CN109376403B - Two-dimensional icing numerical simulation method based on Cartesian self-adaptive reconstruction technology - Google Patents
Two-dimensional icing numerical simulation method based on Cartesian self-adaptive reconstruction technology Download PDFInfo
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Abstract
The invention provides a two-dimensional icing numerical simulation method based on a Cartesian self-adaptive reconstruction technology, a grid reconstruction method based on a Cartesian grid and a principle thereof, wherein the boundary conditions are processed by using a virtual grid method (GCM, ghost Cell Method) due to the non-body-attaching characteristic of the Cartesian grid; introducing a water drop calculation method based on a Cartesian grid; the grid reconstruction method provided by the invention can greatly improve the calculation speed in the grid reconstruction and flow field calculation part. The method is used for calculating the typical mixed ice calculation example, the obtained ice shape result is good in comparison experiment and foreign calculation result, and the reliability and effectiveness of the two-dimensional icing numerical simulation method based on the Cartesian grid are verified.
Description
Technical Field
The invention discloses a two-dimensional icing numerical simulation method based on a Cartesian self-adaptive reconstruction technology, and relates to the technical field of aircraft icing and deicing.
Background
Numerical simulation of icing and icing growth processes has long been a key topic of concern in the aerospace field. Icing is a complex phase change process for which research is designed to cross-fuse multiple disciplines. Tribus in 1949 studied the heat exchange model of water on the cylindrical surface, and then Messinger improved on the basis of the model, a set of water-ice mass and energy conservation equations based on control volume was established, and a mathematical model for aircraft wing icing simulation calculation, namely a well-known Messinger model, was proposed. Subsequently NASA originally developed a software set for icing calculation, version 0.1 was proposed in 1986 for two-dimensional ice prediction, flow field calculation was performed by solving potential flow equations, using lagrangian method to solve water drop motion trajectories and impact ranges, icing model using classical Messinger model, and using autonomously summarized empirical formulas in calculating convective heat transfer of laminar and turbulent flow regions. Then, numerous follow-up and emulating persons generally borrow and reference the NASA development thought to divide icing calculation into four modules: grid reconstruction/generation, flow field calculation, water drop calculation and icing model. The current icing numerical simulation is mostly improved on flow field calculation, water drop calculation and icing models. With the rapid development of computational fluid mechanics, the flow field computing method is endangered; the water drop calculation method has a tendency of rejecting the Lagrangian method and popularizing the Euler method; numerous modifications of the membrane model, the roughness model, etc. have been developed on the icing model.
Research on a grid method is not rare at present, zhu Dongyu attempts to accelerate grid reconstruction to obtain a certain effect by using a spring grid method, but the spring grid method cannot be expected in effect, and Caruso uses Delaunay triangle grids to reduce the difficulty of grid generation of irregular ice shapes. The existence of singular points in the ice shape is unfavorable for the generation of the structural grid; the grid generation speed is low, and the degree of automation is low; the data cannot be inherited in the multi-step method calculation, and the flow field calculation speed is indirectly influenced. The traditional structural grid is still used as a grid method in the existing mainstream icing simulation.
Disclosure of Invention
Aiming at the structural grid reconstruction technology commonly adopted in the current icing numerical simulation, the invention provides a two-dimensional icing numerical simulation method based on the Cartesian adaptive reconstruction technology, which can rapidly and adaptively reconstruct grids according to any complex boundary, and simultaneously reserve the previous calculation data, thereby improving the calculation efficiency. The invention firstly introduces the basic flow of the traditional icing numerical simulation, and further describes the advantages of applying the Cartesian grid method and the adaptive technology thereof to icing calculation.
The invention adopts the following technical scheme for solving the technical problems:
a two-dimensional icing numerical simulation method based on a Cartesian self-adaptive reconstruction technology has a certain difference in grid method and flow field and water drop calculation caused by the grid method as well as the icing numerical simulation method using a structural grid. The specific implementation steps comprise:
step 4, calculating ice shape growth in a period of time according to the icing model;
and 5, reconstructing the calculation grid by taking the increased ice shape as a new boundary.
As a further preferred embodiment of the invention, the data structure of the cartesian grid used in step 1 is stored using a linked list structure. The linked list structure comprises two parts: the method comprises the steps of storing addresses of a linked list node and a grid space in a pointer form in a link table head, wherein the linked list node is internally provided with forward and backward node addresses besides the grid space addresses;
besides basic flow field variables, adjacent unit address information, child grids and father grids are required to be stored in the grid space, the Cartesian grids are non-body-attached unstructured grids, a cross tree structure is formed through connection between the father and child grids and neighbor unit information, and quick positioning and information searching are facilitated. Modifications to linked list nodes do not affect the grid space and vice versa. The Cartesian grid is a non-body-attached non-structural grid, and the type of the grid needs to be judged according to the relative spatial positions of the grid and the boundary, so that the grid participating in calculation is determined;
as a further preferable mode of the present invention, the relative spatial positions of the grid and the boundary are determined by using a ray method;
as a further preferred embodiment of the present invention, the flow field calculation method in step 2 may be any space-time discrete format suitable for cartesian grid. The virtual grid method is used as a non-body-attached Cartesian grid boundary condition, and the specific implementation steps are as follows:
step one, determining a closest symmetry point B of a grid center point of a virtual grid C with respect to a boundary of an object plane;
step two, determining grid cells of four non-virtual grids which surround or are nearest to the point B;
step three, using bilinear interpolation under the condition that four interpolation templates surrounding the point B are found, and using distance weighted linear interpolation when few templates surrounding the point B cannot be found to obtain the current flow field variable of the point B;
and fourthly, determining the corresponding relation of the flow field values between the symmetrical points B and the virtual grid C through the boundary condition relation to obtain the flow field value of the virtual grid C.
As a further preferable scheme of the present invention, the water drop calculation method in step 3 is performed using a lagrangian method, and the implementation steps of the lagrangian method for calculating the water drop trajectory under the condition of cartesian grid are as follows:
step one, traversing a linked list to determine an initial release position of water drops;
step two, searching surrounding proper grids as interpolation templates to obtain a flow field value of the current water drop position;
thirdly, according to a control equation, a four-step Runge-Kutta method is used for solving the displacement of water drops in unit time;
and step four, determining the current grid of the water drops according to the displacement of the water drops.
And (5) circulating the steps to obtain the track of the water drops changing along with time and the impact point on the object plane.
As a further preferred embodiment of the present invention, the icing model in step 4 may be any icing model. The icing model is irrelevant to the Cartesian grid, and a front flow field and water drop calculation is needed to provide a calculation result;
as a further preferred embodiment of the present invention, the mesh reconstruction in step 5 is performed as follows:
step one, loading a new object plane boundary after icing;
reclassifying the existing grids according to the new boundaries;
step three, encrypting the grid according to the new classification result;
and step four, reorganizing the linked list according to the new classification result, and confirming grids participating in calculation.
Compared with the prior art, the invention has the beneficial effects that:
1. the surface grid is not required to be generated first to regenerate the space grid, but the grid required by calculation is generated once, so that the grid generation process is simple and time-saving;
2. compared with the body-attached structural grid, the conversion from a physical space to a calculation space is not needed, so that a Jacobian matrix is not needed to be calculated in flow field calculation, flux calculation is simple, and calculation time is saved. The self-adaption is easy to realize in the flow field calculation, and the flow field calculation is simpler.
3. Compared with unstructured grids, the method has the advantages that the data structure and grid generation are relatively simple, and adaptive calculation is relatively easy.
4. Compared with the structural grid and the non-structural grid, the self-adaptive capacity is stronger, is more suitable for dealing with the detour of complex geometric shapes and the unsteady problems caused by the movement or deformation of objects.
Drawings
FIG. 1 is a schematic diagram of a linked list data structure.
Fig. 2 is a schematic diagram of a computational domain primary encryption.
Fig. 3 is a schematic diagram of a tree structure of a cartesian grid.
Fig. 4 is a schematic diagram of all mesh decision results involved in the calculation.
Fig. 5 is a schematic diagram of a curvature correction method for the symmetry points of the virtual grid.
FIG. 6 is a schematic diagram of a modification to a linked list during grid reconstruction.
FIG. 7 is a graph of the ice pattern calculated in example 1 and a graph of the comparison between foreign calculations and experiments.
Fig. 8 is a graph of the ice type growth calculated in small time steps (1 second) in example 1.
Fig. 9 is a graph of the resulting ice type results using different time steps in example 1.
Fig. 10 is a graph of flow field calculation residuals before and after icing recorded in example 1.
Detailed Description
Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals refer to the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the drawings are exemplary only for explaining the present invention and are not to be construed as limiting the present invention.
The technical scheme of the invention is further described in detail below with reference to the accompanying drawings:
1. cartesian grid
1.1 data Structure of Cartesian grid
The Cartesian grid is stored by using a linked list, and the linked list structure is composed of linked list nodes and grid space. The linked list nodes store the addresses of grid spaces, and the grid spaces store flow field values, neighbor and father-son information required by calculation. The linked list structure is shown in FIG. 1, and is represented using a line block diagram and pseudocode.
Not all linked list structures are used with such structures, and linked list elements may store information directly rather than addresses. The invention discloses a method for rapidly reconstructing a grid linked list, which deliberately adopts a mode of separating linked list nodes from grid space. Three chain tables are used in the calculation to store all grid information: and (5) calculating a linked list by using the background linked list and the full-grid linked list. The background linked list plays a role in backup, and other linked lists can be rebuilt according to the background linked list under the condition that other linked lists are in error; the whole grid linked list records all unencrypted grids, plays an important role in the grid type judgment and neighbor judgment process, and performs corresponding addition/deletion operation on the whole grid linked list for encryption/thickening operation of the grids; the calculation linked list only records grid information participating in flow field calculation, and more temporary variables related to flow field calculation are added at the node level of the linked list.
1.2 Cartesian grid Generation method
A set of Cartesian grids is obtained by infinitely subdividing one or a plurality of large grids, wherein the subdivision mode is generally equal division, for example, a large square grid is equally divided into four small square grids. This subdivision process is called trellis encryption and vice versa is called thickening. The encryption is repeated a specified number of times by a certain rule, such as a region bounded by coordinates. The encryption hierarchy progresses layer by layer up to 7 layers as shown in fig. 2 for a grid generated for a square computational domain of size 2.5m x 2.5 m.
When generating the grid, firstly, generating a 50×50 background grid, and storing by using an array structure. And determining the adjacent relation between the background grids according to the grid array numbers and storing in advance. The background grid is circulated and encrypted, the grid generated during encryption is stored in a dynamic memory, and sub-grid information can be obtained according to the adjacent relation of the background grid. Searching of grid adjacent information according to the figure 3, the grids are encrypted layer by layer to form a cross tree structure, and corresponding adjacent grid units can be found by tracing upwards according to the cross tree structure.
Determining the grid type according to the space positions of the grid units and the object boundary, and realizing by using a ray method: transmitting two rays in the forward direction and the backward direction by taking the center of the grid and four endpoints of the grid as starting points; the intersection point of the ray on one side and the boundary of the object is zero, and the other side is an even number and is considered to be outside; the intersection points of the two side rays are all odd numbers and are considered to be included; given that closed curves in computers use limited sampling points and line segment compositions, double-sided rays can prevent decision errors in some special cases. After the judgment, the grids intersecting with or outside the object plane boundary are screened as grids participating in calculation, and the grids in the calculation domain after the judgment are shown in fig. 4.
2. Icing numerical simulation
And step 1, generating a grid for calculation according to the mode.
where Ω is the control volume, W is the conservation form variable, and F and G are the flux in the x-direction and y-direction, respectively:
in the above formula, p, ρ, u, v, E, H represent the pressure, density, two velocity components in cartesian coordinates, total energy and total enthalpy, respectively.
The control equations are discretized using any space-time discrete format suitable for cartesian grids.
Step 2.1. Cartesian grid boundary condition definition uses a virtual grid method.
And 2.1.1, searching a boundary grid intersecting with the object plane boundary, and internally pushing two layers to serve as virtual grid units.
Step 2.1.2. There is a virtual grid C near the object plane boundary 123 as shown in fig. 5. Finding the symmetry point of the virtual grid C can be defined simply as its mirror point C' with respect to the nearest line segment 23. In order to improve the calculation accuracy, a circumcircle curvature fitting scheme is adopted. When judging the symmetry point of any virtual grid A, 1) firstly finding a point 2 closest to the C point in the sampling points: 2) Determining 1,3 points adjacent to the 2 points in front and behind, and determining a unique circumscribing circle by using the three points; 3) C and the circle center O are taken as straight lines, and a symmetry point C' after curvature correction can be found on the straight lines.
Step 2.1.3. Find four grid cells K1, K2, K3, K4 surrounding the symmetry point or nearest to it as interpolation templates. Bilinear interpolation is used when the interpolation template encloses the symmetry point, and distance weighted linear interpolation is used when the symmetry point cannot be enclosed.
Step 2.1.3.1. Bilinear interpolation:
the variable at any point in the interpolation region can be written as:
W＝a 1 xy+a 2 x+a 3 y+a 4 (3)
wherein a is i For interpolation coefficients corresponding to four interpolation templates respectively, the method can be obtained by carrying four template units into the above system of linear equations and then solving the system of linear equations:
the Vandermande matrix is denoted as [ G ], as further follows:
so to any point A in the interpolation region * The interpolation formula of (2) is:
the processing modes are also different for different boundary condition types, and Dirichletian boundary conditions are considered:
V n ＝0 (7)
in the above, V n Is the wall normal velocity. [ G ] in equation (5)]And corresponding { W ] i The } substitution is:
wherein the subscript n is along the wall normal. Consider the Neumann condition:
in the above formula, T represents temperature.
From the directional derivative definition and directly deriving equation (3) one can get:
wherein subscript B is the wall position, and corresponds to:
step 2.1.3.2. Linear interpolation of distance weights:
the linear interpolation formula for the distance weighting is:
wherein W is ki D, for the conservation variable corresponding to the four interpolation templates respectively i Is interpolation template and interpolation point A * Distance between them.
Step 2.5. Definition of virtual grid cells:
the boundary conditions for a non-viscous flow are defined differently according to the different boundary conditions given by Dadone's study:
ρ A ＝ρ A′ (p A /p A′ ) 1/γ (14)
V n·A ＝-V n，A′ (16)
wherein the subscript A is the virtual grid center position and A' is taken as the symmetry point. V (V) t，A ，V n，A Tangential velocity and normal velocity for virtual grid cell position, V t，A′ ，V n，A′ Tangential velocity and normal velocity are the symmetry points of the virtual grid cell locations.
And 3, calculating the water drop track by adopting a Lagrangian method, wherein a control equation is as follows:
the superscript p in the formula denotes a water droplet dependent variable, V is a velocity vector, a is the windward area of the water droplet, and m is the mass of the water droplet. It was found that the effect of turbulence on the water droplets was not considered in the lagrangian equation. Definition of relative Reynolds number
The Long Geku tower four-step method is used for solving the water drop track, and the specific steps are as follows:
step 3.1, determining the release position and release interval of water drops;
step 3.2, interpolating to determine a flow field value of the space position of the water drop;
step 3.3, solving the displacement of the water drops by using a Long Geku tower four-step method, and tracking the specific positions of the water drops in the grid according to XY components of the displacement;
step 3.4, repeatedly executing the step three on one water drop until the water drop flies out of the calculation domain or the impact object plane, and calculating the next water drop;
step 3.5, repeating the step four until all water drops finish track calculation;
defining a water drop collecting coefficient according to the ratio of the impact position interval and the release interval of two water drops, and obtaining the water drop collecting coefficient distribution on the surface of an object:
step 4, under the condition that the flow field value and the water drop collecting coefficient of the surface are known, any applicable model can be used for the icing model. Taking the classical Messinger model as an example:
m imp +m in -m out -m eva ＝m ice (19)
E imp +E in +E ice +E air -E out -E eva -E conv ＝0 (20)
in the above equation, m in For the liquid water amount flowing into the current control unit by the upstream control unit, the control unit is provided with a water inflow side and a water outflow side, wherein the upstream side is the adjacent control body sharing the water inflow side by the control unit, and the downstream side is the adjacent control body sharing the water outflow side by the control body. m is m imp For supercooling water drop to strike object plane, m eva M for controlling the amount of water evaporated in the unit out M is the amount of liquid water flowing from the current control unit to the downstream control unit ice Is the amount of liquid water that freezes into ice. In the energy equation, E in Represents the energy of the water flowing into the water by the upstream control unit E imp Indicating the energy of supercooled water droplets impinging on the object plane,E ice represents the energy released by freezing the liquid water, E air Representing the energy of pneumatic heating, E eva Represents the energy carried away by evaporation, E out Representing the energy carried by the water flowing out of the control unit, E conv Representing the energy carried away by convective heat transfer. When the water drop and the flow field solving result are known, m can be calculated imp ，m in ，m eva And m in And their corresponding energy terms, and also convective heat transfer E conv And pneumatic heating E air The unknowns are only the freezing coefficient f and the wall temperature T s . The solution of the icing model is a process of pre-estimated correction by applying a method to T s Calculating a corresponding freezing coefficient by giving an assumed initial value, and comparing T according to the freezing coefficient s Is corrected for the hypothetical value of (c).
3. Boundary self-adaption method
The construction method of the Cartesian grid and the prediction flow of the new ice type can be known from the previous step description. In order to rapidly execute multi-step icing prediction, the method adopts a method of reconstructing a linked list and reserving grid space in a reconstruction method, and comprises the following specific steps:
and step 2, traversing the full grid linked list, and carrying out ray type judgment on all grids again. As a preferred option, only grids that may be subject to type changes may be determined within a predictable range of boundary changes;
step 3.1, traversing the full-grid linked list;
step 3.2, screening grids with the type of boundary grids for encryption;
step 3.3, performing type judgment and neighbor judgment on the encrypted grid;
step 3.4, as shown in fig. 6, deleting the current grid node in the full grid linked list immediately, and supplementing the current grid node by using four new encrypted nodes;
and step 4, reconstructing a calculation linked list to complete grid reconstruction.
The reconstruction method of the invention does not involve the deletion and reconstruction of the grid space in the computer memory, and the storage content (flow field value) of the grid space is not affected by the change of the linked list sequence and the content. Therefore, the grid method of the invention has two important advantages compared with the traditional structural grid: the local reconstruction grid is not needed to regenerate the full-field grid; the flow field value of the grid space is reserved, so that the convergence speed of the subsequent flow field calculation is accelerated.
The invention can greatly reduce grid reconstruction time and improve flow field calculation efficiency, so that multi-step prediction is possible by using small icing step length in the traditional method. Typically, the single-step icing time for a multi-step icing prediction is 30 seconds, which can be reduced to a minimum of 1 second after use of the present invention.
An example is given below as a specific example of the disclosed method.
Example one, two-dimensional hybrid icing example, flight Mach 0.2, ambient temperature 259.85K, flight angle of attack 4, total icing time 360 seconds, cloud and fog parameters were droplet equivalent volume diameter (MVD) 20 microns, liquid Water Content (LWC) 1g/m 3, and NACA0012 was used for the airfoil. The ice types under various icing time steps are calculated respectively, the influence of the icing time steps on the calculated result is verified, and the smaller the icing time steps, the more obvious the water overflow phenomenon in the simulation result is. Fig. 7 reflects a comparison of a prediction result using the present invention and foreign commercial software, fig. 8 reflects an ice type growth process predicted at a minimum time step of 1 second, fig. 9 reflects an ice type distinction of different time steps, and fig. 10 reflects an effect of the grid reconstruction method of the present invention on accelerating flow field convergence, and it is possible to find a great degree of accelerated convergence after inherited data by a residual curve of clean airfoil (grid data is not inherited) and frozen airfoil (grid calculation data is inherited).
While the embodiments of the present invention have been described in detail with reference to the drawings, the present invention is not limited to the above-described embodiments, and various changes may be made without departing from the spirit of the present invention within the knowledge of those skilled in the art. While the invention has been described in terms of what are presently considered to be the most practical and preferred embodiments, it is to be understood that the invention is not to be limited to the disclosed embodiments, but on the contrary, is intended to cover various modifications, equivalents, and alternatives falling within the spirit and scope of the invention.
Claims (4)
1. A two-dimensional icing numerical simulation method based on a Cartesian self-adaptive reconstruction technology is characterized by comprising the following steps of: in the two-dimensional icing numerical simulation method, a Cartesian grid is used as a grid method, so that grid rapid reconstruction, grid self-adaptive encryption according to ice type and flow field calculation acceleration convergence after icing are realized, and the method specifically comprises the following steps:
step 1, generating a proper Cartesian grid coverage calculation domain;
step 2, calculating a flow field until convergence; in step 2, the boundary conditions of the cartesian grid are provided by a virtual grid method, which specifically comprises the following steps:
step 2.1, determining a closest symmetry point B of a grid center point of the virtual grid C with respect to the object plane boundary;
step 2.2, determining grid cells of four non-virtual grids surrounding or nearest to the point B;
step 2.3, using bilinear interpolation under the condition that four interpolation templates surrounding the point B are found, and using distance weighted linear interpolation under the condition that few templates surrounding the point B cannot be found to obtain the current flow field variable of the point B;
step 2.4, determining the corresponding relation of the flow field value between the symmetrical point B and the virtual grid C through the boundary condition relation to obtain the flow field value of the virtual grid C;
step 3, calculating a water drop track and an airfoil surface water collection coefficient by using a Lagrangian method;
step 4, calculating ice shape growth in a set time according to the icing model;
step 5, reconstructing a calculation grid by taking the ice shape after growth as a new boundary; in step 5, the specific steps of performing grid adaptive reconstruction on the new frozen boundary are as follows:
step 5.1, replacing the existing boundary with a new ice object boundary;
step 5.2, traversing the full grid linked list, and judging the types of rays again for all grids;
and 5.3, reconstructing a calculation linked list to complete grid reconstruction.
2. The two-dimensional icing numerical simulation method based on the Cartesian adaptive reconstruction technology as set forth in claim 1, wherein: in step 1, the data structure of the cartesian grid is a linked list structure, and the linked list structure consists of linked list nodes and grid space; and storing the address of a grid space in the linked list node, wherein the grid space stores flow field values and neighbor and father-son information required by calculation, and adopts a mode of separating the linked list node from the grid space.
3. The two-dimensional icing numerical simulation method based on the Cartesian adaptive reconstruction technology as set forth in claim 1, wherein: in the step 2, after grid reconstruction, the flow field calculation inherits the convergence data of the previous round, most of the memory space of the grid remains unchanged, and the calculation can greatly reduce the time required for convergence.
4. The two-dimensional icing numerical simulation method based on the Cartesian adaptive reconstruction technology as set forth in claim 1, wherein: in the step 5.2, the grids with the changed types are judged in the boundary variation range, and further local encryption is selected according to the boundary, and the implementation method is as follows:
step 5.2.1, traversing the full grid linked list;
step 5.2.2, encrypting the grids with the screening type being boundary grids;
step 5.2.3, performing type judgment and neighbor judgment on the encrypted grid;
and 5.2.4, deleting the current grid node in the full grid linked list immediately, and supplementing the current grid node by using the encrypted new node.
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| CN112562086B (en) * | 2021-02-22 | 2021-06-18 | 中国空气动力研究与发展中心低速空气动力研究所 | Ice-shaped model curved surface reconstruction method |
| CN113112568B (en) * | 2021-06-08 | 2021-09-07 | 中国空气动力研究与发展中心低速空气动力研究所 | Two-dimensional ice shape simplification method based on arc fitting |
| CN113779904B (en) * | 2021-06-09 | 2023-04-25 | 中国空气动力研究与发展中心低速空气动力研究所 | Icing phase change calculation method based on coupling of continuous liquid film and discrete liquid film |
| CN113486454B (en) * | 2021-09-07 | 2021-11-09 | 中国空气动力研究与发展中心低速空气动力研究所 | Method for calculating target release position of liquid drop |
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