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CN-121980994-A - Two-dimensional shear layer coupling calculation method based on actual shear layer thickness fraction transformation

CN121980994ACN 121980994 ACN121980994 ACN 121980994ACN-121980994-A

Abstract

According to the two-dimensional shear layer coupling calculation method based on the actual shear layer thickness fraction transformation, the calculation domain is stretched by using the actual shear layer thickness, and synchronous coupling implicit solution is carried out on the shear layer thickness and all physical quantities to be solved during calculation, so that calculation grids are unchanged in the process of the shear layer growth, the shear layer thickness is not required to be determined in advance, meanwhile, compared with a separation solution, the method is more suitable for processing a rigid equation, the iterative convergence speed is greatly increased, the robustness is better, and important engineering value and application significance are achieved.

Inventors

  • LIU YANGMIN

Assignees

  • 北京航天动力研究所

Dates

Publication Date
20260505
Application Date
20251231

Claims (10)

  1. 1. A two-dimensional shear layer coupling calculation method based on actual shear layer thickness fraction transformation is characterized by comprising the following steps: determining the linear coordinates of the non-free end of the shear layer in a Cartesian coordinate form, converting the linear coordinates into orthogonal curve coordinates, and determining a calculation starting point and a calculation terminal point; Selecting a control equation corresponding to the two-dimensional axisymmetric shear layer calculation; converting a control equation under an orthogonal curve coordinate system into a control equation under a shear layer thickness fraction coordinate system by using actual shear layer thickness fraction transformation; Performing grid division of the calculation domain section; Determining initial conditions and boundary conditions required by calculation; Dispersing the control equation by adopting a numerical method; coupling linearization is carried out on the quantity to be solved in the discrete equation by adopting a Newton method; determining the flow direction step length in the discrete equation, and solving the equation set; Updating each coefficient in the equation set; Repeatedly confirming the flow direction step length and solving the equation set in each calculation section until reaching the convergence standard, and advancing to the next calculation section; And repeating the calculation of the next section until the calculation end point is reached by taking the previous calculation section as an initial value, and outputting the physical quantity distribution of each calculation section and the key information of the two-dimensional axisymmetric shear layer, including displacement thickness, momentum thickness, shear stress and heat flow information.
  2. 2. The two-dimensional shear layer coupling calculation method based on actual shear layer thickness fraction transformation according to claim 1, wherein: The non-free end of the shear layer comprises a wall surface, an axis, a symmetry plane and a flow direction coordinate reference line.
  3. 3. The two-dimensional shear layer coupling calculation method based on actual shear layer thickness fraction transformation according to claim 1, wherein: the control equation corresponding to the two-dimensional axisymmetric shear layer calculation comprises a continuous equation and a momentum equation, the equation types contained in the control equation are updated according to the shear layer conversion requirement, the continuous equation and the momentum equation are selected, the combination of any scalar equation in an energy equation, a component equation and a turbulence equation is selected, and the energy equation is in a temperature form or a total enthalpy form.
  4. 4. The two-dimensional shear layer coupling calculation method based on actual shear layer thickness fraction transformation according to claim 1, wherein: the actual shear layer thickness fraction conversion formula is as follows: In the formula, To calculate dimensionless axial coordinates in the system, Is the physical dimension axial coordinate in the orthogonal curve coordinate system, To calculate dimensionless normal coordinates in the system, Is the normal coordinate of the physical dimension under the orthogonal curve coordinate system, L is the reference length, Is the physical dimension shear layer thickness under an orthogonal curve coordinate system, Is the dimensionless shear layer thickness in an orthogonal curve coordinate system.
  5. 5. The two-dimensional shear layer coupling calculation method based on actual shear layer thickness fraction transformation according to claim 1, wherein: And the grid division is carried out on the wall surface of the two-dimensional axisymmetric shear layer and the position of the mixing area.
  6. 6. The two-dimensional shear layer coupling calculation method based on actual shear layer thickness fraction transformation according to claim 1, wherein: the initial conditions include boundary layer thickness and physical quantity distribution, the boundary layer thickness is determined according to priori empirical data, the boundary layer thickness formula calculation is used for laminar flow or turbulence plate boundary layer thickness calculation, the boundary layer physical quantity distribution is determined according to a shear layer similarity solution, and the shear layer similarity solution is determined through test values.
  7. 7. The two-dimensional shear layer coupling calculation method based on actual shear layer thickness fraction transformation according to claim 1, wherein: The numerical method is a numerical method which is selected from any one of finite difference, finite volume, finite element and matrix integration and is suitable for parabolic partial differential equation.
  8. 8. The two-dimensional shear layer coupling calculation method based on actual shear layer thickness fraction transformation according to claim 1, wherein: and if the quantity to be solved is a solution of a second-order shear layer equation set, taking pressure as the quantity to be solved.
  9. 9. The two-dimensional shear layer coupling calculation method based on actual shear layer thickness fraction transformation according to claim 1, wherein: the flow step size is reduced at the position where the calculation starting point or other flow gradient changes exceed the threshold value, and step size independence verification is carried out to ensure calculation robustness and accuracy.
  10. 10. The two-dimensional shear layer coupling calculation method based on actual shear layer thickness fraction transformation according to claim 1, wherein: The linear equation set is an asymmetric matrix, and the convergence standard adopts equation residual errors or gradient values of wall physical quantities.

Description

Two-dimensional shear layer coupling calculation method based on actual shear layer thickness fraction transformation Technical Field The invention relates to a two-dimensional shear layer coupling calculation method based on actual shear layer thickness fractional conversion, and belongs to the technical field of shear layer flow analysis. Background The two-dimensional shear layer flow has important application in the design optimization of a plurality of industrial products, such as the fields of flow resistance and heat transfer calculation of spray pipes, air inlets, wings and turbine blades, combustion field calculation of coaxial nozzles and the like, so that the research of the calculation method of the two-dimensional shear layer flow has important significance; Theoretical derivation, experimental investigation and numerical calculation can be employed for analysis of two-dimensional shear layer flow. Because the two-dimensional shear layer equation is strongly nonlinear, the theoretical derivation can only yield solutions in very few cases. The experimental study has poor economy, has safety problems, and has very limited information. The numerical calculation cost is low, the obtained information is comprehensive, the safety problem is avoided, and the universality is high under the condition that the model is correct. However, the calculation time of the full NS equation is costly, sometimes even higher than that of the test, which is very disadvantageous for the preliminary and optimal design of the product. According to the internal flow characteristics of the shear layer, the small term of the NS equation in the flow of the shear layer is omitted, the equation can be simplified into a two-dimensional shear layer equation, the equation is converted into a parabolic equation from an elliptic equation, and the form is greatly simplified. The parabolic equation can be solved by adopting a space propulsion method, so that the calculation speed of the parabolic equation is extremely high and is usually 1-2 orders of magnitude faster than that of full NS calculation, and the parabolic equation is very suitable for the initial design and optimization calculation of industrial products. In the past, the calculation methods based on analysis transformation such as Levy-lees transformation and Falkna-skan transformation have complex transformation forms, and the conversion from physical system to calculation system is troublesome, which is unfavorable for processing the problem of multi-shear layer mixing such as mixed layer or film cooling. The method based on fractional flow function transformation is difficult to control the wall distance, and an additional wall processing means is required to be added. Few methods adopting actual boundary layer thickness fraction transformation are to process the boundary layer thickness by adopting separation calculation, and have complex calculation process and poor robustness. Disclosure of Invention Aiming at the problems of complex calculation flow and poor robustness of the traditional shear layer separation calculation means in the prior art, the invention provides a two-dimensional shear layer coupling calculation method based on actual shear layer thickness fractional conversion. The invention solves the technical problems by the following technical proposal: a two-dimensional shear layer coupling calculation method based on actual shear layer thickness fraction transformation comprises the following steps: determining the linear coordinates of the non-free end of the shear layer in a Cartesian coordinate form, converting the linear coordinates into orthogonal curve coordinates, and determining a calculation starting point and a calculation terminal point; Selecting a control equation corresponding to the two-dimensional axisymmetric shear layer calculation; converting a control equation under an orthogonal curve coordinate system into a control equation under a shear layer thickness fraction coordinate system by using actual shear layer thickness fraction transformation; Performing grid division of the calculation domain section; Determining initial conditions and boundary conditions required by calculation; Dispersing the control equation by adopting a numerical method; coupling linearization is carried out on the quantity to be solved in the discrete equation by adopting a Newton method; determining the flow direction step length in the discrete equation, and solving the equation set; Updating each coefficient in the equation set; Repeatedly confirming the flow direction step length and solving the equation set in each calculation section until reaching the convergence standard, and advancing to the next calculation section; And repeating the calculation of the next section until the calculation end point is reached by taking the previous calculation section as an initial value, and outputting the physical quantity distribution of each calculation secti