CN108763800B - Cavitation compressible flow shock wave dynamics numerical simulation method - Google Patents
Cavitation compressible flow shock wave dynamics numerical simulation method Download PDFInfo
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Abstract
The invention discloses a cavitation compressible flow shock wave dynamics numerical simulation method, and belongs to the field of cavitation compressible flow and shock wave dynamics numerical simulation. The method is characterized by establishing a three-dimensional calculation basin based on three-dimensional geometric modeling software; dividing a three-dimensional computational basin grid based on grid division software; establishing a cavitation compressible flow computational fluid mechanics model; setting an initial boundary condition to carry out numerical calculation of a three-dimensional calculation domain flow field; and post-processing the calculation result based on flow field post-processing software to obtain an unsteady evolution process of the multiphase vacuole structure. The invention is helpful for the deep research of cavitation physical mechanism, can be applied to the fields of cavitation compressible flow and shock wave dynamics numerical simulation and solves the related engineering problems. The fields of cavitation compressible flow and shock wave dynamics numerical simulation engineering application comprise application of hydraulic machinery, ship propellers, aviation turbine pump inducer and underwater supercavity weapons.
Description
Technical Field
The invention relates to a numerical simulation method for cavitation compressible flow shock wave dynamics research, and belongs to the field of cavitation compressible flow and shock wave dynamics numerical simulation.
Background
Cavitation occurs in a low-pressure area of high-speed water flow, is complex multiphase flow comprising violent interphase mass, momentum and energy exchange, phase change and turbulence, is an inevitable phenomenon in the work of hydraulic machinery, ship propellers, aircraft turbine pump inducer, underwater supercavity weapons and the like, and can induce violent pressure pulsation, vibration and noise. The deep understanding of the cavitation mechanism is the premise of effectively inhibiting unfavorable cavitation and avoiding cavitation damage in engineering, and has important scientific significance and engineering value. Cavitation is characterized by the generation, polymerization and collapse of steam cavities with different scales, has complex cavitation/cavitation cluster-turbulence structure interaction, is very difficult to accurately measure in experiments, and numerical simulation is an important means for cavitation research.
The cavitation flow is the compressible multiphase flow containing phase change with high compressibility, in the cavitation numerical simulation, the velocity, pressure and temperature between vapor and liquid phases are considered to be balanced and the vapor/liquid density is not changed usually based on the assumption of phase-to-phase balance and incompressible assumption, the incompressible cavitation numerical simulation method can predict the cavitation instability phenomena such as the growth of an attached cavity, the generation and propulsion of back jet, the cavity fracture and the falling process of cavitation, but can not accurately capture the phenomena related to cavitation compressibility, such as cavitation induced pressure pulsation, pressure pulse, cavity collapse phenomena, cavitation shock wave dynamics and the like, which relate to the cavitation transient load problem concerned in engineering practice, and experiments show that: the cavity fracture and shedding process has a back jet mechanism and a shock wave mechanism, the shock wave mechanism can cause more violent unsteady characteristics, and the shock wave mechanism is closely related to cavitation compressibility. On the other hand, a nonuniform unstable severe phase change process exists in the cavitation flow field, the coupling of phase change and compressibility enables the cavitation mechanism to be more complex, and the challenge to numerical calculation is larger. The cavitation flow has the characteristic of high density ratio of vapor-liquid phases, the difference of vapor-liquid compressibility is large, meanwhile, the sound velocity distribution of a cavitation flow field has the characteristic of large span, the cavitation area can reach more than 10 Mach numbers from 1450m/s in pure water to 3-5m/s in vapor-liquid mixed phase medium, and the introduction of fluid compressibility provides new challenges for capturing vapor-liquid free interfaces and the like. It is important and necessary to develop compressible cavitation flow.
OpenFOAM is used as large open source software, is a C + + class library based on a finite volume method, provides a platform for relevant scientific researchers to develop software, and carries out cavitation compressible flow numerical simulation research comprehensively considering liquid and steam compressibility based on OpenFOAM so as to realize accurate simulation of cavitation laser dynamics and have important guiding significance for deep understanding of cavitation mechanism and solving of practical problems concerned in the engineering field.
Disclosure of Invention
The invention discloses a cavitation compressible flow shock wave dynamics numerical simulation method, which aims to solve the technical problem of realizing cavitation compressible flow shock wave dynamics numerical simulation, is beneficial to deep research on a cavitation physical mechanism, can be applied to the field of cavitation compressible flow and shock wave dynamics numerical simulation, and solves the related engineering problems. The fields of cavitation compressible flow and shock wave dynamics numerical simulation engineering application comprise application of hydraulic machinery, ship propellers, aviation turbine pump inducer and underwater supercavity weapons.
The purpose of the invention is realized by the following technical scheme.
The invention discloses a cavitation compressible flow shock wave dynamics numerical simulation method, which is based on three-dimensional geometric modeling software to establish a three-dimensional calculation basin; dividing a three-dimensional computational basin grid based on grid division software; establishing a cavitation compressible flow computational fluid mechanics model; setting an initial boundary condition to carry out numerical calculation of a three-dimensional calculation domain flow field; and post-processing the calculation result based on flow field post-processing software to obtain an unsteady cavity evolution process of the multiphase cavity structure, wherein the unsteady cavity evolution process comprises the growth of an attachment type cavity, the generation and propulsion of back jet flow, the generation and propagation of cavity fracture and cavity shedding, the generation and propagation of shedding cavity collapse shock waves and the interaction between the shedding cavity collapse shock waves and the cavity, and the evolution of a cavitation turbulent structure in the unsteady process is analyzed to obtain the cavity collapse shock wave characteristics.
The cavitation compressible flow shock wave dynamics numerical simulation method disclosed by the invention is applied to the fields of cavitation compressible flow and shock wave dynamics numerical simulation, realizes the cavitation compressible flow shock wave dynamics numerical simulation, is favorable for deep research on a cavitation physical mechanism, and can solve related engineering problems.
The invention discloses a cavitation compressible flow shock wave dynamics numerical simulation method, which comprises the following steps:
the method comprises the following steps: establishing a three-dimensional calculation basin based on three-dimensional geometric modeling software;
for a given hydrofoil model, a three-dimensional calculation watershed is established based on the size of a test section based on three-dimensional geometric modeling software, the upstream inflow region from the inlet of the watershed to the front edge of the hydrofoil is a hydrofoil upstream inflow region, the downstream wake region from the tail edge of the hydrofoil to the outlet of the watershed is a hydrofoil downstream wake region, in order to ensure the uniform inflow and the full development of the wake, the upstream region is at least more than two times of the chord length of the hydrofoil, the downstream region is at least more than five times of the chord length of the hydrofoil, the span distance of the hydrofoil is the width of the test section, the hydrofoil is positioned at the center of the test section, and the height direction is the height of the test section.
The three-dimensional geometric modeling software in the first step comprises PRO/E, SolidWorks, CATIA and the like.
And step one, the lengths of the upstream area and the downstream area are comprehensively determined according to the calculation precision and the efficiency.
Step two: dividing a three-dimensional computational basin grid based on grid division software;
and (3) carrying out grid division on the three-dimensional calculation watershed in the step one, carrying out grid encryption on the periphery of the hydrofoil to capture more flow details, encrypting a selected area of a tail trace at the downstream of the hydrofoil, and accurately capturing falling cavity transportation, collapse and shock wave generation and propagation details through encrypting the selected area.
The flow details comprise accurate prediction of the collapse process of the cavitation clusters with different scales, and cavity-induced wall pressure pulsation, pressure pulse strength and pulse load positions.
The grid division software in the step two comprises ANSYS-ICEM, Pointwise, Hypermesh, snapHexMesh, GAMBIT and the like.
And step two, the length (l) of the selected area is determined according to the transportation path and the collapse position of the shedding cavitation cloud cluster, and the width (w) of the selected area is determined by a formula (1).
w＝5l·sinθ (1)
In the formula, θ is the hydrofoil angle of attack.
The encryption length (l) of the tail trace at the downstream of the hydrofoil is determined by the position of the cavity collapse shock wave, and the calculation precision and efficiency are comprehensively considered.
Step three: establishing a cavitation compressible flow computational fluid mechanics model;
and establishing a cavitation compressible flow computational fluid mechanics model which comprises a cavitation compressible flow control equation set, a physical model, a vapor/liquid phase thermodynamic state equation, a cavitation model and a turbulence model.
Step 3.1: and establishing a cavitation compressible flow control equation set according to the mass conservation, the momentum conservation and the energy conservation.
The cavitation compressible flow control equation comprises a continuity equation, a momentum equation, an energy equation and a phase gas-containing rate transport equation, which are respectively as follows:
in the formula, ρm,U,p,μm,e,K,κm,m+,m-,UrAnd t is medium density, velocity vector, pressure, dynamic viscosity, internal energy, kinetic energy, thermal conductivity, evaporation coefficient, condensation coefficient, relative velocity and time between phases, respectively. When c is going toαWhen the value is less than or equal to 1, Ur,f＝cα|φf|/|Sf|nf，
Is kinetic energy, αeff＝α1κ1/cv1+α2κ2/cv2,k1,k2,cv1And cv2Thermal conductivity, specific heat capacity of the liquid and vapor phases, respectively. The subscripts m, l, and v represent the miscible medium, I is the unit tensor, and σ is the surface tension.
Step 3.2: establishing a homogeneous medium multiphase flow model and a physical model for cavitation compressible flow numerical simulation.
Based on a homogeneous medium equilibrium model, phase pressure, velocity and temperature equilibrium, the thermodynamic state of a fluid is defined by the density and internal energy of the mixture, with thermodynamic parameters for water and water vapor as shown in table 1:
TABLE 1 fluid parameters in thermodynamic model
In order to consider the gas-liquid heat transfer function, the saturated steam pressure of the water steam is expressed by a saturated steam pressure-temperature relation function.
Region of pure liquid phase, p>pvThe internal energy of the ratio is expressed as
el＝cv,l(T-T0)+el,0 (6)
Wherein, cv,lIs the constant specific heat of water, and the reference temperature T0Lower internal energy is el,0The pressure in the pure water body is calculated by the Tatt Tait equation
The detailed parameters are shown in table 1, the temperature change in the water body is small in consideration of the high specific heat capacity property of the water body, and the saturated steam pressure in the Tatt Tait equation are set as fixed values at the ambient temperature.
Region of pure steam, p<pvInternal specific energy of
e＝cv,v(T-T0)+ev,0 (8)
In the formula, cv,vThe specific heat capacity of steam is. The pressure is obtained from the ideal gas equation of state
pv＝ρvRvTv (9)
Wherein R isvIs the gas constant.
In the vapor-liquid mixed phase region, p ═ pm＝pvThe pressure is equal to the saturated steam pressure, p ═ psat(T) internal energy of
e＝(αvcv,v+αlcv,l)(T-T0)+el,0 (10)
And calculating the distribution of the acoustic velocity of the cavitation vapor-liquid miscible medium along with the gas void ratio based on a Williams Wallis acoustic velocity formula without considering phase change and an acoustic velocity formula with considering phase change. Wherein the Williams Wallis velocity of sound is
The sound velocity containing phase change is:
in the formula, Cp,lIs the specific heat capacity of water,. lv,refIs the latent heat of vaporization.
Step 3.3: a cavitation compressible flow cavitation model based on the flat plate evaporation/condensation theory.
The method is characterized in that a cavitation compressible flow cavitation model based on a transport equation form is adopted, a cavitation source item is used for simulating the inter-phase mass exchange rate, the exchange rate comprises evaporation and condensation rates, the cavitation source item contains pressure p, density rho, gas content alpha and an empirical coefficient, and when the vapor/liquid phase compressibility is considered, the cavitation source item is changed relative to an incompressible source item, namely the compressibility influences the inter-phase mass exchange rate. In the calculation of cavitation compressible flow, a Saito cavitation model based on the flat plate evaporation/condensation theory is adopted, the model considers the temperature change of a medium, and the condensation rate and the evaporation rate are respectively
In the formula, CcIs the coefficient of coagulation, CeIs the evaporation coefficient.
Step 3.5: and establishing a cavitation compressible flow turbulence model based on scale self-adaptation.
The scale self-adaptive SAS turbulence model belongs to a turbulence model of coupled RANS-LES, has the advantages of being independent of local grid scale in conversion, can overcome the defects of a separation vortex turbulence model DES, has obvious advantages in consideration of the fact that cavitation flow is complex multi-phase flow with space-time multi-scale, and is based on the SST
In the formula (I), the compound is shown in the specification,
ζ2＝3.51,σ Ф2/3, C2, L is the length of the modelling turbulence
LvkIs von Karman length
Pk＝μtS，
κ＝0.41，
RANS calculation of turbulent viscosity μt eqIs composed of
Large vortex simulation calculation of turbulence viscosity
Comprises the following steps:
in the SST-SAS turbulence model, the turbulence viscosity μtTake a value of
Wherein, the large vortex simulated turbulence viscosity adopts an LES-WALE turbulence model to model the vortex viscosity coefficient.
And 3.5, the scale self-adaptive mesoscale is a von Karman scale.
Equations (2), (3), (4), (5), (13), (14), (15) and (16) constitute a cavitation compressible flow equation system.
Step 3.6: and solving a cavitation compressible flow control equation set.
Step 3.6.1: in order to solve the cavitation compressible flow field in the three-dimensional calculation domain in the first step and the second step, firstly, initializing the speed, the temperature, the pressure and the liquid volume fraction, and solving a phase fraction transport equation (5) and cavitation model source terms (13) and (14);
step 3.6.2: solving a momentum prediction equation (3);
step 3.6.3: solving a temperature transport equation (4);
step 3.6.4: solving a compressible pressure equation (3) and carrying out pressure correction;
step 3.6.5: solving turbulence equations (15) and (16);
step 3.6.6: judging whether the calculation time is reached, finishing the calculation and realizing the establishment of a compressible computational fluid mechanics model; or to proceed to the next calculation.
Step four: setting an initial boundary condition to carry out numerical calculation of a three-dimensional calculation domain flow field;
in a solver, according to test working conditions, the incoming flow speed at an inlet of a three-dimensional basin, the pressure at an outlet of the three-dimensional basin, the surface of a hydrofoil model in the three-dimensional computing basin, the upper boundary, the lower boundary, the front boundary and the rear boundary of the three-dimensional computing basin are non-slip wall surface boundary conditions, and meanwhile, the pressure of an inlet and an outlet adopts a non-reflection pressure condition to avoid the reflection of shock waves at the inlet and the outlet; and solving the three-dimensional calculation basin cavitation compressible flow field in the first step and the second step, and performing numerical calculation of the flow field by using a cavitation compressible flow solver to obtain a numerical calculation result of the three-dimensional basin.
Step five: and post-processing the calculation result based on flow field post-processing software to obtain an unsteady cavity evolution process of the multi-phase cavity structure, wherein the unsteady cavity evolution process comprises the growth of an attachment type cavity, the generation and propulsion of back jet flow, the breakage of the cavity, the falling of the cavity, the generation and propagation of falling cavity collapse shock waves and the interaction between the falling cavity collapse shock waves and the cavity, and the evolution of a cavitation turbulent structure in the unsteady process is analyzed to obtain the cavity collapse shock wave characteristics.
Further comprises the following steps: the method described in the first step to the fifth step is applied to the field of cavitation compressible flow and shock wave dynamics numerical simulation, so that the cavitation compressible flow shock wave dynamics numerical simulation is realized, the deep research on a cavitation physical mechanism is facilitated, and the related engineering problems can be solved.
And sixthly, applying the cavitation compressible flow and shock wave dynamics numerical simulation engineering to the fields of hydraulic machinery, ship propellers, aviation turbine pump inducer and underwater supercavity weapons.
When the method in the first step to the fifth step is applied to cavitation numerical simulation of the inducer or the hydraulic machine, the influence of cavity collapse on the performance of the actual inducer, the hydraulic machine and the like is obtained, and a basis is provided for avoiding cavitation damage in actual application.
And fifthly, the flow field Post-processing software comprises Paraview, Tecplot, ANSYS-Post and the like.
Has the advantages that:
1. according to the cavitation compressible flow shock wave dynamics numerical simulation method, the compressibility of a vapor phase and compressibility of a liquid phase in a cavitation flow field are comprehensively considered through a water phase Tait equation and a vapor phase ideal gas state equation, a more complete physical model for cavitation compressible flow numerical simulation is established, and further cavitation simulation accuracy is improved.
2. According to the cavitation compressible flow shock wave dynamics numerical simulation method, the selected area of the tail trace at the downstream of the hydrofoil is encrypted in the second step, so that the accurate simulation of the collapse process of the large-scale falling cavity structure can be realized, and particularly the accurate simulation of the cavity collapse shock wave dynamics process can be realized.
3. According to the numerical simulation method for cavitation compressible flow shock wave dynamics, the selected areas around the hydrofoil and the downstream wake are encrypted in the second step, and the water phase Tait equation and the steam phase ideal gas state equation in the third step are adopted, so that the simulation of the cavitation flow wave dynamics can be realized, more importantly, the collapse pressure pulsation, the pressure pulse intensity and the position of cavitation clusters with different scales can be accurately predicted, the information of cavitation load is provided for the operation of an inducer and a hydraulic machine, and the basis is provided for the optimization design of the cavitation load.
4. The cavitation compressible flow shock wave dynamics numerical simulation method is applied to the fields of cavitation compressible flow and shock wave dynamics numerical simulation, realizes cavitation compressible flow shock wave dynamics numerical simulation, is favorable for deep research on cavitation physical mechanism, and can solve related engineering problems.
Drawings
FIG. 1 is a flow chart of a cavitation compressible flow shock dynamics numerical simulation method of the present invention;
FIG. 2 is a cross-sectional dimension of a hydrofoil model of a cavitation compressible flow shock wave dynamics numerical simulation method of the present invention;
FIG. 3 is a diagram of air vapor liquid medium thermodynamic state p-v of a cavitation compressible flow shock wave dynamics numerical simulation method of the present invention;
FIG. 4 is a cavitation medium sound velocity distribution of a cavitation compressible flow shock wave dynamics numerical simulation method of the present invention;
FIG. 5 is a flow chart of solving a control equation of a numerical simulation method of cavitation compressible flow shock wave dynamics;
FIG. 6 is the shock wave and cavity interaction process predicted by the cavitation compressible flow shock wave dynamics numerical simulation method of the present invention, wherein: FIG. 6a is t0The shock wave is generated at the moment, t is shown in FIG. 6b0The location of the propagation of the shock wave at time +2ms, t in FIG. 6c0The location of the propagation of the shock wave at time +4ms, t in FIG. 6d0The location of the propagation of the shock wave at time +6ms, t in FIG. 6e0The location of the propagation of the shock wave at time +8ms, t in FIG. 6f0The +10ms instant shock propagation position.
Detailed Description
For a better understanding of the objects and advantages of the present invention, reference should be made to the following detailed description taken in conjunction with the accompanying drawings and examples.
Example 1:
as shown in fig. 1, the method for simulating dynamics of cavitation compressible flow shock wave disclosed in this embodiment includes the following steps:
the method comprises the following steps: establishing a three-dimensional calculation basin based on three-dimensional geometric modeling software;
for a given hydrofoil model, a three-dimensional calculation watershed is established for the size of a test section based on three-dimensional geometric modeling software, the upstream inflow region from the inlet of the watershed to the front edge of the hydrofoil is a hydrofoil upstream inflow region, the downstream wake region from the tail edge of the hydrofoil to the outlet of the watershed is a hydrofoil downstream wake region, in order to ensure the uniform inflow and the full development of the wake and the calculation efficiency, the upstream region is two times of the chord length of the hydrofoil, the downstream region is five times of the chord length of the hydrofoil, the span distance of the hydrofoil is the width of the test section, the hydrofoil is positioned in the center of the test section, and the height direction is the height of the test section.
Step two: dividing a three-dimensional computational basin grid based on grid division software;
and D, performing grid division on the three-dimensional calculation watershed in the step I by using ANASYS-ICEM, performing grid encryption on the periphery of the hydrofoil to capture more flow details, encrypting a hydrofoil downstream trail area with the length being one time of the length of the hydrofoil, and accurately capturing falling cavity transportation and collapse and shock wave generation and propagation details by encrypting the selected area.
Step three: establishing a cavitation compressible flow computational fluid mechanics model;
and establishing a cavitation compressible flow computational fluid mechanics model which comprises a cavitation compressible flow control equation, a physical model, a vapor/liquid phase thermodynamic state equation, a cavitation model and a turbulence model.
Step 3.1: and establishing a cavitation compressible flow control equation set according to the mass conservation, the momentum conservation and the energy conservation.
The cavitation compressible flow control equation set comprises a continuity equation, a momentum equation, an energy equation and a phase gas void transport equation, which are respectively as follows:
in the formula, ρm,U,p,μm,e,K,κm,m+,m-,UrAnd t is medium density, velocity vector, pressure, dynamic viscosity, internal energy, kinetic energy, thermal conductivity, evaporation coefficient, condensation coefficient, relative velocity and time between phases, respectively. When c is going toαWhen the value is less than or equal to 1, Ur,f＝cα|φf|/|Sf|nf，
Is kinetic energy, αeff＝α1κ1/cv1+α2κ2/cv2,k1,k2,cv1And cv2Thermal conductivity, specific heat, of the liquid and vapor phases, respectively. The subscripts m, l, and v represent the miscible medium, I is the unit tensor, and σ is the surface tension.
Step 3.2: establishing a homogeneous medium multiphase flow model and a physical model for cavitation compressible flow numerical simulation.
Based on a homogeneous medium equilibrium model, phase pressure, velocity and temperature equilibrium, the thermodynamic state of a fluid is defined by the density and internal energy of the mixture, with thermodynamic parameters for water and water vapor as shown in table 1:
TABLE 1 fluid parameters in thermodynamic model
The saturated vapor pressure of water vapor is related to temperature by:
in the formula, the coefficient a1＝-7.85823,a2＝1.83991,a3＝-11.78110,a4＝22.67050,a5＝-15.93930,a6＝1.77516,l1＝1,l2＝1.5,l3＝3.0,l4＝4.0,l5＝4.0and l61.77516 according to the International Association for the Properties of Water and Steam (IAPWS)Obtained by fitting and obtained by taking the dimensionless temperature theta as 1-T/TcAnd (4) showing.
Region of pure liquid phase, p>pvThe internal energy of the ratio is expressed as
el＝cv,l(T-T0)+el,0 (6)
Wherein the specific heat of constant volume of water is cv,l＝4180.0J kg-1K-1Reference temperature T0The internal energy is e under 273.15Kl,0＝617J kg-1The pressure in the pure water body is calculated by the Tatt Tait equation
The detailed parameters are shown in table 1, the temperature change in the water body is small in consideration of the high specific heat capacity property of the water body, and the saturated steam pressure in the Tatt Tait equation are set as fixed values at the ambient temperature.
Region of pure steam, p<pvInternal specific energy of
e＝cv,v(T-T0)+ev,0 (8)
In the formula, cv,vThe specific heat capacity of steam is. The pressure is obtained from the ideal gas equation of state
pv＝ρvRvTv (9)
Wherein the specific heat capacity of steam is cv,v＝1410.8J kg-1 K-1. The pressure is obtained from the ideal gas equation of state
In the vapor-liquid mixed phase region, p ═ pm＝pvThe pressure is equal to the saturated steam pressure, p ═ psat(T), the thermodynamic state of vapor-liquid mixed phase in cavitation medium is shown in figure 3, and the specific internal energy is
e＝(αvcv,v+αlcv,l)(T-T0)+el,0 (10)
The distribution of the acoustic velocity of the cavitation vapor-liquid miscible medium along with the gas void ratio is calculated based on a Williams Wallis acoustic velocity formula without considering the phase change and an acoustic velocity formula with considering the phase change, as shown in figure 4. Wherein the Williams Wallis velocity of sound is
The sound velocity containing phase change is:
in the formula, Cp,l＝4184.4J kg-1K-1Latent heat of vaporization ofv,ref＝2453.5×103J kg-1。
Step 3.3: a cavitation compressible flow cavitation model based on the flat plate evaporation/condensation theory.
A compressible flow cavitation model based on a transport equation form is adopted, a cavitation source item is used for simulating an interphase mass exchange rate, the exchange rate comprises an evaporation rate and a condensation rate, the cavitation source item contains pressure p, density rho, a gas content rate alpha and an empirical coefficient, and when vapor/liquid phase compressibility is considered, the cavitation source item is changed relative to an incompressible source item, namely the compressibility influences the interphase mass exchange rate. In the calculation of cavitation compressible flow, a Saito cavitation model based on the flat plate evaporation/condensation theory is adopted, the model considers the temperature change of a medium, and the condensation rate and the evaporation rate are respectively
In the formula, CcIs the coefficient of coagulation, CeIs the evaporation coefficient, under normal conditions, Cc＝Ce＝0.1。
Step 3.5: and establishing a cavitation compressible flow turbulence model based on scale self-adaptation.
The scale self-adaptive SAS turbulence model belongs to a turbulence model of coupled RANS-LES, has the advantages of being independent of local grid scale in conversion, can overcome the defects of a separation vortex turbulence model DES, has obvious advantages in consideration of the fact that cavitation flow is complex multi-phase flow with space-time multi-scale, and is based on the SST
In the formula (I), the compound is shown in the specification,
ζ2＝3.51,σ Ф2/3, C2, L is the length of the modelling turbulence
LvkIs von Karman length
Pk＝μtS，
κ＝0.41，
RANS calculation of turbulent viscosity
Is composed of
Large vortex simulation calculation of turbulence viscosity
Comprises the following steps:
in the SST-SAS turbulence model, the turbulence viscosity μtTake a value of
Wherein, the large vortex simulated turbulence viscosity adopts an LES-WALE turbulence model to model the vortex viscosity coefficient.
And 3.5, the scale self-adaptive mesoscale is a von Karman scale.
Equations (2), (3), (4), (5), (13), (14), (15) and (16) constitute a cavitation compressible flow equation system.
Step 3.6: and solving a cavitation compressible flow control equation set.
Step 3.6.1: in order to solve the cavitation compressible flow field in the three-dimensional calculation domain in the first step and the second step, firstly, initializing the speed, the temperature, the pressure and the liquid volume fraction, and solving a phase fraction transport equation (5) and cavitation model source terms (13) and (14);
step 3.6.2: solving a momentum prediction equation (3);
step 3.6.3: solving a temperature transport equation (4);
step 3.6.4: solving a compressible pressure equation (3) and carrying out pressure correction;
step 3.6.5: solving turbulence equations (15) and (16);
step 3.6.6: judging whether the calculation time is reached, finishing the calculation and finishing the calculation of cavitation compressible flow; or to proceed to the next calculation.
Step four: setting an initial boundary condition to carry out numerical calculation of a three-dimensional calculation domain flow field;
in a solver, the incoming flow speed at the inlet of the three-dimensional basin, the pressure at the outlet of the three-dimensional basin, the surface of a hydrofoil model in the three-dimensional calculation basin, the upper boundary, the lower boundary, the front boundary and the rear boundary of the three-dimensional calculation basin are set to be non-slip wall surface boundary conditions, and the pressure of the inlet and the pressure of the outlet adopt a non-reflection pressure condition to avoid the reflection of shock waves at the inlet and the outlet. And (4) performing numerical calculation of the flow field by using a cavitation compressible flow solver to obtain a numerical calculation result of the three-dimensional flow field.
Step five: and post-processing the calculation result based on Paraview post-processing software to obtain an unsteady cavity evolution process of the multiphase cavity structure, wherein the unsteady cavity evolution process comprises the growth of an attachment cavity, the generation and propulsion of a back jet, the breakage of the cavity, the falling of the cavity, the generation and propagation of a falling cavity collapse shock wave and the interaction between the falling cavity collapse shock wave and the cavity, and the evolution of the cavitation turbulent structure in the unsteady process is analyzed to obtain the characteristics of the cavity collapse shock wave. The interaction process of the shock wave and the cavity is shown in figure 6.
Step six: the method described in the first step to the fifth step is applied to the field of cavitation compressible flow and shock wave dynamics numerical simulation, so that the cavitation compressible flow shock wave dynamics numerical simulation is realized, the deep research on a cavitation physical mechanism is facilitated, and the related engineering problems can be solved.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (6)
1. A cavitation compressible flow shock wave dynamics numerical simulation method is characterized in that: comprises the following steps of (a) carrying out,
the method comprises the following steps: establishing a three-dimensional calculation basin based on three-dimensional geometric modeling software;
for a given hydrofoil model, establishing a three-dimensional calculation watershed based on a test section size based on three-dimensional geometric modeling software, wherein the watershed inlet to the hydrofoil front edge is an upstream inflow region of the hydrofoil, the hydrofoil tail edge to the watershed outlet is a downstream wake region of the hydrofoil, in order to ensure the uniform inflow and the full development of the wake, the upstream region is at least more than two times of the chord length of the hydrofoil, the downstream region is at least more than five times of the chord length of the hydrofoil, the span distance of the hydrofoil is the test section width, the hydrofoil is positioned at the center of the test section, and the height direction is the test section height;
step two: dividing a three-dimensional computational basin grid based on grid division software;
carrying out grid division on the three-dimensional calculation watershed in the step one, carrying out grid encryption on the periphery of the hydrofoil to capture more flow details, encrypting a selected area of a tail trace at the downstream of the hydrofoil, and accurately capturing falling cavity transportation, collapse and shock wave generation and propagation through encrypting the selected area;
the flow details comprise the steps of accurately predicting the falling and collapse processes of cavitation clusters with different scales, and the pressure pulsation, the pressure pulse strength and the pulse load position of the cavity-induced wall surface;
step three: establishing a cavitation compressible flow computational fluid mechanics model;
establishing a cavitation compressible flow computational fluid mechanics model, which comprises a cavitation compressible flow control equation set, a physical model, a vapor/liquid phase thermodynamic state equation, a cavitation model and a turbulence model;
step four: setting an initial boundary condition to carry out numerical calculation of a three-dimensional calculation domain flow field;
in a solver, according to test working conditions, the incoming flow speed at an inlet of a three-dimensional basin, the pressure at an outlet of the three-dimensional basin, the surface of a hydrofoil model in the three-dimensional computing basin, the upper boundary, the lower boundary, the front boundary and the rear boundary of the three-dimensional computing basin are non-slip wall surface boundary conditions, and meanwhile, the pressure of an inlet and an outlet adopts a non-reflection pressure condition to avoid the reflection of shock waves at the inlet and the outlet; solving the three-dimensional calculation basin cavitation compressible flow field in the first step and the second step, and performing numerical calculation of the flow field by using a compressible cavitation solver to obtain a numerical calculation result of the three-dimensional basin;
step five: and post-processing the calculation result based on flow field post-processing software to obtain an unsteady cavity evolution process of the multiphase cavity structure, wherein the unsteady cavity evolution process comprises the growth of an attachment type cavity, the generation and propulsion of back jet flow, the generation and propagation of cavity fracture and cavity shedding, the generation and propagation of shedding cavity collapse shock waves and the interaction between the shedding cavity collapse shock waves and the cavity, and the evolution of a cavitation turbulent structure in the unsteady process is analyzed to obtain the cavity collapse shock wave characteristics.
2. A cavitation compressible flow shock dynamics numerical simulation method as claimed in claim 1 wherein: and step six, the method in the step one to the step five is applied to the field of cavitation compressible flow and shock wave dynamics numerical simulation, so that the cavitation compressible flow shock wave dynamics numerical simulation is realized, the deep research on a cavitation physical mechanism is facilitated, and the related engineering problems can be solved.
3. A cavitation compressible flow shock dynamics numerical simulation method as claimed in claim 1 or 2 wherein: the concrete realization method of the third step is as follows,
step 3.1: establishing a cavitation compressible flow control equation set according to mass conservation, momentum conservation and energy conservation;
the cavitation compressible flow control equation set comprises a continuity equation, a momentum equation, an energy equation and a phase gas void transport equation, which are respectively as follows:
in the formula, ρm,U,p,μm,e,K,κm,m+,m-,UrAnd t is medium density, velocity vector, pressure, dynamic viscosity, internal energy, kinetic energy, thermal conductivity, evaporation coefficient, condensation coefficient, relative velocity and time between phases, respectively; when c is going toαWhen the value is less than or equal to 1, Ur,f＝cα|φf|/|Sf|nf，
Is kinetic energy, αeff＝α1κ1/cv1+α2κ2/cv2,k1,k2,cv1And cv2Thermal conductivity, specific heat of the liquid and vapor phases, respectively; subscripts m, l, and v represent the miscible medium, I is the unit tensor, and σ is the surface tension;
step 3.2: establishing a homogeneous medium multiphase flow model and a physical model for cavitation compressible flow numerical simulation;
based on a homogeneous medium equilibrium model, phase pressure, velocity and temperature equilibrium, the thermodynamic state of a fluid is defined by the density and internal energy of the mixture, with thermodynamic parameters for water and water vapor as shown in table 1:
TABLE 1 fluid parameters in the thermodynamic model
In order to consider the gas-liquid heat transfer function, the saturated steam pressure of the water steam is expressed by a saturated steam pressure-temperature relation function;
region of pure liquid phase, p>pvThe internal energy of the ratio is expressed as
el＝cv,l(T-T0)+el,0 (6)
Wherein, cv,lIs the specific heat of water with constant volumeReference temperature T0Lower internal energy is el,0The pressure in the pure water body is calculated by the Tatt Tait equation
The detailed parameters are shown in a table 1, the temperature change in the water body is very small in consideration of the high specific heat capacity property of the water body, and saturated steam pressure in a Tatt Tait equation are set as constant values at ambient temperature;
region of pure steam, p<pvInternal specific energy of
e＝cv,v(T-T0)+ev,0 (8)
In the formula, cv,vThe specific heat capacity of the steam is; the pressure is obtained from the ideal gas equation of state
pv＝ρvRvTv (9)
Wherein R isvIs the gas constant;
in the vapor-liquid mixed phase region, p ═ pm＝pvThe pressure is equal to the saturated steam pressure, p ═ psat(T) internal energy of
e＝(αvcv,v+αlcv,l)(T-T0)+el,0 (10)
Calculating to obtain the distribution of the acoustic velocity of the cavitation vapor-liquid miscible medium along with the gas void ratio based on a Williams Wallis acoustic velocity formula without considering phase change and an acoustic velocity formula with considering phase change; wherein the Williams Wallis velocity of sound is
The sound velocity containing phase change is:
in the formula (I), the compound is shown in the specification,Cp,lis the specific heat capacity of water,. lv,refIs the latent heat of vaporization;
step 3.3: a cavitation compressible flow cavitation model based on a flat plate evaporation/condensation theory;
adopting a cavitation compressible flow cavitation model based on a transport equation form, wherein a cavitation source term is used for simulating an interphase mass exchange rate, the exchange rate comprises an evaporation rate and a condensation rate, the cavitation source term contains pressure p, density rho, gas content alpha and an empirical coefficient, and when the vapor/liquid phase compressibility is considered, the cavitation source term is changed relative to an incompressible source term, namely the compressibility influences the interphase mass exchange rate; in the calculation of cavitation compressible flow, a Saito cavitation model based on the flat plate evaporation/condensation theory is adopted, the model considers the temperature change of a medium, and the condensation rate and the evaporation rate are respectively
When p is>pvHour (13)
In the formula, CcIs the coefficient of coagulation, CeIs the evaporation coefficient;
step 3.5: establishing a cavitation compressible flow turbulence model based on scale self-adaptation;
the scale self-adaptive SAS turbulence model belongs to a turbulence model of coupled RANS-LES, has the advantages of being independent of local grid scale in conversion, can overcome the defects of a separation vortex turbulence model DES, has obvious advantages in consideration of the fact that cavitation flow is complex multi-phase flow with space-time multi-scale, and is based on the SST
In the formula (I), the compound is shown in the specification,
ζ2＝3.51,σФ2/3, C2, L is the length of the modelling turbulence
LvkIs von Karman length
Pk＝μtS，
κ＝0.41，
RANS calculation of turbulent viscosity μt eqIs composed of
Large vortex simulation calculation of turbulence viscosity
Comprises the following steps:
in the SST-SAS turbulence model, the turbulence viscosity μtTake a value of
Wherein, the large vortex simulated turbulence viscosity adopts an LES-WALE turbulence model to model a vortex viscosity coefficient;
3.5, the scale self-adaptive mesoscale is a von Karman scale;
the equations (2), (3), (4), (5), (13), (14), (15) and (16) form a cavitation compressible flow control equation set;
step 3.6: and C, calculating the compressible flow field in the three-dimensional calculation flow field in the step one and the step two, and solving a cavitation compressible flow equation set.
4. A cavitation compressible flow shock dynamics numerical simulation method as claimed in claim 3 wherein: the specific implementation method of step 3.6 is as follows,
step 3.6.1: initializing speed, temperature, pressure and liquid volume fraction, and solving phase fraction transport equation
And cavitation model source term
When p is>pvWhen (13) and
when p is<pvTime (14);
step 3.6.2: solving momentum prediction equations
Step 3.6.3: solving a temperature transport equation
Step 3.6.4: solving compressible pressure equations
Carrying out pressure correction;
step 3.6.5: solving turbulence equations
And
step 3.6.6: judging whether the calculation time is reached, finishing the calculation and realizing the establishment of a compressible computational fluid mechanics model; or to proceed to the next calculation.
5. A cavitation compressible flow shock dynamics numerical simulation method as claimed in claim 3 wherein: the three-dimensional geometric modeling software of the step one is PRO/E, SolidWorks or CATIA;
and step one, the lengths of the upstream area and the downstream area are comprehensively determined according to the calculation precision and the efficiency.
6. A cavitation compressible flow shock dynamics numerical simulation method as claimed in claim 3 wherein: the grid division software in the step two is ANSYS-ICEM, Pointwise, Hypermesh, snap HexMesh or GAMBIT;
secondly, determining the length (l) of the selected area according to a transportation path and a collapse position of the falling cavitation cloud cluster, wherein the width (w) of the selected area is determined by a formula (1);
w＝5l·sinθ (1)
in the formula, theta is the attack angle of the hydrofoil;
the encryption length (I) of the wake downstream of the hydrofoil is determined by the position of the cavity collapse shock wave, and the calculation precision and efficiency are comprehensively considered.
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