in, The density of the working fluid is expressed in kg / m³. 3 ; The fluid velocity is expressed in m / s. The diffuser's cross-sectional area is expressed in meters (m²). 2 .

[0095] Considering wall friction losses, the momentum conservation equation can be expressed as:

[0096] (2)

[0097] Where p is the hydrostatic pressure, and the unit is Pa; Frictional resistance experienced by a fluid element, expressed in N / m. 3 The friction force calculation model is derived from the Haland empirical model or other models and is treated as an additional source term during the calculation process.

[0098] (3)

[0099] (4)

[0100] in, denoted as surface roughness, d as equivalent diameter, and Re as fluid Reynolds number. lg This represents a common logarithm with base 10.

[0101] The relationship between the diameter and the cross-sectional area in the above equation can be expressed by the following formula:

[0102] (5)

[0103] The energy equation describing the flow within the diffuser is:

[0104] (6)

[0105] in, The specific heat capacity at constant pressure of the fluid. This refers to the static temperature of the fluid.

[0106] Objective function of variable gradient in one-dimensional flow The term is defined as the spatial rate of change of momentum along the flow direction, and its unit is kg / s². 2 It is easy to see from the form that the momentum gradient is a function of fluid density, velocity and spatial coordinates.

[0107] (7)

[0108] Where m is the mass flow rate.

[0109] When the flow is incompressible, the above equations include fluid velocity. Diffuser cross-sectional area The four variables to be solved are pressure p and temperature T, which can be solved by equations (1) to (7). When the flow is compressible, a gas state equation is also required to ensure the closure of the equation set. The added state equation can be an ideal gas model or another gas model that considers the effects of real gas, depending on the actual flow parameters and operating conditions. The example here only gives the ideal gas state equation:

[0110] (8)

[0111] in, is the gas constant.

[0112] This model can be used with different gas models to achieve more refined diffuser innovation design based on the application background of the diffuser. It only requires obtaining the state parameters of the gas under the operating conditions of the diffuser through experimental testing technology and existing gas models. It can realize the profile curve analysis of the diffuser under extreme operating conditions such as real gas effect, low vacuum, high temperature, and rarefied gas, thereby obtaining a diffuser with better performance.

[0113] For non-ideal gas conditions, the ideal gas equation of state can be replaced with the corresponding gas equation of state (e.g., Redlich-Kwong equation, Peng-Robinson equation, etc.), while the solution framework of the equation set remains unchanged. For extreme conditions such as rarefied gases, it can be applied within the range where the continuous medium assumption holds.

[0114] After determining the one-dimensional design mathematical model of the diffuser, the finite difference discretization method can be used to calculate the variation of the diffuser cross-sectional area with the flow direction. First, combining the variable gradient condition and the mass conservation condition, i.e., equations (1) and (7), the discrete form of the equation is obtained as follows:

[0115] (9)

[0116] (10)

[0117] Among them, subscript and +1 indicates that after discretization along the flow direction, the th... The and the first +1 physical quantities at spatial discrete nodes. Starting from 1 and incrementing, node 1 corresponds to the diffuser inlet, and node 𝑁 corresponds to the diffuser outlet.

[0118] Furthermore, considering The constants are determined by the import boundary conditions, therefore for all internal nodes:

[0119] (11)

[0120] After updating the flow field parameters, the temperature field distribution can be calculated based on the new flow field data and the energy conservation equation.

[0121] (12)

[0122] The one-dimensional static pressure within the diffuser can be calculated using the momentum conservation equation.

[0123] (13)

[0124] in, Let be the hydrostatic pressure at the nth discrete node along the flow direction. Let be the hydrostatic pressure at the (x+1)th discrete node along the flow direction. Frictional resistance source term The value at the (x+1)th discrete node is calculated using formulas (3) and (4).

[0125] Finally, the gas density distribution is updated based on the gas model's equation of state:

[0126] (14)

[0127] The calculation boundary condition is: inlet total temperature. Import mass flow rate Inlet cross-sectional area outlet static pressure .

[0128] (15)

[0129] in, , and The fluid density, velocity, and cross-sectional area at the diffuser inlet are respectively given as inlet boundary conditions, while the outlet static pressure is used as the boundary condition for inverse pressure solution.

[0130] To accelerate convergence and improve computational stability, an iterative solution method is used to solve the above equations (9) to (15). The overall process of the iterative solution is to first assume the initial density and velocity distribution, then solve for the area, pressure, temperature, and density in sequence, and then update until convergence. The density, velocity, and temperature can be initialized according to the inlet parameters. The residuals of solving all equations satisfy 10 -3 The model can be considered converged (the specific definition of the convergence criterion is: the maximum relative change in the density field between two adjacent iterations is less than 10).-3 This yields the variation law of the cross-sectional geometric parameters along the moving direction.

[0131] When the cross-section is circular, the surface curve is directly obtained from equation (5). When the cross-section is rectangular, the surface space coordinates of the single-sided contraction can be obtained according to geometric conditions, such as specifying the aspect ratio or fixing a dimension in one direction.

[0132] Verification of calculation results. Based on the diffuser profile curves obtained above, a three-dimensional geometric model of the diffuser is established and a fluid numerical calculation grid is generated. The flow characteristics inside the diffuser are calculated and analyzed using three-dimensional numerical simulation, including performance indicators such as flow field distribution, flow separation, boundary layer growth law, wall static pressure distribution, static pressure recovery coefficient, and total pressure loss.

[0133] Iterative optimization design of diffusers. By combining optimization theory, the optimal objective function based on the design input conditions is found, and finally a curve-wall diffuser with a thin boundary layer, resistance to adverse pressure gradients, and a high pressure recovery coefficient is obtained in the design space.

[0134] Example 3;

[0135] Based on Embodiment 1, the present invention will be described in conjunction with specific data and examples:

[0136] Example 1: Calculation of curved-wall diffuser configuration with elementary functions as the objective momentum gradient function.

[0137] Taking an axisymmetric diffuser as an example, the inlet cross-sectional area A0 = 0.04m² 2 The diffuser length L = 1.2 m, inlet temperature T0 = 300 K, air velocity u0 = 100 m / s, outlet pressure p = 101.3 kPa, and the gas model adopted is an ideal gas model. According to formula (7) and mass conservation condition (1), the law of diffuser geometry changing with different elementary functions can be obtained. Based on this, a database of ordinary elementary functions and diffuser profile and flow characteristics of curved walls can be established, providing theoretical data for rapid analysis and prediction for subsequent curve optimization.

[0138] The target momentum gradient function for Cases 1 through 4 is only a function of spatial coordinates:

[0139] ;

[0140] ;

[0141] ;

[0142] ;

[0143] The target momentum gradient function for Cases 5 and 6 is a coupled function of spatial coordinates and dimensionless velocity:

[0144] ;

[0145] ;

[0146] Among them, the wall friction model adopts formula (4), where x is the axial distance from the diffuser inlet, in meters (m), and the value range is 0≤x≤L, where L is the diffuser length; the numerical coefficients in each function This is an amplitude adjustment factor used to adjust the magnitude of the momentum gradient to match the specific working conditions (such as inlet velocity, density, and geometric scale). Designers can scale and adjust it according to the actual design conditions.

[0147] Constant terms in the function (such as 1, 1.45, 0.22) are used to adjust the function near the entry point. The initial slope or curvature of the function, and the overall shape of the function along the path, are adjusted to avoid singularities or to obtain the desired momentum gradient distribution trend.

[0148] When the variable gradient objective function λ contains a coupling term of velocity λ or density λ (such as Case 5 and Case 6), in each round of iterative solution, the variable gradient objective function of each node is first calculated based on the currently estimated velocity field, and then substituted into the discrete equation (10) for solution. Since λ depends on the variable to be solved, the Picard iteration method can be used, substituting the velocity value of the previous round as a known quantity, and repeatedly updating until the density field, velocity field, and area distribution simultaneously satisfy the convergence condition.

[0149] In this embodiment, a one-dimensional coordinate system is established along the flow direction with the center of the diffuser inlet section as the origin. The diffuser length is L=1.2m, therefore x∈[0,1.2]m.

[0150] Under the premise of a fixed diffuser length, this paper seeks to optimize the target momentum gradient function to achieve a high pressure recovery coefficient and resistance to adverse pressure gradients in the diffuser. Figure 1 The program corresponding to the solution flow of the diffuser profile curves shown is as follows: the diffuser profile radius is obtained through formula (5), and the final calculation results of the profile curves of Case 1 to Case 6 in this case are as follows. Figure 2 As shown.

[0151] Given geometric constraints, diffuser design based on variable momentum gradient objective functions offers more design freedom than traditional straight-wall diffuser design because it theoretically allows for countless combinations of elementary functions. By establishing the mapping relationship between the elementary functions and the diffuser profile curves, a momentum gradient objective function suitable for a specific design expectation can be quickly selected. For example, when strictly limiting flow separation within the diffuser is required, objective function families represented by Case 4 or Case 5 should be selected as much as possible to better adjust the distribution of the velocity gradient in the diffuser and suppress flow separation; when a higher pressure recovery coefficient is needed, objective function families of Case 3 type should be considered.

[0152] Besides the elementary functions in this embodiment, other types of elementary and transcendental functions can all be used as objective functions within a certain range. Theoretically, all elementary functions can be expressed as infinite series. In the form of the series, only the coefficients of the above series need to be determined during the solution process, where 𝑥 is the coordinate along the flow direction, 𝑘 is the non-negative integer index, and 𝑎 is the coefficient of the series. 𝑘 represents the undetermined coefficients of the series expansion. The coefficients are determined through optimization. 𝑘 The value of allows for flexible control over the shape of the target momentum gradient function. Therefore, the target momentum function can be represented as a combination of elementary functions or as an infinite series. When constructing a database, the infinite series form is easier to implement in template-based programming.

[0153] Example 2: Numerical analysis of the flow field inside the diffuser when the target momentum gradient function is a proportional function.

[0154] Taking an axisymmetric diffuser as an example, the inlet cross-sectional area A0 = 0.04 m² 2 The diffuser length is L = 1.2 m, the inlet temperature is T0 = 300 K, the air velocity is u0 = 100 m / s, and the outlet pressure is p = 101.3 kPa. An ideal gas model is used. The target momentum function is expressed as λ = cx or a constant function λ = c, where c is a constant coefficient. The value of the constant coefficient c can be estimated based on the inlet momentum flow rate and the desired rate of change of momentum, or determined through subsequent optimization. This case study compares and analyzes the performance of a curved-wall diffuser with c values ​​of -200, -250, and -300 with that of a traditional straight-wall diffuser under the same conditions, including important parameters such as the flow field distribution characteristics, pressure distribution patterns, and boundary layer thickness growth patterns within the diffuser.

[0155] Verification of solution correctness. Comparison of one-dimensional and three-dimensional velocity distribution calculation results, for example. Figures 3-4As shown, because one-dimensional calculations cannot account for the influence of the boundary layer on velocity distribution, the velocity along the central axis in three-dimensional model is higher than that in one-dimensional analysis, and the velocity deviation increases with the thickness of the boundary layer. Comparing the cross-sectional average velocity, the calculation results from one-dimensional and three-dimensional models are in good agreement. However, because the one-dimensional model cannot account for viscous friction losses, the cross-sectional average velocity calculated by the three-dimensional model is about 8% lower than that in one-dimensional model. Comparing the pressure distribution results, the higher velocity along the central axis in the three-dimensional model leads to higher dynamic pressure than the one-dimensional calculation result. Ultimately, this results in a lower pressure recovery effect than the theoretical design target, which can be addressed by further reducing the outlet profile curvature to improve the pressure recovery coefficient.

[0156] Figure 5 The images show the velocity distribution contours of the curved-wall diffuser and the conventional straight-wall diffuser with the same parameters in a three-dimensional numerical simulation of this case. For the conventional straight-wall diffuser, the velocity field distribution within the diffuser exhibits a parabolic pattern, and the cross-sectional velocity non-uniformity is significantly higher than that of the curved-wall diffuser with a variable gradient. It is evident that the curved-wall diffuser obtained by the method of this invention can significantly improve the uniformity of the outlet flow field, playing a crucial role in enhancing the performance of downstream components, especially in achieving efficient and stable combustion with a stable air-fuel ratio and reducing thermo-acoustic vibrations during combustion within the engine combustion chamber.

[0157] Meanwhile, analysis of the near-wall velocity distribution reveals that the flow separation point in a conventional straight-wall diffuser occurs significantly earlier than in a curved-wall diffuser, and the velocity boundary layer thickens along the flow direction much faster in the curved-wall diffuser. Therefore, the kinetic energy loss due to viscous friction in a curved-wall diffuser is significantly lower than that in a conventional straight-wall diffuser, further explaining... Figure 3 The velocity value along the central axis of the 3D model is higher than that of the 1D model, and the deviation increases along the flow direction. Therefore, the curved-wall diffuser with a target momentum gradient function that is directly proportional to the target momentum gradient function has lower viscous losses and a more uniform outlet velocity field distribution. This makes it more applicable to diffuser designs that need to meet this type of function. This is another significant advantage of the curved-wall diffuser provided by the method of this invention compared to the traditional straight-wall diffuser in terms of the inability to achieve qualitative or quantitative control of flow field characteristics.

[0158] Figure 6 This is a 3D numerical simulation of the pressure distribution contour plots of the curved wall diffuser and the conventional straight wall diffuser with the same parameters in this case. In the conventional straight wall diffuser, the pressure rises rapidly near the inlet section, the pressure gradient gradually decreases along the flow direction, the pressure field distribution is more uniform, the pressure gradient is uniform, and the adverse pressure gradient is suppressed.

[0159] Figure 7 This study demonstrates the growth pattern of the velocity boundary layer thickness along the flow direction in both straight-wall diffusers and linear momentum gradient curved-wall diffusers (λ=cx form). The boundary layer thickness λ is defined as the normal distance from the wall surface to the point where the local velocity reaches 99% of the core flow velocity. Data were extracted and statistically analyzed from multiple cross-sections along the diffuser axis.

[0160] In this invention, a steady-state solver based on RANS can be used in the CFD process, and the turbulence model can be selected from... model, wall Keep it around 1.

[0161] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0162] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A diffuser design method based on variable variable gradient, characterized in that, The method includes: A one-dimensional flow analysis model of the fluid inside the diffuser is established, which includes the mass conservation equation, the momentum conservation equation, and the energy conservation equation. Specify a variable gradient objective function λ along the fluid flow direction. The variable gradient objective function λ is defined as the spatial rate of change of fluid momentum along the flow direction, and is a function of the coordinate x along the flow direction, or, the variable gradient objective function λ is the ratio of the fluid density to the coordinate x along the flow direction. and fluid velocity The coupling function of at least two of them; The variable gradient objective function λ is coupled with the mass conservation equation. Combined with the given inlet and outlet boundary conditions, the closed equation set consisting of the coupled mass conservation equation, momentum conservation equation, energy conservation equation and gas state equation is solved iteratively to update the pressure field and temperature field along the fluid flow direction until the calculation converges, and the variation law A(x) of the diffuser cross-sectional area along the flow direction is obtained. The diffuser profile curve is generated based on the cross-sectional area variation law A(x); when the variable gradient objective function only varies with spatial position, the calculation method of λ is expressed as follows: ； Where A is the cross-sectional area of ​​the diffuser; The differential equation for the mass conservation equation of one-dimensional flow within the diffuser is: ； Considering wall friction losses, the momentum conservation equation is expressed as: ； Where p is the hydrostatic pressure of the fluid; The frictional resistance experienced by the fluid element is calculated as follows: ； ； in, denoted as surface roughness, d as equivalent diameter, Re as fluid Reynolds number, f as Darcy friction factor, and lg as the common logarithm base 10. The relationship between the equivalent diameter and the diffuser cross-sectional area is expressed as: ； The energy equation describing the flow within the diffuser is: ； in, The specific heat capacity at constant pressure of the fluid. This refers to the static temperature of the fluid.

2. The diffuser design method based on variable gradient according to claim 1, characterized in that, The iterative solution steps include: The coupled mass conservation equation and the variable gradient objective function λ are discretized using the finite difference method to obtain a discrete set of equations. Based on the inlet boundary conditions and combined with the outlet boundary conditions, the fluid velocity at each discrete node along the fluid flow direction is obtained by iteratively solving the discrete-form equations. And the diffuser cross-sectional area A, and then the variation law A(x) of the diffuser cross-sectional area along the flow direction is obtained.

3. The diffuser design method based on variable gradient according to claim 1, characterized in that, The momentum conservation equation includes a frictional resistance source term to characterize wall friction loss. .

4. The diffuser design method based on variable gradient according to claim 3, characterized in that, The frictional resistance source term The calculations were performed based on an empirical model that considers the fluid Reynolds number and the relative roughness of the diffuser wall.

5. The diffuser design method based on variable gradient according to claim 1, characterized in that, In the closed set of equations, the energy conservation equation is coupled with the gas state equation to be applicable to diffuser design for compressible fluids.

6. The diffuser design method based on variable gradient according to claim 1, characterized in that, When the variable gradient objective function λ is a function of the coordinate x along the flow direction, it is expressed as an elementary function, a combination of elementary functions, a transcendental function, or an infinite series; when the variable gradient objective function λ is a function of the coordinate x along the flow direction and the fluid density... and fluid velocity The coupling function of at least two of them, λ is denoted as This is achieved by introducing it as a source term into the momentum equation for discrete solution.

7. The diffuser design method based on variable gradient according to claim 1, characterized in that, The method further includes: A three-dimensional geometric model of the diffuser is established based on the generated diffuser profile curve. Three-dimensional computational fluid dynamics numerical simulations were performed on the three-dimensional geometric model to verify and evaluate the flow field characteristics and performance indicators inside the diffuser.

8. The diffuser design method based on variable gradient according to claim 7, characterized in that, The method further includes: Based on the evaluation results of the three-dimensional computational fluid dynamics numerical simulation, adjust the form of the variable gradient objective function λ or its parameters. Repeat the steps of solving the one-dimensional flow analysis model and performing three-dimensional computational fluid dynamics numerical simulation until the diffuser's performance indicators meet the preset design goals, thereby achieving iterative optimization of the diffuser profile curve.

9. The diffuser design method based on variable gradient according to claim 1, characterized in that, The diffuser is a wind tunnel diffuser, a compressor diffuser, or a gas ejector diffuser.

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