A solution method for the transitional turbulent flow field of underwater vehicles with temperature gradients

Abstract

The present invention proposes a method for solving the transition turbulent flow field of an underwater vehicle including a temperature gradient. By directly calling the underwater boundary layer transition turbulence model considering the temperature gradient for CFD solution, the prediction of the boundary layer transition position and transition process of the underwater vehicle under the wall thermal control condition is realized. First, the incompressible similarity equation group including the temperature equation is solved, and a database of underwater boundary layer characteristic parameters is established. A linear stability analysis is performed under given flow conditions to obtain the transition momentum thickness Reynolds number under different flow conditions, and the fitting relationship between the transition momentum thickness Reynolds number and the flow condition is obtained as the transition criterion; the transition criterion is implanted into the source term of the transition model to obtain the underwater boundary layer transition prediction model considering the temperature gradient, and finally, the generation source term and the destruction source term of the turbulent kinetic energy transport equation in the Menter SST turbulence model are modified according to the transition prediction model to obtain the underwater boundary layer transition turbulence model considering the temperature gradient.

Description

Technical Field

[0001] The present invention relates to the technical field of computational fluid dynamics, and in particular to a method for solving a transitional turbulent flow field of an underwater vehicle containing a temperature gradient. Background Art

[0002] Boundary layer transition is a common physical phenomenon in fluid mechanics, which describes the process of fluid changing from a stable laminar state to a chaotic turbulent state. This transition phenomenon is not only common in nature, but also plays a vital role in engineering applications. For example, boundary layer transition is directly related to the surface friction resistance distribution, heat flow distribution and noise level of aircraft and underwater vehicles, which in turn affects their performance and safety. In view of this, accurately predicting boundary layer transition is one of the key factors to improve the design level of aircraft and underwater vehicles.

[0003] In aircraft turbulence or underwater flow problems, the incoming flow is usually relatively calm, that is, the incoming flow turbulence is small, and the transition form is dominated by natural transition. The transition prediction methods based on stability theory, represented by the method, predict transition positions that are in good agreement with experimental results. However, the transition prediction methods based on stability theory are not suitable for modern large-scale parallel computing architectures, such as unstructured grids and large-scale parallel computing. On the contrary, the transition prediction model based on local variable solution is compatible with modern computational fluid dynamics (CFD) technology, and is therefore sought after by scholars and engineers. In recent years, many excellent transition prediction models have emerged in the field of aerospace, such as the famous Transition model. In contrast, research on underwater boundary layer transition models is relatively lagging behind. Although in general, the boundary layer transition prediction on underwater vehicles can borrow the transition prediction model constructed in the air, when there is a temperature gradient in the flow field (such as wall heating or cooling), the transition prediction model constructed based on air will no longer be applicable to the underwater flow environment due to the significant difference in the thermodynamic properties of air and water.

[0004] As a classic flow control method, wall heating and cooling are often used in engineering practice to actively control the transition position. For example, by optimizing the wall heat flux, the boundary layer transition position can be delayed or triggered in advance. In early wind tunnel experiments, researchers found that in an air environment, heating the wall will accelerate the occurrence of the transition, that is, the transition position moves upstream; while cooling the wall can effectively delay the transition and make the transition position move downstream. However, due to the opposite viscosity of water and air, researchers speculate that the effect of wall heating or cooling will show the opposite trend in an underwater environment. Specifically, in water, heating the wall will delay the boundary layer transition, while cooling the wall will make the transition occur earlier. This speculation has been confirmed in water tunnel experiments. In this context, wall heating has been gradually applied to the design of underwater vehicles and has become a solution to delay the occurrence of transition. Through wall thermal control, surface friction resistance can be significantly reduced, while suppressing flow noise caused by turbulence, thereby improving the overall performance of the entire vehicle.

[0005] Although wall thermal control has shown great application potential in controlling the underwater boundary layer transition, the current transition prediction method with wall thermal control still adopts the traditional transition prediction idea, that is, firstly establishing the boundary layer equation, then solving the eigenvalue through linear stability theory according to the estimated initial eigenvalue, and integrating along the flow direction to obtain the distribution of the amplitude amplification factor N, and finally estimating the critical value of N to obtain the transition position. For example, Chinese patent application with publication number CN114528665, "A method for predicting the transition position of an underwater flat plate boundary layer with wall heating / cooling", and Chinese patent application with publication number CN118607085A, "A method for predicting the transition of an underwater curved surface boundary layer with wall heating / cooling", both use this traditional transition prediction method, which has the following problems: the calculation process is complicated, in which initial values ​​or estimated values ​​need to be provided based on the engineering experience of the technicians in many places, resulting in the calculation results being closely related to the engineering experience of the technicians; due to the constraints of the linear stability theory itself, this method can only predict the transition position of flat plate structures or simple curved surfaces, and cannot be applied to the prediction of transition turbulent flow fields under complex structures.

[0006] At present, there is a lack of a set of open, accurate and efficient transition prediction models and flow field solution methods for the prediction of transition turbulent flow fields of underwater vehicles with three-dimensional geometric shapes and wall thermal control. This gap has, to a certain extent, led to the inability to quickly iterate design solutions through means based on numerical simulation, thereby slowing down the design cycle and optimization process of underwater vehicles. Therefore, for underwater environments, constructing a transition prediction model and flow field solution method that is suitable for three-dimensional complex flow fields and can simultaneously consider the effects of thermal boundary conditions is not only of important academic value, but also of practical engineering significance. Summary of the invention

[0007] In order to make up for the deficiencies in the existing underwater boundary layer transition prediction model and improve the prediction accuracy and practicability of the boundary layer transition position and transition process of underwater vehicles under wall thermal control conditions, the present invention proposes a method for solving the underwater vehicle transition turbulent flow field containing temperature gradient, targeting the temperature gradient effect caused by the wall thermal control of underwater vehicles. By establishing an underwater boundary layer transition turbulence model considering the temperature gradient, the underwater boundary layer transition turbulence model considering the temperature gradient is directly called for CFD solution when actually calculating the flow field, so that the boundary layer transition position and transition process of underwater vehicles under wall thermal control conditions can be predicted. Not only the transition position under complex configuration is output, but also the transition process can be obtained, providing accurate and reliable technical support for underwater vehicles to achieve flow control through wall thermal control, so as to meet the needs of actual engineering applications.

[0008] The technical solution of the present invention is:

[0009] The method for solving the transitional turbulent flow field of an underwater vehicle including a temperature gradient comprises the following steps:

[0010] Step 1: Establish a three-dimensional model of the underwater vehicle, create a computational grid, and apply flow field boundary conditions to obtain a computational model of the underwater vehicle; the flow field boundary conditions include wall heating and cooling boundary conditions;

[0011] Step 2: Use a CFD solver embedded with a transition turbulence model to solve the flow field of the underwater vehicle calculation model established in step 1 to obtain the transition position and transition process;

[0012] The transition turbulence model is obtained through the following process:

[0013] Step 2.1: Establish underwater boundary layer characteristic parameter database:

[0014] The underwater boundary layer characteristic parameter database includes pressure gradient, incoming flow temperature, temperature difference between the wall and the incoming flow, and underwater boundary layer characteristic parameters at corresponding positions;

[0015] Step 2.2: Using the underwater boundary layer characteristic parameter database established in step 2.1, perform linear stability analysis under given flow conditions to obtain the transition momentum thickness Reynolds number under several different flow conditions. , the transition momentum thickness Reynolds number is obtained by fitting The fitting relationship with the flow conditions is used as a transition criterion; the flow conditions include pressure gradient, incoming flow temperature, temperature difference between the wall and the incoming flow, and turbulence of the incoming flow;

[0016] Step 2.3: implant the transition criterion constructed in step 2.2 into the source term of the transition model based on the intermittent factor transport equation to obtain the underwater boundary layer transition prediction model considering the temperature gradient;

[0017] Step 2.4: According to the underwater boundary layer transition prediction model considering the temperature gradient obtained in step 2.3, modify the generation source term and the destruction source term of the turbulent kinetic energy transport equation in the Menter SST turbulence model to obtain the underwater boundary layer transition turbulence model considering the temperature gradient; the underwater boundary layer transition turbulence model considering the temperature gradient is composed of the turbulent kinetic energy transport equation, the turbulent specific dissipation rate transport equation and the underwater boundary layer transition prediction model considering the temperature gradient.

[0018] Furthermore, in step 2.1, according to the pressure gradient, the incoming flow temperature, and the temperature difference between the wall and the incoming flow, the underwater boundary layer characteristic parameters at the corresponding position are obtained by solving the incompressible similarity equation group including the temperature equation; based on different pressure gradients, different incoming flow temperatures, and different temperature difference conditions between the wall and the incoming flow, the corresponding underwater boundary layer characteristic parameters are obtained to form an underwater boundary layer characteristic parameter database; the underwater boundary layer characteristic parameters include boundary layer velocity type and temperature type.

[0019] Further, in step 2.1, the incompressible similarity equations including the temperature equation are obtained by the following process:

[0020] First, the tensor form of the control equation of the incompressible fluid in the underwater boundary layer containing the temperature gradient is established considering the temperature equation:

[0021]

[0022]

[0023]

[0024] in, For the The dimensioned coordinate components in the directions, Corresponding to the Cartesian coordinate system direction; Indicates that the fluid The dimensioned velocity components in each direction, Corresponding to the Cartesian coordinate system direction; For the The dimensioned coordinate components in the directions, Corresponding to the Cartesian coordinate system , , direction; Indicates that the fluid The dimensioned velocity components in each direction, Corresponding to the Cartesian coordinate system direction; is the dimensioned time, is the dimensionless fluid density, is the dimensionless fluid pressure, is the dimensionless dynamic viscosity coefficient, is the dimensionless fluid temperature, is the dimensionless specific heat of the fluid, is the dimensionless fluid thermal conductivity;

[0025] Introduce Falkner-Skan transform:

[0026]

[0027] in is the transformed normal coordinate, is the dimensioned streamwise coordinate, is the dimensioned normal coordinate, is the norm of the dimensioned velocity at the edge of the boundary layer, is the dimensioned dynamic viscosity coefficient at the edge of the boundary layer, To set a constant;

[0028] The incompressible similarity equations including the temperature equation are derived as follows:

[0029]

[0030]

[0031]

[0032] in is the dimensionless streamwise velocity, and its dimensionless form is , is the dimensioned streamwise velocity; and are newly introduced variables, defined as , , is the Hartree pressure gradient factor, is the Prandtl number; are intermediate parameters, respectively defined as

[0033]

[0034]

[0035]

[0036] in, is the dimensionless fluid heat transfer coefficient at the edge of the boundary layer, is the dimensioned temperature at the edge of the boundary layer.

[0037] Furthermore, in step 2.2, for a certain flow condition, the corresponding transition momentum thickness Reynolds number is obtained: The process is:

[0038] According to the turbulence of the incoming flow , using the Mack relation, we can get the critical N value corresponding to the transition;

[0039] Using the critical N value, a linear stability analysis is performed on the boundary layer similarity solution under a given flow condition to obtain the transition momentum thickness Reynolds number under the corresponding flow condition. .

[0040] Furthermore, in step 2.2, the transition momentum thickness Reynolds number obtained by fitting is The fitting relationship with the flow condition is:

[0041]

[0042] in is the shape factor, , , , All are intermediate variables; specifically:

[0043]

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050] In the formula, is the dimensioned temperature at the edge of the boundary layer, is the dimensionless temperature at the wall, is the local Thwaites pressure gradient factor, is the dimensionless incoming flow temperature, is the dimensionless temperature difference between the wall and the incoming flow.

[0051] Furthermore, for an axisymmetric underwater vehicle, the following formula is used to correct the shape factor:

[0052]

[0053] in, is the shape factor after axisymmetry correction.

[0054] Furthermore, the underwater boundary layer transition prediction model considering the temperature gradient obtained in step 2.3 is:

[0055]

[0056] in, represents the intermittent factor, is the model constant; and They correspond to the generation source term and the destruction source term of the intermittent factor respectively:

[0057]

[0058]

[0059] in is the modulus of the dimensionless velocity strain rate tensor, is the norm of the dimensionless vorticity, and are all setting coefficients, , , They are all model functions and have the following form:

[0060]

[0061]

[0062]

[0063]

[0064]

[0065]

[0066] in, is the dimensionless turbulent dynamic viscosity coefficient; is the local Thwaites pressure gradient factor and the dimensionless incoming temperature and the dimensionless temperature difference between the wall and the incoming flow function; the transition momentum thickness Reynolds number Substitute the fitting relationship with the flow condition into In the calculation of the transition criterion, the transition model based on the intermittent factor transport equation is implemented.

[0067] Furthermore, in step 2.3, the local Thwaites pressure gradient factor According to the formula

[0068]

[0069] The model of the dimensioned velocity at the edge of the boundary layer is Solve the Bernoulli equation locally using the incompressible form:

[0070]

[0071] in, is the dimensionless pressure of the incoming flow, is the dimensionless velocity modulus of the incoming flow, is the dimensioned pressure at the edge of the boundary layer.

[0072] Furthermore, in step 2.4, the modified turbulent kinetic energy transport equation is:

[0073]

[0074] in is the dimensionless turbulent kinetic energy, is the model constant, and Generate and destroy source terms for the modified turbulent kinetic energy: , , and These are the generation source terms and destruction source terms of the turbulent kinetic energy transport equation in the original Menter SST turbulence model.

[0075] Beneficial effects:

[0076] The present invention aims at the temperature gradient effect caused by the thermal control of the underwater vehicle wall, and proposes a solution method for the underwater vehicle transition turbulent flow field containing a temperature gradient. By directly calling the underwater boundary layer transition turbulence model considering the temperature gradient for CFD solution, the prediction of the boundary layer transition position and transition process of the underwater vehicle under the wall thermal control condition can be realized. In the process of establishing the underwater boundary layer transition turbulence model considering the temperature gradient, firstly, by solving the incompressible similarity equation group containing the temperature equation, an underwater boundary layer characteristic parameter database is established. Using the underwater boundary layer characteristic parameter database, a linear stability analysis is performed under given flow conditions to obtain the transition momentum thickness Reynolds number under several different flow conditions. , the transition momentum thickness Reynolds number is obtained by fitting The fitting relationship between the flow condition and the transition criterion is used as the transition criterion; the transition criterion is then implanted into the source term of the transition model to obtain the underwater boundary layer transition prediction model considering the temperature gradient. Finally, according to the underwater boundary layer transition prediction model considering the temperature gradient, the generation source term and the destruction source term of the turbulent kinetic energy transport equation in the Menter SST turbulence model are modified to obtain the underwater boundary layer transition turbulence model considering the temperature gradient. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 : Underwater vehicle computational domain and computational grid settings;

[0078] Figure 2 : Prediction of underwater vehicle surface friction drag coefficient and near-wall turbulent kinetic energy distribution under adiabatic wall conditions; is the turbulent kinetic energy, is the surface friction coefficient, is the intermittent factor, represents experimental value;

[0079] Figure 3 : The predicted surface friction drag coefficient of underwater vehicles and the distribution of turbulent kinetic energy near the wall when the wall heating power is 26.6kw; is the turbulent kinetic energy, is the surface friction coefficient, is the intermittent factor, represents experimental value;

[0080] Figure 4 : The predicted surface friction drag coefficient of underwater vehicles and the distribution of turbulent kinetic energy near the wall when the wall heating power is 75.4kw; is the turbulent kinetic energy, is the surface friction coefficient, is the intermittent factor, represents experimental value;

[0081] Figure 5: The predicted surface friction drag coefficient of underwater vehicles and the distribution of turbulent kinetic energy near the wall when the wall heating power is 93.3kw; is the turbulent kinetic energy, is the surface friction coefficient, is the intermittent factor, Represents experimental value. DETAILED DESCRIPTION

[0082] The following describes the method for solving the transitional turbulent flow field of an underwater vehicle including a temperature gradient proposed by the present invention in conjunction with a specific embodiment:

[0083] Step 1: Establish a three-dimensional model of the underwater vehicle, create a computational grid, and apply flow field boundary conditions to obtain a computational model of the underwater vehicle; the flow field boundary conditions include wall heating and cooling boundary conditions;

[0084] Step 2: Use a CFD solver embedded with a transition turbulence model to solve the flow field of the underwater vehicle calculation model established in step 1 to obtain the transition position and transition process;

[0085] The transition turbulence model is obtained through the following process:

[0086] Step 2.1: Establish underwater boundary layer characteristic parameter database:

[0087] The underwater boundary layer characteristic parameter database includes pressure gradient, incoming flow temperature, wall and incoming flow temperature difference, and underwater boundary layer characteristic parameters at corresponding positions; according to the pressure gradient, incoming flow temperature, wall and incoming flow temperature difference, the underwater boundary layer characteristic parameters at corresponding positions are obtained by solving an incompressible similarity equation group including a temperature equation; based on different pressure gradients, different incoming flow temperatures, and different wall and incoming flow temperature difference conditions, corresponding underwater boundary layer characteristic parameters are obtained to form an underwater boundary layer characteristic parameter database; the underwater boundary layer characteristic parameters include boundary layer velocity type and temperature type.

[0088] Compared with the traditional incompressible similarity equations, the present invention proposes an incompressible similarity equation group including the temperature equation when calculating the characteristic parameters of the underwater boundary layer. The specific derivation process is as follows:

[0089] Specifically, considering the temperature equation, the tensor form of the control equation of the underwater boundary layer incompressible fluid containing the temperature gradient is expressed as follows:

[0090]

[0091]

[0092]

[0093] in, For the The dimensioned coordinate components in the directions, Corresponding to the Cartesian coordinate system direction; Indicates that the fluid The dimensioned velocity components in each direction, Corresponding to the Cartesian coordinate system direction. Similarly, For the The dimensioned coordinate components in the directions, Corresponding to the Cartesian coordinate system , , direction; Indicates that the fluid The dimensioned velocity components in each direction, Corresponding to the Cartesian coordinate system direction. is the dimensioned time, is the dimensionless fluid density, is the dimensionless fluid pressure, is the dimensionless dynamic viscosity coefficient, is the dimensionless fluid temperature, is the dimensionless specific heat of the fluid, is the dimensionless fluid thermal conductivity.

[0094] Next, the Falkner-Skan transform is introduced:

[0095]

[0096] in is the transformed normal coordinate, is the dimensioned streamwise coordinate, is the dimensioned normal coordinate, is the norm of the dimensioned velocity at the edge of the boundary layer, is the dimensioned dynamic viscosity coefficient at the edge of the boundary layer, To set a constant.

[0097] Thus, the incompressible similarity equations including the temperature equation are derived as follows:

[0098]

[0099]

[0100]

[0101] In the above equation, is the dimensionless streamwise velocity, and its dimensionless form is , is the dimensioned streamwise velocity; and is a newly introduced variable, defined as , , is the Hartree pressure gradient factor, is the Prandtl number. are intermediate parameters, respectively defined as

[0102]

[0103]

[0104]

[0105] in, is the dimensionless fluid heat transfer coefficient at the edge of the boundary layer, is the dimensioned temperature at the edge of the boundary layer.

[0106] The incompressible similarity equations derived above, including the temperature equation, can be expressed in a form that depends only on local flow parameters and geometric parameters. For each actual physical situation, there is a corresponding boundary layer similarity solution, namely, the boundary layer velocity type and temperature type. By traversing different pressure gradients, incoming flow temperatures, and wall and incoming flow temperature differences, a database of underwater boundary layer characteristic parameters can be established.

[0107] Step 2.2: Using the underwater boundary layer characteristic parameter database established in step 2.1, perform linear stability analysis under given flow conditions to obtain the transition momentum thickness Reynolds number under several flow conditions. ; Fitting to get the transition momentum thickness Reynolds number The fitting relationship with the flow conditions is used as the transition criterion; the flow conditions include pressure gradient, incoming flow temperature, temperature difference between the wall and the incoming flow, and incoming flow turbulence.

[0108] For a certain flow condition, the corresponding transition momentum thickness Reynolds number is obtained The process is:

[0109] According to the turbulence of the incoming flow , using the Mack relation, we can get the critical N value corresponding to the transition;

[0110] Using the critical N value, a linear stability analysis is performed on the boundary layer similarity solution under a given flow condition to obtain the transition momentum thickness Reynolds number under the corresponding flow condition. .

[0111] The specific theoretical derivation process is:

[0112] First, define the following dimensionless method:

[0113]

[0114] in, For the The dimensionless coordinate components in the directions, Corresponding to the Cartesian coordinate system direction; Indicates that the fluid The dimensionless velocity components in the directions, Corresponding to the Cartesian coordinate system direction; is the dimensionless fluid pressure, is the dimensionless fluid temperature, is the dimensionless time, is the dimensionless fluid density, is the dimensionless dynamic viscosity coefficient, is the dimensionless fluid thermal conductivity. is the dimensioned reference length, is the dimensionless fluid density at the edge of the boundary layer, and the rest of the variables are defined the same as before.

[0115] Decompose the flow variable into the form of superposition of time-averaged value and disturbance value:

[0116]

[0117] in, is the dimensionless fluid pressure after time-average, The time average The dimensionless velocity components in all directions, is the dimensionless fluid temperature after time-average. Correspondingly, is the dimensionless fluid pressure of the disturbance, For the disturbance The dimensionless velocity components in all directions, is the dimensionless fluid temperature of the disturbance.

[0118] Substituting the decomposed flow variables into the control equation of the underwater boundary layer incompressible fluid containing the temperature gradient, the perturbation equation is derived as follows:

[0119]

[0120] in is the dimensionless streamwise coordinate, is the dimensionless normal coordinate, is the dimensionless spanwise coordinate, the perturbation , , , , , , , , , , , is the coefficient matrix, and its specific form is as follows:

[0121]

[0122]

[0123]

[0124]

[0125]

[0126]

[0127]

[0128]

[0129]

[0130]

[0131] D = 0 0 0 0 0 0 0 ∂ u ̄ ∂y 0 - 1 Re ∂τ ∂y ∂ u ̄ ∂y + τ ∂ 2 u ̄ ∂ y 2 0 0 0 0 0 0 0 ∂ w ̄ ∂y 0 - 1 Re ∂τ ∂y ∂ w ̄ ∂y + τ ∂ 2 w ̄ ∂ y 2 0 0 ∂ T ̄ ∂y 0 - 1 R ( ∂σ ∂y ∂ T ̄ ∂y + σ ∂ 2 T ̄ ∂ y 2 )- Ec Re [ τ ( ∂ u ̄ ∂y ) 2 + τ ( ∂ w ̄ ∂y ) 2 ]

[0132]

[0133]

[0134] In the above formula, is the dimensionless dynamic viscosity coefficient after time-average, is the incoming flow Reynolds number, is the Eckert number; is the dimensionless fluid thermal conductivity after time-average; is the dimensionless streamwise velocity after time-average; is the dimensionless spanwise velocity after time-average.

[0135] Assume the disturbance Satisfy the following form:

[0136]

[0137] in, The corresponding disturbance amplitude is is the imaginary number symbol, and are the streamwise wave number and the spanwise wave number, respectively. is the frequency, represents complex conjugate. Substituting the above formula into the perturbation equation, the linear stability equation is derived as:

[0138]

[0139] fixed and is a real number, and Write in plural form , is the real part, is the imaginary part, the linear stability equation is transformed into a generalized eigenvalue solution problem:

[0140]

[0141]

[0142]

[0143]

[0144] is the unit matrix; the eigenvalue obtained by solving the above generalized eigenvalue problem is the streamwise wave number , its imaginary part The negative value of corresponds to the growth rate of the disturbance amplitude in the flow direction, and the disturbance amplification factor is obtained by integrating it along the flow direction. :

[0145]

[0146]

[0147] in, is the momentum thickness Reynolds number at the location where the disturbance starts to grow, is the local momentum thickness Reynolds number, and the definitions of other variables are the same as above.

[0148] According to the Mack relationship

[0149]

[0150] Input flow turbulence , we get the critical N value, that is Using the critical N value and the perturbation amplification factor calculation formula, the transition momentum thickness Reynolds number corresponding to the critical N value is inversely solved. .

[0151] Using the transition momentum thickness Reynolds number under several flow conditions , the transition momentum thickness Reynolds number is obtained by fitting The fitting relationship with the flow condition is used as the transition criterion, and the fitting relationship is:

[0152]

[0153]

[0154]

[0155]

[0156]

[0157]

[0158]

[0159]

[0160] In the above formula, is the dimensioned temperature at the edge of the boundary layer, is the dimensionless temperature at the wall. is the shape factor, given by the local Thwaites pressure gradient factor , dimensionless incoming flow temperature and the dimensionless temperature difference between the wall and the incoming flow In addition, for the axisymmetric underwater vehicle, the following correction is introduced using the experimental results:

[0161]

[0162] in, is the shape factor after axisymmetry correction.

[0163] Step 2.3: The transition criterion constructed in step 2.2 is implanted into the source term of the transition model based on the intermittent factor transport equation to obtain the underwater boundary layer transition prediction model considering the temperature gradient:

[0164]

[0165] in, represents the intermittent factor, represents laminar flow, Indicates turbulence, and its value between 0 and 1 corresponds to the transition process. is the model constant, which is usually 1. and They correspond to the generation source term and the destruction source term of the intermittent factor respectively:

[0166]

[0167]

[0168] In the above formula, is the modulus of the dimensionless velocity strain rate tensor, is the norm of the dimensionless vorticity. , , Represents a model function in the following form:

[0169]

[0170]

[0171]

[0172]

[0173]

[0174]

[0175] in, is the dimensionless turbulent dynamic viscosity coefficient; is a factor for the local Thwaites pressure gradient and the dimensionless incoming temperature and the dimensionless temperature difference between the wall and the incoming flow The function form is as follows:

[0176]

[0177] in

[0178]

[0179] The definitions of other variables are the same as above. The coefficients in the intermittent factor transport equation are fixed as:

[0180]

[0181] The transition momentum thickness Reynolds number of the structure Substitute the fitting relationship with the flow condition into , that is, the transition criterion constructed by the present invention is implanted into the transition model based on the intermittent factor transport equation.

[0182] Local Thwaites pressure gradient factor The following formulas need to be combined for iterative solution:

[0183]

[0184]

[0185] The dimensionless velocity at the edge of the boundary layer is Solve the Bernoulli equation locally using the incompressible form:

[0186]

[0187] in, is the dimensionless pressure of the incoming flow, is the dimensionless velocity modulus of the incoming flow, is the dimensioned pressure at the edge of the boundary layer. So far, all the physical quantities used in the intermittent factor transport equation can be obtained locally, which meets the requirements of large-scale parallel computing of modern CFD solvers.

[0188] Step 2.4: According to the underwater boundary layer transition prediction model considering the temperature gradient obtained in step 2.3, the generation source term and the destruction source term of the turbulent kinetic energy transport equation in the Menter SST turbulence model are modified to obtain the underwater boundary layer transition turbulence model considering the temperature gradient; the underwater boundary layer transition turbulence model considering the temperature gradient is composed of the turbulent kinetic energy transport equation, the turbulent specific dissipation rate transport equation and the underwater boundary layer transition prediction model considering the temperature gradient; wherein the turbulent kinetic energy transport equation is:

[0189]

[0190] In the above formula, is the dimensionless turbulent kinetic energy, is a model constant whose value is consistent with that in the original Menter SST turbulence model. and is the modified turbulent kinetic energy generating source term and destroying source term, the specific form is:

[0191]

[0192]

[0193] in, and They are the source term and destruction term of the turbulent kinetic energy transport equation in the original Menter SST turbulence model. The transport equations of follow the original Menter SST turbulence model. Finally, we get The three-equation transition turbulence model is embedded in the CFD solver to achieve the numerical prediction of the transition turbulence flow field of underwater vehicles with temperature gradient.

[0194] Example verification:

[0195] In order to verify the accuracy of the underwater boundary layer transition turbulent flow field solution technology considering the influence of temperature gradient proposed in the present invention, the underwater vehicle transition experiment with a rotating body shape with wall heating disclosed by Lauchle et al. was used to verify it. The transition conditions of the underwater vehicle surface under the adiabatic wall and different wall heating powers were simulated respectively, and the results were compared with the experimental results. The calculation conditions are shown in the following table:

[0196] Table 1 Calculation conditions of underwater vehicle

[0197]

[0198] In the above table, is the inlet flow turbulence, is the inlet flow velocity, is the incoming flow temperature, is the temperature difference between the wall and the incoming flow.

[0199] The calculation results show that the prediction system proposed in the present invention has high accuracy in predicting underwater boundary layer transition including the influence of temperature gradient, and shows good potential for engineering application.

[0200] The above are only preferred embodiments of the present invention. The protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims

1. A method for solving the transitional turbulent flow field of an underwater vehicle containing a temperature gradient, characterized in that: The following steps are involved: Step 1: Establish a three-dimensional model of the underwater vehicle, create a computational grid, and apply flow field boundary conditions to obtain a computational model of the underwater vehicle; the flow field boundary conditions include wall heating and cooling boundary conditions; Step 2: Use a CFD solver embedded with a transition turbulence model to solve the flow field of the underwater vehicle calculation model established in step 1 to obtain the transition position and transition process; The transition turbulence model is obtained through the following process: Step 2.1: Establish underwater boundary layer characteristic parameter database: The underwater boundary layer characteristic parameter database includes pressure gradient, incoming flow temperature, temperature difference between the wall and the incoming flow, and underwater boundary layer characteristic parameters at corresponding positions; Step 2.2: Using the underwater boundary layer characteristic parameter database established in step 2.1, perform linear stability analysis under given flow conditions to obtain the transition momentum thickness Reynolds number under several different flow conditions. , the transition momentum thickness Reynolds number is obtained by fitting The fitting relationship with the flow conditions is used as a transition criterion; the flow conditions include pressure gradient, incoming flow temperature, temperature difference between the wall and the incoming flow, and turbulence of the incoming flow; Step 2.3: implant the transition criterion constructed in step 2.2 into the source term of the transition model based on the intermittent factor transport equation to obtain the underwater boundary layer transition prediction model considering the temperature gradient; Step 2.4: According to the underwater boundary layer transition prediction model considering the temperature gradient obtained in step 2.3, modify the generation source term and the destruction source term of the turbulent kinetic energy transfer equation in the MenterSST turbulence model to obtain the underwater boundary layer transition turbulence model considering the temperature gradient; the underwater boundary layer transition turbulence model considering the temperature gradient is composed of the turbulent kinetic energy transfer equation, the turbulent specific dissipation rate transport equation and the underwater boundary layer transition prediction model considering the temperature gradient.

2. A method for solving the transitional turbulent flow field of an underwater vehicle containing a temperature gradient according to claim 1, characterized in that: In step 2.1, according to the pressure gradient, the incoming flow temperature, and the temperature difference between the wall and the incoming flow, the underwater boundary layer characteristic parameters at the corresponding position are obtained by solving the incompressible similarity equation group including the temperature equation; based on different pressure gradients, different incoming flow temperatures, and different temperature difference conditions between the wall and the incoming flow, the corresponding underwater boundary layer characteristic parameters are obtained to form an underwater boundary layer characteristic parameter database; the underwater boundary layer characteristic parameters include boundary layer velocity type and temperature type.

3. A method for solving the transitional turbulent flow field of an underwater vehicle containing a temperature gradient according to claim 2, characterized in that: In step 2.1, the incompressible similarity equations including the temperature equation are obtained by the following process: First, the tensor form of the control equation of the incompressible fluid in the underwater boundary layer containing the temperature gradient is established considering the temperature equation: in, For the The dimensioned coordinate components in the directions, Corresponding to the Cartesian coordinate system direction; Indicates that the fluid The dimensioned velocity components in each direction, Corresponding to the Cartesian coordinate system direction; For the The dimensioned coordinate components in the directions, Corresponding to the Cartesian coordinate system , , direction; Indicates that the fluid The dimensioned velocity components in each direction, Corresponding to the Cartesian coordinate system direction; is the dimensioned time, is the dimensionless fluid density, is the dimensionless fluid pressure, is the dimensionless dynamic viscosity coefficient, is the dimensionless fluid temperature, is the dimensionless specific heat of the fluid, is the dimensionless fluid thermal conductivity; Introduce Falkner-Skan transform: in is the transformed normal coordinate, is the dimensioned streamwise coordinate, is the dimensioned normal coordinate, is the norm of the dimensioned velocity at the edge of the boundary layer, is the dimensioned dynamic viscosity coefficient at the edge of the boundary layer, To set a constant; The incompressible similarity equations including the temperature equation are derived as follows: in is the dimensionless streamwise velocity, and its dimensionless form is , is the dimensioned streamwise velocity; and are newly introduced variables, defined as , , is the Hartree pressure gradient factor, is the Prandtl number; are intermediate parameters, respectively defined as in, is the dimensionless fluid heat transfer coefficient at the edge of the boundary layer, is the dimensioned temperature at the edge of the boundary layer.

4. The method for solving the transitional turbulent flow field of an underwater vehicle containing a temperature gradient according to claim 1, characterized in that: In step 2.2, for a certain flow condition, the corresponding transition momentum thickness Reynolds number is obtained: The process is: According to the turbulence of the incoming flow , using the Mack relation, we can get the critical N value corresponding to the transition; Using the critical N value, a linear stability analysis is performed on the boundary layer similarity solution under a given flow condition to obtain the transition momentum thickness Reynolds number under the corresponding flow condition. .

5. The method for solving the transitional turbulent flow field of an underwater vehicle containing a temperature gradient according to claim 3, characterized in that: In step 2.2, the transition momentum thickness Reynolds number obtained by fitting is The fitting relationship with the flow condition is: in is the shape factor, , , , All are intermediate variables; specifically: In the formula, is the dimensioned temperature at the edge of the boundary layer, is the dimensionless temperature at the wall, is the local Thwaites pressure gradient factor, is the dimensionless incoming flow temperature, is the dimensionless temperature difference between the wall and the incoming flow.

6. A method for solving the transitional turbulent flow field of an underwater vehicle containing a temperature gradient according to claim 5, characterized in that: For axisymmetric underwater vehicles, the following formula is used to correct the shape factor: in, is the shape factor after axisymmetry correction.

7. The method for solving the transitional turbulent flow field of an underwater vehicle including a temperature gradient according to claim 5, characterized in that: The underwater boundary layer transition prediction model considering the temperature gradient obtained in step 2.3 is: in, represents the intermittent factor, is the model constant; and They correspond to the generation source term and the destruction source term of the intermittent factor respectively: in is the modulus of the dimensionless velocity strain rate tensor, is the norm of the dimensionless vorticity, and are all setting coefficients, , , They are all model functions and have the following form: in, is the dimensionless turbulent dynamic viscosity coefficient; is the local Thwaites pressure gradient factor and the dimensionless incoming temperature and the dimensionless temperature difference between the wall and the incoming flow function; the transition momentum thickness Reynolds number Substitute the fitting relationship with the flow condition into In the calculation of the transition criterion, the transition model based on the intermittent factor transport equation is implemented.

8. A method for solving the transitional turbulent flow field of an underwater vehicle containing a temperature gradient according to claim 7, characterized in that: In step 2.3, the local Thwaites pressure gradient factor According to the formula The model of the dimensioned velocity at the edge of the boundary layer is Solve the Bernoulli equation locally using the incompressible form: in, is the dimensionless pressure of the incoming flow, is the dimensionless velocity modulus of the incoming flow, is the dimensioned pressure at the edge of the boundary layer.

9. A method for solving the transitional turbulent flow field of an underwater vehicle containing a temperature gradient according to claim 7, characterized in that: In step 2.4, the modified turbulent kinetic energy transport equation is: in is the dimensionless turbulent kinetic energy, is the model constant, and Generate and destroy source terms for the modified turbulent kinetic energy: , , and These are the generation source terms and destruction source terms of the turbulent kinetic energy transport equation in the original Menter SST turbulence model.

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