CN102141064A - Method for constructing turbulence model by spatial filtering method - Google Patents

Abstract

The invention aims to disclose a method for constructing a turbulence model by a spatial filtering method. By simulating full-channel turbulence of an axial-flow pump of the turbulence model, corresponding flow details can be obtained, flowing in all flow passage components can be qualitatively recognized, the energy and cavitation performance of the axial-flow pump can be estimated quantitatively according to a calculation result, and the mechanisms of important hydraulic characteristics such as hydraulic cavitation, hydraulic vibration and the like are disclosed, so that theoretical and technical basis is provided for researching and developing a water pump or a water turbine device with high performance, large flow and a high water head and the aim of the invention is fulfilled.

Description

The spatial filtering method is set up the construction method of turbulence model

Technical field

The present invention relates to a kind of construction method, set up the construction method of turbulence model in particularly a kind of hydraulic machinery by the spatial filtering method.

Background technique

Along with the construction of the south water to north and Three Gorges hydraulic engineering, water pump, water 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 runnability in water power plant, 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 machinery 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 running shaft are at random, because the complexity of turbulent flow, be difficult to grasp the turbulence state of hydraulic machinery inside by test, and computation fluid dynamics (CFD) theory and method, be familiar with the hydraulic machinery turbulent flow to us a kind of new approach is provided, to disclosing the complex relationship between hydraulic machinery flow field flow characteristic and structural dynamic characteristic, has potential advantage.

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

Summary of the invention

The object of the present invention is to provide a kind of spatial filtering method to set up the construction method of turbulence model, solve existing the problems referred to above that exist, adopt the pulsation of spatial filtering method " simplification " turbulent flow, the additional turbulence model of structure on instantaneous Navier-Stokes equations based.

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

A kind of spatial filtering method is set up the construction method of turbulence model, it is characterized in that, it comprises the steps:

(1) adopt finite volume method structure filter function, and instantaneous Navier-Stokes equation is carried out Shelving, under the absolute frame of right angled coordinates form, the governing equation of setting up instantaneous flowing state is:

$\frac{\∂}{\∂t}\left(\mathrm{\ρ}{\stackrel{\‾}{u}}_i\right)+\frac{\∂}{\∂x_j}\left(\mathrm{\ρ}{\stackrel{\‾}{u}}_i{\stackrel{\‾}{u}}_j\right)=-\frac{\stackrel{\‾}{\∂p}}{\∂x_i}+\frac{\∂}{\∂x_j}\left(\mathrm{\μ}\frac{\∂{\stackrel{\‾}{u}}_i}{\∂x_j}\right)-\frac{{\∂\mathrm{\τ}}_{\mathrm{ij}}}{\∂x_j}$

In the formula, the amount that has line "-" is filtered field variable, τ _IjBe inferior grid scale stress model;

(2) it is as follows to set up inferior grid scale stress model:

${\mathrm{\τ}}_{\mathrm{ij}}-\frac{1}{3}{\mathrm{\τ}}_{\mathrm{kk}}{\mathrm{\δ}}_{\mathrm{ij}}=-2{\mathrm{\μ}}_t{\stackrel{\‾}{S}}_{\mathrm{ij}}$

In the formula, μ _tThe sticking coefficient in the whirlpool of inferior grid yardstick, the sticking coefficient in the whirlpool of inferior grid yardstick is set to ${\mathrm{\μ}}_t={\left(C_s\mathrm{\Δ}\right)}^2\left|\stackrel{\‾}{S}\right|;$

(3) divide computing grid, pass through formula:

${\stackrel{\‾}{S}}_{\mathrm{ij}}=\frac{1}{2}(\frac{\stackrel{\‾}{{\∂u}_i}}{\∂x_j}+\frac{\stackrel{\‾}{{\∂u}_j}}{\∂x_j}),\left|\stackrel{\‾}{S}\right|=\sqrt{2{\stackrel{\‾}{S}}_{\mathrm{ij}}{\stackrel{\‾}{S}}_{\mathrm{ij}}},\mathrm{\Δ}={\left({\mathrm{\Δ}}_x{\mathrm{\Δ}}_y{\mathrm{\Δ}}_z\right)}^{1/3}$ Computing node,

In the formula, Δ _iRepresentative is along the axial size of mesh opening of i, c _sIt is the Smagorinsky constant;

(4) equation in step (1), (2) (3) 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 separated 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 computational domain discretization, promptly on space coordinates and time coordinate, continuous computational domain is split into many grid cell [bins, then, on grid cell [bin, be algebraic equation with governing equation and turbulent flow additional equation are discrete.

In one embodiment of the invention, described separated 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 momentum equation, obtains velocity field; Then find the solution the pressure correction equation of setting up by continuity equation, obtain the correction 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 machinery, can estimate the energy and the Cavitation Characteristics of hydraulic machinery by mathematical procedure.

Spatial filtering method of the present invention is set up the construction method of turbulence model, axial-flow pump full tunnel turbulent flow simulation by 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 characteristics such as hydraulic machinery cavitation and hydraulic vibration, thereby, realize purpose of the present invention for research and development high-performance, big flow, high 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 mode of execution of this case and be obtained to be well understood to.

Description of drawings

Fig. 1 sets up the schematic flow sheet of the construction method of turbulence model for spatial filtering method of the present invention;

Fig. 2 is the schematic representation 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, spatial filtering method of the present invention is set up the construction method of turbulence model, and it comprises the steps:

(1) adopt finite volume method structure filter function, and instantaneous Navier-Stokes equation is carried out Shelving, under the absolute frame of right angled coordinates form, the governing equation of setting up instantaneous flowing state is:

$\frac{\∂}{\∂t}\left(\mathrm{\ρ}{\stackrel{\‾}{u}}_i\right)+\frac{\∂}{\∂x_j}\left(\mathrm{\ρ}{\stackrel{\‾}{u}}_i{\stackrel{\‾}{u}}_j\right)=-\frac{\stackrel{\‾}{\∂p}}{\∂x_i}+\frac{\∂}{\∂x_j}\left(\mathrm{\μ}\frac{\stackrel{\‾}{{\∂u}_i}}{\∂x_j}\right)-\frac{{\∂\mathrm{\τ}}_{\mathrm{ij}}}{{\∂x}_j}$

In the formula, the amount that has line "-" is filtered field variable, τ _IjBe inferior grid scale stress model;

(2) it is as follows to set up inferior grid scale stress model:

${\mathrm{\τ}}_{\mathrm{ij}}-\frac{1}{3}{\mathrm{\τ}}_{\mathrm{kk}}{\mathrm{\δ}}_{\mathrm{ij}}=-2{\mathrm{\μ}}_t{\stackrel{\‾}{S}}_{\mathrm{ij}}$

In the formula, μ _tBe the sticking coefficient in whirlpool of inferior grid yardstick, the sticking coefficient in the whirlpool of inferior grid yardstick is set to ${\mathrm{\μ}}_i={\left(C_s\mathrm{\Δ}\right)}^2\left|\stackrel{\‾}{S}\right|;$

(3) divide computing grid, pass through formula:

${\stackrel{\‾}{S}}_{\mathrm{ij}}=\frac{1}{2}(\frac{\stackrel{\‾}{{\∂u}_i}}{\∂x_j}+\frac{\stackrel{\‾}{{\∂u}_j}}{\∂x_j}),\left|\stackrel{\‾}{S}\right|=\sqrt{2{\stackrel{\‾}{S}}_{\mathrm{ij}}{\stackrel{\‾}{S}}_{\mathrm{ij}}},\mathrm{\Δ}={\left({\mathrm{\Δ}}_x{\mathrm{\Δ}}_y{\mathrm{\Δ}}_z\right)}^{1/3}$ Computing node,

In the formula, Δ _iRepresentative is along the axial size of mesh opening of i, c _sIt is the Smagorinsky constant;

(4) equation in step (1), (2) (3) 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 separated 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:

In order to simulate turbulent flow, require the size of computing grid should be on the one hand even as big as comprising the maximum whirlpool that occurs in the turbulent motion, require the yardstick of computing grid should be small enough to differentiate the motion in minimum whirlpool on the other hand.Yet with regard to present computer capacity, the smallest dimension of the computing grid that can adopt the still yardstick than minimum whirlpool is a lot of greatly.

Therefore, can only abandon simulation to the motion in whirlpool on the full size scope, and only the turbulent motion bigger than mesh scale directly calculated by instantaneous Navier-Stokes equation, then simulate for the influence that the vortex pair large scale of small scale is moved, thereby formed large eddy simulation (LES) method by setting up model.

In Large eddy simulation method, at first need set up a kind of mathematical filtering function, from turbulent flow instantaneous motion equation, the little whirlpool of scale ratio filter function yardstick is filtered, thereby decomposite the motion equation of describing the maelstrom field, and the influence of the little vortex pair that is filtered big whirlpool motion then embodies by introduce the additional stress item in the motion equation of maelstrom field.

Adopt the implicit filter function of finite volume method itself to construct filter function, and after instantaneous Navier-Stokes equation carried out Shelving, under the absolute frame of right angled coordinates form, the governing equation of describing its instantaneous flowing state became:

$\frac{\∂}{\∂t}\left(\mathrm{\ρ}{\stackrel{\‾}{u}}_i\right)+\frac{\∂}{\∂x_j}\left(\mathrm{\ρ}{\stackrel{\‾}{u}}_i{\stackrel{\‾}{u}}_j\right)=-\frac{\stackrel{\‾}{\∂p}}{\∂x_i}+\frac{\∂}{{\∂x}_j}\left(\mathrm{\μ}\frac{\stackrel{\‾}{{\∂u}_i}}{{\∂x}_j}\right)-\frac{{\∂\mathrm{\τ}}_{\mathrm{ij}}}{\∂x_j}$

In the formula, the amount that has line "-" is filtered field variable, τ _IjBe inferior grid scale stress model (SGS model).

Inferior grid scale stress model (SGS model) has embodied the influence of the little vortex pair that is filtered big whirlpool motion, occupies crucial status in large eddy simulation (LES) method.By various application of model effects are compared, up-to-date inferior grid scale stress model (SGS model) is as follows:

${\mathrm{\τ}}_{\mathrm{ij}}-\frac{1}{3}{\mathrm{\τ}}_{\mathrm{kk}}{\mathrm{\δ}}_{\mathrm{ij}}=-2{\mathrm{\μ}}_t{\stackrel{\‾}{S}}_{\mathrm{ij}}$

In the formula, μ _tBe the sticking coefficient in whirlpool of inferior grid yardstick, be recommended as: ${\mathrm{\μ}}_i={\left(C_s\mathrm{\Δ}\right)}^2\left|\stackrel{\‾}{S}\right|$

Wherein,

${\stackrel{\‾}{S}}_{\mathrm{ij}}=\frac{1}{2}(\frac{\stackrel{\‾}{\∂u_i}}{{\∂x}_j}+\frac{\stackrel{\‾}{\∂u}j}{\∂x_i}),\left|\stackrel{\‾}{S}\right|=\sqrt{2{\stackrel{\‾}{S}}_{\mathrm{ij}}{\stackrel{\‾}{S}}_{\mathrm{ij}}},\mathrm{\Δ}={\left({\mathrm{\Δ}}_x{\mathrm{\Δ}}_y{\mathrm{\Δ}}_z\right)}^{1/3}$

In the formula, Δ _iRepresentative is along the axial size of mesh opening of i, c _sIt is the Smagorinsky constant.

Large eddy simulation (LES) method is to the capacity requirement height of computer, but can find the solution instantaneous Navier-Stokes equation because of it, therefore, aspect the non-steady pressure pulsation of finding the solution the hydraulic machinery flow field, has special advantage.

Before given problem being carried out turbulent flow calculating, at first will be with the computational domain discretization, promptly on space coordinates and time coordinate, continuous computational domain is split into many grid cell [bins, then, on grid cell [bin, 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 momentum equation, when speed is write out with common variable φ, have

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

φ in the formula _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 computational efficiency 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 separated 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 separated 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 set of equation, in this algorithm, at first uses the pressure field of a conjecture to separate momentum equation, obtains velocity field; Then find the solution the pressure correction equation of setting up by continuity equation, obtain the correction 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 machinery 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 machinery, can estimate the energy and the Cavitation Characteristics of hydraulic machinery by mathematical procedure.

The axial-flow pump analysis example

Now selecting the widely used axial-flow pump of project of South-to-North water diversion is analytic target.Known water pump impeller diameter is 300mm, and the number of blade is 6, and rated flow is 350L/s, and rated speed is 1450r/min.Adopt non-structured grid, large eddy simulation (LES) model and SIMPLEC algorithm, carried out full tunnel turbulent flow simulation under 6 flow points.

As shown in Figure 2, the left side is a pressure side among the figure, and the right is a suction surface; Provided when design conditions, 0 ° of blade angle 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 isopleth continuously smooth is parallel to blade import and outlet generally.In the corresponding position, pressure side pressure is higher than suction surface pressure, thereby forms the pressure gradient in the circumference of impeller face.

Because the aerofoil profile length at wheel rim place is big than wheel hub,, cause the pressure in close wheel rim outlet port on the blade pressure surface obviously high than other zone so wheel rim place blade is many to the current acting.In addition, also can see the low pressure area of vacuum side of blade significantly, be positioned at the position near the import wheel rim, minimum relative pressure is-7.05 * 10 ⁴Pa, the NPSHr that calculates of pressure meter is 7.3m thus, cavitation number σ is 0.98, and is very approaching with test result.

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 result that obtain are identical substantially.

The effect of implementing

Theory and method that spatial filtering method of the present invention is set up the construction method of turbulence model move to maturity, axial-flow pump full tunnel turbulent flow simulation based on the LES turbulence model, 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 axial-flow pump have been done quantitative estimating,, shown that numerical result is believable with model test basically identical as a result.

The construction method that spatial filtering method of the present invention is set up turbulence model provides a kind of new means for analyzing the inner complicated turbulent flow flow field of hydraulic machinerys such as water pump, water turbine, along with spatial filtering method of the present invention is set up the further perfect of the theoretical and numerical method of the construction method of turbulence model, might be from disclosing the mechanism of important hydraulic characteristics 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 head water pump or water turbine equipment.

More than show and described basic principle of the present invention and major 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 specification 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. a spatial filtering method is set up the construction method of turbulence model, it is characterized in that it comprises the steps:

(1) adopt finite volume method structure filter function, and instantaneous Navier-Stokes equation is carried out Shelving, under the absolute frame of right angled coordinates form, the governing equation of setting up instantaneous flowing state is:

$\frac{\∂}{\∂t}\left(\mathrm{\ρ}{\stackrel{\‾}{u}}_i\right)+\frac{\∂}{\∂x_j}\left(\mathrm{\ρ}{\stackrel{\‾}{u}}_i{\stackrel{\‾}{u}}_j\right)=-\frac{\stackrel{\‾}{\∂p}}{\∂x_i}+\frac{\∂}{\∂x_j}\left(\mathrm{\μ}\frac{\stackrel{\‾}{\∂u_i}}{\∂x_j}\right)-\frac{{\∂\mathrm{\τ}}_{\mathrm{ij}}}{{\∂x}_j}$

In the formula, the amount that has line "-" is filtered field variable, τ _IjBe inferior grid scale stress model;

(2) it is as follows to set up inferior grid scale stress model:

${\mathrm{\τ}}_{\mathrm{ij}}-\frac{1}{3}{\mathrm{\τ}}_{\mathrm{kk}}{\mathrm{\δ}}_{\mathrm{ij}}=-2{\mathrm{\μ}}_t{\stackrel{\‾}{S}}_{\mathrm{ij}}$

In the formula, μ _tBe the sticking coefficient in whirlpool of inferior grid yardstick, the sticking coefficient in the whirlpool of inferior grid yardstick is set to ${\mathrm{\μ}}_t={\left(C_s\mathrm{\Δ}\right)}^2\left|\stackrel{\‾}{S}\right|;$

(3) divide computing grid, pass through formula:

${\stackrel{\‾}{S}}_{\mathrm{ij}}=\frac{1}{2}(\frac{\stackrel{\‾}{\∂u_i}}{\∂x_j}+\frac{\stackrel{\‾}{\∂u_j}}{{\∂x}_j}),\left|\stackrel{\‾}{S}\right|=\sqrt{2{\stackrel{\‾}{S}}_{\mathrm{ij}}{\stackrel{\‾}{S}}_{\mathrm{ij}}},\mathrm{\Δ}={\left({\mathrm{\Δ}}_x{\mathrm{\Δ}}_y{\mathrm{\Δ}}_z\right)}^{1/3}$ Computing node,

In the formula, Δ _iRepresentative is along the axial size of mesh opening of i, c _sIt is the Smagorinsky constant;

4) equation in step (1), (2) (3) 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 separated 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 computational domain discretization, promptly on space coordinates and time coordinate, continuous computational domain is split into many grid cell [bins, then, on grid cell [bin, 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 separated 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 momentum equation, obtains velocity field; Then find the solution the pressure correction equation of setting up by continuity equation, obtain the correction 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 machinery, can estimate the energy and the Cavitation Characteristics of hydraulic machinery by mathematical procedure.

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