CN102141464A - Construction method for establishing turbulence model with Reynolds time-mean method - Google Patents

Abstract

The invention aims to disclose a construction method for establishing a turbulence model with a Reynolds time-mean method. Through whole flow passage three-dimensional turbulence calculation based on a k-epsilon double equation turbulence model, corresponding flowing details are obtained, and flowing in each flow passage component can be qualitatively understood; the energy and the cavitation performance of an axial flow pump are quantitatively predicted according to a calculation result, and mechanisms of important hydraulic characteristics of hydraulic machinery cavitation, hydraulic vibration and the like are revealed, thereby theoretical and technical bases are supplied for researching and developing a water pump or a hydraulic turbine with high performance, large flow and high water head, and the purposes of the invention are reached.

Description

Equal method is set up the construction method of turbulence model during a kind of Reynolds

Technical field

The present invention relates to a kind of construction method, be particularly related to a kind of in order to study the hydraulic operation characteristic, computational fluid dynamics (CFD) theory is applied to the hydraulic turbulent flow analysis with method, and equal method is set up the construction method that turbulence model is estimated hydraulic energy response and Cavitation Characteristics during by Reynolds.

Background technology

Along with the construction of the south water to north and Three Gorges hydraulic engineering, water pump, the hydraulic turbine are as crucial Hydromotive machine apparatus, and its capacity and size are in continuous increase.From the large pumping station of having gone into operation and the ruuning situation in power station, problems such as the vibration of large-scale unit ubiquity, cavitation, (efficient) deficiency of exerting oneself.Vibration and characteristic such as cavitation are direct relevant with the water pressure fluctuation of flow passage components, and the key that addresses these problems is effectively to grasp and control the flow field of corresponding flow passage components.

Observation shows, the hydraulic internal flow is in turbulence state as a rule, the flow field is formed by stacking by the turbulence vortex of various different scales, these turbulence vortex have rotational structure, the size of turbulence vortex and the distribution of the direction of turning axle are at random, because the complicacy of turbulent flow, be difficult to grasp the turbulence state of hydraulic inside by test, and computational fluid dynamics (CFD) theory and method, be familiar with the hydraulic turbulent flow to us a kind of new approach is provided, to disclosing the complex relationship between hydraulic flow field flow characteristics and structural dynamic characteristic, has potential advantage.

Flowing in the hydraulic can be thought to press, time-dependent Three dimensional Turbulent Flow, because turbulent flow has the height pulsating nature on the microscale, be used to describe instantaneous Navier-Stokes equation non-linear of turbulent flow in addition, and the diversity of hydraulic boundary condition, make equation not have analytic solution, even can not describe the relevant whole details that flow of three-dimensional time with direct Numerical (DNS) method.

Summary of the invention

Equal method is set up the construction method of turbulence model when the object of the present invention is to provide a kind of Reynolds, solve existing the problems referred to above that exist, equal method is to turbulent flow pulsation in addition " simplifications ", the turbulence model that structure adds on instantaneous Navier-Stokes equations based when adopting Reynolds.

Technical matters solved by the invention can realize by the following technical solutions:

Equal method is set up the construction method of turbulence model during a kind of Reynolds, it is characterized in that it comprises the steps:

Equal method is regarded the transient motion of turbulent flow by pairing two of mean value and pulsating quantity as and is flowed and are formed by stacking when (1) adopting Reynolds, the time all be that under the absolute frame of rectangular coordinate form, the governing equation of setting up instantaneous flow state is down:

$\frac{\∂}{\∂t}\left(\mathrm{\ρ}{u}_i\right)+\frac{\∂}{\∂x_j}\left({\mathrm{\ρu}}_i{u}_j\right)=-\frac{\∂p}{\∂x_i}+\frac{\∂}{{\∂x}_j}(\mathrm{\μ}\frac{{\∂u}_i}{\∂x_j}-\mathrm{\ρ}\stackrel{\‾}{{u_i}^{\′}{u_j}^{\′}})+S_i$

(2) introduce the sticking coefficient μ in whirlpool _t, by the sticking coefficient μ in whirlpool _tSet up the relation of Reynolds stress and average velocity gradient:

$-\mathrm{\ρ}\stackrel{\‾}{{u_i}^{\′}{u_j}^{\′}}={\mathrm{\μ}}_t(\frac{{\∂u}_i}{\∂x_j}+\frac{\∂u_i}{\∂x_j})-\frac{2}{3}(\mathrm{\ρk}+{\mathrm{\μ}}_t\frac{\∂u_i}{\∂x_j}){\mathrm{\δ}}_{\mathrm{ij}}$

In the formula, μ _tBe the sticking coefficient in whirlpool, u _iBe time averaged velocity, δ _IjBe " Kronecker delta " symbol, k is a tubulence energy;

(3) according to determining the sticking coefficient μ in whirlpool _tDifferential equation number, standard k-ε model has been proposed; In standard k-ε model, tubulence energy k and dissipative shock wave ε are two fundamental unknown variables, and corresponding transport equation is:

$\frac{\∂\left(\mathrm{\ρk}\right)}{\∂t}+\frac{\∂\left(\mathrm{\ρ}{\mathrm{ku}}_i\right)}{\∂x_i}=\frac{\∂}{\∂x_j}\left[(\mathrm{\μ}+\frac{{\mathrm{\μ}}_t}{{\mathrm{\σ}}_k})\frac{\∂k}{\∂x_j}\right]+G_k+G_b-\mathrm{\ρ\ϵ}-Y_M+S_k$

$\frac{\∂\left(\mathrm{\ρ\ϵ}\right)}{\∂t}+\frac{\∂\left({\mathrm{\ρ\ϵu}}_i\right)}{{\∂x}_i}=\frac{\∂}{\∂x_j}\left[(\mathrm{\μ}+\frac{{\mathrm{\μ}}_t}{{\mathrm{\σ}}_{\mathrm{\ϵ}}})\frac{\∂\mathrm{\ϵ}}{\∂x_j}\right]+C_{1\mathrm{\ϵ}}\frac{\mathrm{\ϵ}}{k}(G_k+C_{3\mathrm{\ϵ}}{G}_b)-C_{2\mathrm{\ϵ}}\mathrm{\ρ}\frac{{\mathrm{\ϵ}}^2}{k}+S_{\mathrm{\ϵ}}$

Wherein, G _kBe the generation item of the tubulence energy k that causes by average velocity gradient, G _bBe the generation item of the tubulence energy k that causes by buoyancy, Y _MRepresentative can be pressed the contribution of pulsation expansion in the turbulent flow, C _{1 ε}, C _{2 ε}And C _{3 ε}Be empirical constant, σ _kAnd σ _εBe respectively the Prandtl number corresponding with tubulence energy k and dissipative shock wave ε, S _kAnd S _εIt is user-defined source item;

(4) step (1) (2) (3) equation being dispersed is algebraic equation, sets up discrete equation, has

$\left(\frac{a_P}{a}\right){\mathrm{\φ}}_P=\underset{\mathrm{nb}}{\mathrm{\Σ}}{a}_{\mathrm{nb}}{\mathrm{\φ}}_{\mathrm{nb}}+b+(1-a)\frac{a_P}{a}{\mathrm{\φ}}_P^o$

In the formula, φ _NbBe φ _pAdjoint point speed, a _PAnd a _NbBe coefficient, φ _P ^oSeparate for last layer takes second place, a is a relaxation factor,

Be the algebraic equation source item, b is the constant component in the source item;

(5) adopt the separate type solution, sequentially, one by one find the solution each variable Algebraic Equation set in the discrete equation;

(6) whether check result restrains.If do not restrain, as new conjecture, repeat this process with the result that obtains.

In one embodiment of the invention, before calculating, at first will be with the zoning discretize, promptly on volume coordinate and time coordinate, continuous zoning is split into many grid cells, then, on grid cell, be algebraic equation with governing equation and turbulent flow additional equation are discrete.

In one embodiment of the invention, described separate type solution is divided into original variable method and non-original variable method.

In one embodiment of the invention, described original variable method is meant at first uses the pressure field of a conjecture to separate the equation of momentum, obtains velocity field; Then find the solution the pressure correction equation of setting up by continuity equation, obtain the modified value of pressure field; Utilize pressure correction value renewal speed field and pressure field then; Whether last check result restrains.If do not restrain,, repeat this process with the pressure field that obtains pressure field as new conjecture.

In one embodiment of the invention, by after calculating the velocity field and pressure field distribution under a certain operating mode of hydraulic, can estimate the energy and the Cavitation Characteristics of hydraulic by mathematical procedure.

Equal method is set up the construction method of turbulence model during Reynolds of the present invention, by calculating based on the three-dimensional permanent turbulent flow of the full runner of k-ε both sides journey turbulence model, obtain the corresponding details that flows, can understanding qualitatively be arranged to mobile in each flow passage components, according to result of calculation energy, the cavitation performance of axial flow pump have been done quantitative estimating, disclosed the mechanism of important hydraulic performances such as hydraulic machinery cavitation and hydraulic vibration, thereby, realize purpose of the present invention for research and development high-performance, big flow, high water head water pump or water turbine equipment provide the theory and technology foundation.

Characteristics of the present invention can be consulted the detailed description of the graphic and following better embodiment of this case and be obtained to be well understood to.

Description of drawings

Fig. 1 during for Reynolds of the present invention equal method set up the schematic flow sheet of the construction method of turbulence model;

Fig. 2 is the synoptic diagram of design conditions lower blade surface pressure distribution;

Fig. 3 is the curve synoptic diagram of pump head and efficient under the design conditions.

Embodiment

For technological means, creation characteristic that the present invention is realized, reach purpose and effect is easy to understand, below in conjunction with concrete diagram, further set forth the present invention.

Embodiment

As shown in Figure 1, equal method is set up the construction method of turbulence model during Reynolds of the present invention, and it comprises the steps:

Equal method is regarded the transient motion of turbulent flow by pairing two of mean value and pulsating quantity as and is flowed and are formed by stacking when (1) adopting Reynolds, the time all be that under the absolute frame of rectangular coordinate form, the governing equation of setting up instantaneous flow state is down:

$\frac{\∂}{\∂t}\left({\mathrm{\ρu}}_i\right)+\frac{\∂}{\∂x_j}\left(\mathrm{\ρ}{u}_i{u}_j\right)=-\frac{\∂p}{\∂x_i}+\frac{\∂}{\∂x_j}(\mathrm{\μ}\frac{{\∂u}_i}{\∂x_j}-\mathrm{\ρ}\stackrel{\‾}{{u_i}^{\′}{u_j}^{\′}})+S_i$

(2) introduce the sticking coefficient μ in whirlpool _t, by the sticking coefficient μ in whirlpool _tSet up the relation of Reynolds stress and average velocity gradient:

$-\mathrm{\ρ}\stackrel{\‾}{{u_i}^{\′}{u_j}^{\′}}={\mathrm{\μ}}_t(\frac{\∂u_i}{\∂x_j}+\frac{\∂u_i}{{\∂x}_j})-\frac{2}{3}(\mathrm{\ρk}+{\mathrm{\μ}}_t\frac{\∂u_i}{\∂x_j}){\mathrm{\δ}}_{\mathrm{ij}}$

In the formula, μ _tBe the sticking coefficient in whirlpool, u _iBe time averaged velocity, δ _IjBe " Kronecker delta " symbol, k is a tubulence energy;

(3) according to determining the sticking coefficient μ in whirlpool _tDifferential equation number, standard k-ε model has been proposed; In standard k-ε model, tubulence energy k and dissipative shock wave ε are two fundamental unknown variables, and corresponding transport equation is:

$\frac{\∂\left(\mathrm{\ρk}\right)}{\∂t}+\frac{\∂\left(\mathrm{\ρk}{u}_i\right)}{\∂x_i}=\frac{\∂}{\∂x_j}\left[(\mathrm{\μ}+\frac{{\mathrm{\μ}}_t}{{\mathrm{\σ}}_k})\frac{\∂k}{{\∂x}_j}\right]+G_k+G_b-\mathrm{\ρ\ϵ}-Y_M+S_k$

$\frac{\∂\left(\mathrm{\ρ\ϵ}\right)}{\∂t}+\frac{\∂\left(\mathrm{\ρ\ϵ}{u}_i\right)}{{\∂x}_i}=\frac{\∂}{{\∂x}_j}\left[(\mathrm{\μ}+\frac{{\mathrm{\μ}}_t}{{\mathrm{\σ}}_{\mathrm{\ϵ}}})\frac{\∂\mathrm{\ϵ}}{{\∂x}_j}\right]+C_{1\mathrm{\ϵ}}\frac{\mathrm{\ϵ}}{k}(G_k+C_{3\mathrm{\ϵ}}{G}_b)-C_{2\mathrm{\ϵ}}\mathrm{\ρ}\frac{{\mathrm{\ϵ}}^2}{k}+S_{\mathrm{\ϵ}}$

Wherein, G _kBe the generation item of the tubulence energy k that causes by average velocity gradient, G _bBe the generation item of the tubulence energy k that causes by buoyancy, Y _MRepresentative can be pressed the contribution of pulsation expansion in the turbulent flow, C _{1 ε}, C _{2 ε}And C _{3 ε}Be empirical constant, σ _kAnd σ _εBe respectively the Prandtl number corresponding with tubulence energy k and dissipative shock wave ε, S _kAnd S _εIt is user-defined source item;

(4) step (1) (2) (3) equation being dispersed is algebraic equation, sets up discrete equation, has

$\left(\frac{a_P}{a}\right){\mathrm{\φ}}_P=\underset{\mathrm{nb}}{\mathrm{\Σ}}{a}_{\mathrm{nb}}{\mathrm{\φ}}_{\mathrm{nb}}+b+(1-a)\frac{a_P}{a}{\mathrm{\φ}}_P^o$

In the formula, φ _NbBe φ _pAdjoint point speed, a _PAnd a _NbBe coefficient, φ _P ^oSeparate for last layer takes second place, a is a relaxation factor,

Be the algebraic equation source item, b is the constant component in the source item;

(5) adopt the separate type solution, sequentially, one by one find the solution each variable Algebraic Equation set in the discrete equation;

(6) whether check result restrains.If do not restrain, as new conjecture, repeat this process with the result that obtains.

Specify as follows:

Equal method is to turbulent flow pulsation in addition " simplification " during by Reynolds, the transient motion of turbulent flow is regarded as by mean value and pairing two mobile being formed by stacking of pulsating quantity, like this, the time all be down, under the absolute frame of rectangular coordinate form, the instantaneous Navier-Stokes equation of describing its instantaneous flow state becomes:

$\frac{\∂}{\∂t}\left(\mathrm{\ρ}{u}_i\right)+\frac{\∂}{{\∂x}_j}\left(\mathrm{\ρ}{u}_i{u}_j\right)=-\frac{\∂p}{\∂x_i}+\frac{\∂}{{\∂x}_j}(\mathrm{\μ}\frac{{\∂u}_i}{\∂x_j}-\mathrm{\ρ}\stackrel{\‾}{{u_i}^{\′}{u_j}^{\′}})+S_i$

The time have more with respect to instantaneous Navier-Stokes equation in the equation that all flows

, be defined as Reynolds stress.Owing to increased Reynolds stress, therefore, make the governing equations sealing of system, must introduce new turbulence model (equation).

In these computing method, directly do not handle Reynolds stress item, but introduce the sticking coefficient μ in whirlpool _t, then turbulent stress is expressed as μ _tFunction.Coefficient μ is glued in the whirlpool _tSet up the relation of Reynolds stress and average velocity gradient:

$-\mathrm{\ρ}\stackrel{\‾}{{u_i}^{\′}{u_j}^{\′}}={\mathrm{\μ}}_t(\frac{\∂u_i}{{\∂x}_j}+\frac{{\∂u}_i}{\∂x_j})-\frac{2}{3}(\mathrm{\ρk}+{\mathrm{\μ}}_t\frac{{\∂u}_i}{\∂x_j}){\mathrm{\δ}}_{\mathrm{ij}}$

In the formula, μ _tBe the sticking coefficient in whirlpool, u _iBe time averaged velocity, δ _IjBe " Kronecker delta " symbol, k is a tubulence energy.

The key of calculating is to determine the sticking coefficient μ in whirlpool _tAccording to determining μ _tDifferential equation number, standard k-ε model has been proposed.In standard k-ε model, tubulence energy k and dissipative shock wave ε are two fundamental unknown variables, and corresponding transport equation is:

$\frac{\∂\left(\mathrm{\ρk}\right)}{\∂t}+\frac{\∂\left({\mathrm{\ρku}}_i\right)}{\∂x_i}=\frac{\∂}{\∂x_j}\left[(\mathrm{\μ}+\frac{{\mathrm{\μ}}_t}{{\mathrm{\σ}}_k})\frac{\∂k}{{\∂x}_j}\right]+G_k+G_b-\mathrm{\ρ\ϵ}-Y_M+S_k$

$\frac{\∂\left(\mathrm{\ρ\ϵ}\right)}{\∂t}+\frac{\∂\left(\mathrm{\ρ\ϵ}{u}_i\right)}{{\∂x}_i}=\frac{\∂}{{\∂x}_j}\left[(\mathrm{\μ}+\frac{{\mathrm{\μ}}_t}{{\mathrm{\σ}}_{\mathrm{\ϵ}}})\frac{\∂\mathrm{\ϵ}}{\∂x_j}\right]+C_{1\mathrm{\ϵ}}\frac{\mathrm{\ϵ}}{k}(G_k+C_{3\mathrm{\ϵ}}{G}_b)-C_{2\mathrm{\ϵ}}\mathrm{\ρ}\frac{{\mathrm{\ϵ}}^2}{k}+S_{\mathrm{\ϵ}}$

Wherein, G _kBe the generation item of the tubulence energy k that causes by average velocity gradient, G _bBe the generation item of the tubulence energy k that causes by buoyancy, Y _MRepresentative can be pressed the contribution of pulsation expansion in the turbulent flow, C _{1 ε}, C _{2 ε}And C _{3 ε}Be empirical constant, σ _kAnd σ _εBe respectively the Prandtl number corresponding with tubulence energy k and dissipative shock wave ε, S _kAnd S _εIt is user-defined source item.

The solving equation number is few, computing velocity is high, precision also can satisfy characteristics such as requirement of engineering because of k-ε two equation models have, and becomes most widely used turbulence model at present.

Before given problem being carried out turbulent flow calculating, at first will be with the zoning discretize, promptly on volume coordinate and time coordinate, continuous zoning is split into many grid cells, then, on grid cell, is algebraic equation with governing equation and turbulent flow additional equation are discrete.Set up partial differential equation that discrete equation is about to describe flow process and transform into algebraically side's group on each node.In the SIMPLEC algorithm, use the discretization method of finite volume method, for the equation of momentum, when speed is write out with common variable φ, have

$\left(\frac{a_P}{a}\right){\mathrm{\φ}}_P=\underset{\mathrm{nb}}{\mathrm{\Σ}}{a}_{\mathrm{nb}}{\mathrm{\φ}}_{\mathrm{nb}}+b+(1-a)\frac{a_P}{a}{\mathrm{\φ}}_P^o$

In the formula, φ _NbBe φ _pAdjoint point speed, a _PAnd a _NbBe coefficient, φ _P ^oSeparate for last layer takes second place, a is a relaxation factor, Be the algebraic equation source item, b is the constant component in the source item.

Finite volume method at present commonly used is because of all guaranteeing the conservativeness of governing equation to any one group of CONTROL VOLUME, and counting yield height, applicability are strong, so becomes present most popular discretization method.

After setting up the discrete equation group by finite volume method, can adopt the separate type solution, sequentially, one by one find the solution each variable Algebraic Equation set; According to whether directly finding the solution original variable u, v, w and p, the separate type solution is divided into original variable method and non-original variable method, generally adopts the original variable method based on the pressure correction principle at present.

Famous pressure correction theory is the semi implicit algorithm (SIMPLE algorithm) of coupling pressure system of equations, in this algorithm, at first uses the pressure field of a conjecture to separate the equation of momentum, obtains velocity field; Then find the solution the pressure correction equation of setting up by continuity equation, obtain the modified value of pressure field; Utilize pressure correction value renewal speed field and pressure field then; Whether last check result restrains.If do not restrain,, repeat this process with the pressure field that obtains pressure field as new conjecture.

Facts have proved that improved SIMPLEC algorithm can effectively be found the solution the non-permanent turbulent flow in the various flow passage components of hydraulic on semi implicit algorithm (SIMPLE algorithm) basis.

After the velocity field and pressure field distribution that calculate by turbulent flow under a certain operating mode of hydraulic, can estimate the energy and the Cavitation Characteristics of hydraulic by mathematical procedure.

The centrifugal pump analysis example

Now selecting the widely used centrifugal pump of water supply project is analytic target.Known water pump impeller diameter is 450mm, and the number of blade is 6, and rated flow is 350L/s, and rated speed is 1450r/min.Adopt non-structured grid, RNG k-ε model and SIMPLEC algorithm, carried out full tunnel turbulent flow simulation under 6 flow points.

As shown in Figure 2, provided when design conditions the blade surface pressure distribution that calculates.As can be seen from the figure, blade surface pressure raises to outlet gradually from import, and pressure isoline continuously smooth is parallel to blade import and outlet generally.In the corresponding position, pressure face pressure is higher than suction surface pressure, thereby forms the pressure gradient in the circumference of impeller face.

As shown in Figure 3, design conditions down-off-head curve and flow-efficiency curve have been provided.As can be seen from Figure, calculating lift coincide relatively goodly with the actual measurement lift.The optimum point that calculates is at Q=345L/s, and the actual measurement optimum point is at Q=331L/s, but the optimum efficiency absolute value is more or less the same, and illustrate and predicts that the result and the external characteristics test findings that obtain are identical substantially.

The effect of implementing

Equal method is set up the construction method of turbulence model during Reynolds of the present invention theory and method move to maturity, the three-dimensional permanent turbulent flow of the full runner of centrifugal pump based on k-ε both sides journey turbulence model is calculated, obtained the mobile details that conforms to actual conditions, can understanding qualitatively have been arranged to mobile in each flow passage components thus.According to result of calculation energy, the cavitation performance of centrifugal pump have been done quantitative estimating,, shown that numerical result is believable with model test basically identical as a result.

The construction method that equal method is set up turbulence model during Reynolds of the present invention provides a kind of new means for analyzing the inner complicated turbulent flow flow field of hydraulics such as water pump, the hydraulic turbine, theoretical and numerical method is further perfect along with CFD, might be from disclosing the mechanism of important hydraulic performances such as hydraulic machinery cavitation and hydraulic vibration in essence, thus the theory and technology foundation provided for research and development high-performance, big flow, high water head water pump or water turbine equipment.

More than show and described ultimate principle of the present invention and principal character and advantage of the present invention.The technician of the industry should understand; the present invention is not restricted to the described embodiments; that describes in the foregoing description and the instructions just illustrates principle of the present invention; without departing from the spirit and scope of the present invention; the present invention also has various changes and modifications; these changes and improvements all fall in the claimed scope of the invention, and the claimed scope of the present invention is defined by appending claims and equivalent thereof.

Claims (5)

1. equal method is set up the construction method of turbulence model during a Reynolds, it is characterized in that it comprises the steps:

Equal method is regarded the transient motion of turbulent flow by pairing two of mean value and pulsating quantity as and is flowed and are formed by stacking when (1) adopting Reynolds, the time all be that under the absolute frame of rectangular coordinate form, the governing equation of setting up instantaneous flow state is down:

$\frac{\∂}{{\∂}_t}\left(\mathrm{\ρ}{u}_i\right)+\frac{\∂}{{\∂x}_j}\left(\mathrm{\ρ}{u}_i{u}_j\right)=-\frac{\∂p}{\∂x_i}+\frac{\∂}{\∂x_j}(\mathrm{\μ}\frac{\∂u_i}{\∂x_j}-\mathrm{\ρ}\stackrel{\‾}{{u_i}^{\′}{u_j}^{\′}})+S_i$

(2) introduce the sticking coefficient μ in whirlpool _t, by the sticking coefficient μ in whirlpool _tSet up the relation of Reynolds stress and average velocity gradient:

$-\mathrm{\ρ}\stackrel{\‾}{{u_i}^{\′}{u_j}^{\′}}={\mathrm{\μ}}_t(\frac{\∂u_i}{\∂x_j}+\frac{\∂u_j}{\∂x_j})-\frac{2}{3}(\mathrm{\ρk}+{\mathrm{\μ}}_t\frac{\∂u_i}{\∂x_j}){\mathrm{\δ}}_{\mathrm{ij}}$

In the formula, μ _tBe the sticking coefficient in whirlpool, u _iBe time averaged velocity, δ _IjBe " Kronecker delta " symbol, k is a tubulence energy;

(3) according to determining the sticking coefficient μ in whirlpool _tDifferential equation number, standard k-ε model has been proposed; In standard k-ε model, tubulence energy k and dissipative shock wave ε are two fundamental unknown variables, and corresponding transport equation is:

$\frac{\∂\left(\mathrm{\ρk}\right)}{\∂t}+\frac{\∂\left(\mathrm{\ρk}{u}_i\right)}{\∂x_i}=\frac{\∂}{\∂x_j}\left[(\mathrm{\μ}+\frac{{\mathrm{\μ}}_t}{{\mathrm{\σ}}_k})\frac{\∂k}{\∂x_j}\right]+G_k+G_b-\mathrm{\ρ\ϵ}-Y_M+S_k$

$\frac{\∂\left(\mathrm{\ρ\ϵ}\right)}{\∂t}+\frac{\∂\left(\mathrm{\ρ\ϵ}{u}_i\right)}{\∂x_i}=\frac{\∂}{\∂x_j}\left[(\mathrm{\μ}+\frac{{\mathrm{\μ}}_t}{{\mathrm{\σ}}_k})\frac{\∂\mathrm{\ϵ}}{\∂x_j}\right]+C_{1\mathrm{\ϵ}}\frac{\mathrm{\ϵ}}{k}(G_k+C_{3\mathrm{\ϵ}}{G}_b)-C_{2\mathrm{\ϵ}}\mathrm{\ρ}\frac{{\mathrm{\ϵ}}^2}{k}+S_{\mathrm{\ϵ}}$

Wherein, G _kBe the generation item of the tubulence energy k that causes by average velocity gradient, G _bBe the generation item of the tubulence energy k that causes by buoyancy, Y _MRepresentative can be pressed the contribution of pulsation expansion in the turbulent flow, C _{1 ε}, C _{2 ε}And C _{3 ε}Be empirical constant, σ _kAnd σ _εBe respectively the Prandtl number corresponding with tubulence energy k and dissipative shock wave ε, S _kAnd S _εIt is user-defined source item;

(4) step (1) (2) (3) equation being dispersed is algebraic equation, sets up discrete equation, has

$\left(\frac{a_P}{a}\right){\mathrm{\φ}}_P=\underset{\mathrm{nb}}{\mathrm{\Σ}}{a}_{\mathrm{nb}}{\mathrm{\φ}}_{\mathrm{nb}}+b+(1-a)\frac{a_P}{a}{\mathrm{\φ}}_P^o$

In the formula, φ _NbBe φ _pAdjoint point speed, a _PAnd a _NbBe coefficient, φ _P ^oSeparate for last layer takes second place, a is a relaxation factor,

Be the algebraic equation source item, b is the constant component in the source item;

(5) adopt the separate type solution, sequentially, one by one find the solution each variable Algebraic Equation set in the discrete equation;

(6) whether check result restrains.If do not restrain, as new conjecture, repeat this process with the result that obtains.

2. construction method as claimed in claim 1, it is characterized in that, before calculating, at first will be with the zoning discretize, promptly on volume coordinate and time coordinate, continuous zoning is split into many grid cells, then, on grid cell, be algebraic equation with governing equation and turbulent flow additional equation are discrete.

3. construction method as claimed in claim 1 is characterized in that, described separate type solution is divided into original variable method and non-original variable method.

4. construction method as claimed in claim 3 is characterized in that, described original variable method is meant at first uses the pressure field of a conjecture to separate the equation of momentum, obtains velocity field; Then find the solution the pressure correction equation of setting up by continuity equation, obtain the modified value of pressure field; Utilize pressure correction value renewal speed field and pressure field then; Whether last check result restrains.If do not restrain,, repeat this process with the pressure field that obtains pressure field as new conjecture.

5. construction method as claimed in claim 1 is characterized in that, by after calculating the velocity field and pressure field distribution under a certain operating mode of hydraulic, can estimate the energy and the Cavitation Characteristics of hydraulic by mathematical procedure.

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