CN102270257B - Method for designing and calculating fluid passage - Google Patents

Abstract

The invention discloses a method for designing and calculating a fluid passage. The fluid passage is designed in an optimal mode according to the interaction between fluid and a passage by three stages, namely a stage that the fluid begins contacting the inner wall surface of the passage, a stage that the fluid continuously flows on the inner wall surface of the passage, and a stage that a derivative dny/dxn corresponding to the fluid is reduced; the fluid passage is calculated by the following steps of: obtaining a derivative dny/dxn corresponding curve through the three stages; symmetrically projecting the obtained ideal work curve shape along an X axle to obtain a negative curve of the ideal work curve and finally forming a complete ideal work curve; and moving the ideal curve up and down for required width in the direction vertical to a coordinate plane or rotating the ideal curve around a certain rotation shaft to obtain a sectorial curved surface or a closed round curved surface to obtain the required ideal curved surface. The problems of consumption, loss and waste of a large amount of energy caused by fluid compact and eddy during flowing of fluid are solved.

Description

A kind of design of fluid passage, computing method

Technical field

The technical program belongs to hydromechanical basic technology field, specifically a kind of design of fluid passage, computing method.

Background technology

The fluid passage is widely used in the prior art, its designing requirement is also very high, because, reasonably the fluid passage has rational hydrodynamic characteristic, can realize under the identical flow state, energy consumption (this energy consumption comprise the energy consumption of resisting fluid and the energy consumption of fluid self) is minimum, and better effects if is most effective.

For example, in the structure of the cooling system of automobile etc., as shown in Figure 6, wherein, the cooling draught that head-on wind produces is come from the automobile front, by the lattice coral air inlet in the automobile radiator grille 9, enters the front of water tank 4; Then brush water tank, the condenser surface of heat, the heat of water tank, condenser surface is taken away, thereby play cooling effect.By calculating, find that the Area comparison of air inlet is little, the area of air inlet only has 29.9% of water tank area, will affect the installation effectiveness coefficient of cooling system, affects the cooling power of cooling system.

In order to address this problem, in the prior art, in the bottom of water tank front wind scooper has been installed specially, as shown in Figure 7.Windstream walking around below the bumper directs into the water tank front and brushes water tank, and water tank is played cooling effect.Although front face area has increased, if the flow state of fluid is bad, remain the requirement of not satisfying cooling system.Therefore still need to take some measures, improve air intake efficiency.In the situation of condition restriction harshness, the difficulty that improves air intake efficiency is very large.

Summary of the invention

In order to solve the above-mentioned problems in the prior art, the present invention proposes a kind of design and calculation method of fluid passage, concrete technical scheme is as follows:

A kind of design of fluid passage, computing method are according to the form arrangement of the interaction force between fluid and the passage with the best, and a minute three phases designs respectively:

1) design of fluid and vias inner walls surface beginning contact phase:

The derivative d of vias inner walls surface curve ⁿY/dx ⁿParameter as the vias inner walls surface; Described derivative is second derivative or higher derivative;

If the derivative d of vias inner walls surface curve starting point ⁿY/dx ⁿEqual zero, and smoothly increase by linear relation, so that the work quality in this stage is the most desirable;

2) fluid continues the design in mobile stage on the vias inner walls surface:

If should the stage, described derivative d ⁿY/dx ⁿBe a constant, make the impact of air-flow and working curved surface as much as possible little;

3) the derivative d that fluid is corresponding ⁿY/dx ⁿReduce the design in stage:

This stage is step 1) the reverse procedure of first stage, namely allow derivative d ⁿY/dx ⁿEqual zero at last by linear relation decline;

4) obtain derivative d by above-mentioned three phases ⁿY/dx ⁿCorresponding curve uses n curve with this derivative d again ⁿY/dx ⁿNot round and smooth junction smooth connection is got up in the corresponding curve, obtains at last the ideal operation curve;

5) corresponding above-mentioned four steps of ideal operation curve are divided into five intervals;

6) ideal operation curve shape obtained above is obtained the negative curve of ideal operation curve along the X-axis symmetry, again this negative curve integrated moving forward, and end to end with the ideal operation curve, with regard to the ideal operation curve of complete; This complete ideal operation curve is altogether by ten intervals, be made of ten function curves;

7) functional equation that each is interval carries out integration n time, obtains each interval curvilinear equation of complete ideal operation curve;

8) at the interval of each curvilinear equation function, input a series of x numerical value, each interval curvilinear equation of substitution just obtains vias inner walls surface ideal curve;

9) ideal curve on the direction perpendicular to coordinate plane, move up and down needed width, perhaps ideal curve is rotated around some turning axles, obtain the round surface of a fan-shaped curved surface or sealing, just obtained needed ideal surface.

Described derivative d ⁿY/dx ⁿPreferred second derivative d ²Y/dx ², i.e. n=2;

Step 1) in, second derivative is the parameter on the vias inner walls surface of sign energy exchange;

Step 2) in, second derivative is a constant, makes the impact of air-flow and working curved surface as much as possible little, thereby noise reduction, reduces energy loss.

Described step 6) in, the source of ten equations and according to being, from the optimal job requirement of serviceability, efficient and energy conversion, and ten equations that write out.

According to similar thinking, also can write out another kind of 15 system of equations or 20 system of equations; Also not necessarily present 36 of unknown numbers may be 50 or 80, and the form of function is quadratic equation not necessarily also, also can be cubic equation, biquadratic equation or equation more in many ways time, at last can be the curve solution out, and the practicality of paying.Therefore, any curved surface except present used flat shape is all within the technical program protection domain.

According to the fourier series principle: any function no matter be trigonometric function, logarithmic function, geometric function etc., can expand into the fourier series that is comprised of polynomial expression.The functional form of each interval functional equation that the technical program adopts is exactly the polynomial expression formula.According to the fourier series principle, the computing method of the functional equation that each is interval are applicable to any mathematical function expression formula.This has just illustrated from mathematical theory: any curved surface except present used flat shape, and all within the technical program protection domain.

Below, the optimal way in conjunction with n=2 further specifies this method:

A kind of design of fluid passage, computing method, step comprises:

1) design of fluid and vias inner walls surface beginning contact phase is shown in Fig. 1 bottom

Interactional power between so-called fluid and the passage and the exchange of energy, with the requirement of optimum Working, running business into particular one to dissolve to release is exactly again:

(1) acting force and energy exchange are as far as possible little, particularly starting point; Power and energy exchange are little just easily to be realized, and, exchange process most effective, Minimal energy loss.

(2) the as far as possible little limit of power and energy exchange is exactly 0; Therefore, we are 0 with regard to the energy exchange that makes starting point;

According to Newton second law: the parameter of sign energy exchange is second derivative d ²Y/dx ², above the mathematic(al) representation of second be: d ²Y/dx ²=0

Be the second derivative d of vias inner walls surface curve ²Y/dx ²It is the parameter on the vias inner walls surface of sign energy exchange;

If the second derivative d of vias inner walls surface curve starting point ²Y/dx ²Equalling zero, namely is to allow the exchange of starting point energy reach desirable ultimate limit state;

(3) second derivative of curve smoothly increases by linear relation after the starting point, so that the work quality in this stage is the most desirable; Linear relation be Newtonian mechanics and occurring in nature the most general, the most basic, the most direct, also be best variation relation, increase by other any curved line relations, all do not reach the perfect condition of linear relation;

2) fluid continues the design in mobile stage on the vias inner walls surface

If should the stage, described second derivative d ²Y/dx ²Be a constant, do not change, make the energy exchange of air-flow and wind scooper curved surface, under the state that does not change, carry out stably, therefore can not produce gas shock or impact as much as possible little, thereby noise reduction, reduce energy loss.

3) fluid acceleration reduces the design in stage

This stage is the reverse procedure of first stage, namely allows second derivative d ²Y/dx ²Equal zero at last by linear relation decline;

4) obtaining acceleration curve by above-mentioned three phases is: an oblique line that makes progress, a horizontal line and a downward oblique line.Cusp has appearred in two intersection point places at three accelerating curves, means the not round and smooth singular point that occurs of acceleration change, and this exchange to energy is disadvantageous.In this, with two quafric curves junction not round and smooth in this acceleration curve is coupled together again, obtain at last desirable accelerating curve;

5) desirable accelerating curve is divided into five intervals, five equations, five curves according to above-mentioned four steps; Each curve has corresponding interval in X-axis, all is in x coordinate axis top, all is positive number.

6) the desirable accelerating curve that five positive acceleration curve combinations obtained above is formed on the right of this curve, oppositely becomes the negative acceleration curve again and re-uses once, thereby obtain a complete desirable accelerating curve, shown in Fig. 1 bottom.

7) with the acceleration equation in ten intervals, integration once obtains the rate equation of desirable wind scooper curve, i.e. curvilinear motion rate equation;

8) step 7) the curvilinear motion rate equation that obtains again integration once obtain consisting of each interval curvilinear equation of vias inner walls surface ideal curve,

9) at the interval of ten curvilinear equation functions, input a series of x numerical value, the curvilinear equation in ten intervals of substitution just obtains vias inner walls surface ideal curve.Shown in Fig. 1 top;

10) ideal curve in the coordinate plane vertical direction, move up and down needed width, perhaps obtain a fan-shaped curved surface or closed circular curved surface around the rotation of some turning axles, be exactly needed ideal surface.

Desirable accelerating curve called after " open auspicious curve ", the ideal surface called after " is opened auspicious curved surface ", five acceleration equations and combinations thereof and once " open auspicious equation " with quadratic integral equation called after accordingly.Open auspicious equation, open auspicious curve and the Kai Rui curved surface can be applied in a lot of technical field, such as blade shape design, the reduced section sub design of pipeline industry and the spoon of blade design of domestic electric fan industry etc. of the blower fan industry of industrial circle.

Simultaneously, open auspicious equation also can be applied in other, technical field more widely.For example: design, the artificial tourist sight of " sand washing gate " correlation surface of hydraulic and electric engineering department, for example: Huangguoshu Waterfall adds one such as the structure of Fig. 9, flying to flow and under waterfall, become the huge colored waterfall landscape of various styles design, change present stiff state.Become rich and varied so that scenery is more graceful.The cost increase is also few.Because it is very high manually to make various fountain costs, uses the ideal surface drainage, only need a small amount of investment, just can reach desirable effect.

Such as the structure of Fig. 9, the accelerating curve that it consists of multiple style waterfall landscape is the combination of some accelerating curves shown in Figure 8.The starting point of a rear accelerating curve and coordinate curve is exactly the terminal point of last accelerating curve and coordinate curve, the horizontal coordinate direction of last curve curve after the tangential direction of its terminal point is exactly.So arrange the combination of designing and calculating several curves out, just consisted of a petal of the waterfall landscape of style design.By adjusting combination and the shape of accelerating curve, just can adjust shape and the size of petal.By the method, can designing and calculating go out any petal of needs and the shape of spending, be placed under the huge waterfall, obtain wanting the shape of any flower, thereby beautify waterfall.

Figure 8 shows that the combined situation of three accelerating curves, simultaneously, the combination of other any shapes and any amount of accelerating curve that meets this method is all within the protection domain of opening auspicious curve and Kai Rui curved surface.

Open that auspicious curve can also be taken apart, segmentation uses.Be a complete cyclic process because open auspicious curved surface, the air-flow in a place, the high efficiency another place that directs into goes.For example the horizontal gas flow below the bumper, cooling effect has been gone on the high efficiency water tank plane that directs into.Sometimes, do not need to carry out complete air-flow conversion and guiding yet, only be fine with a part yet.And effect also can be better.For example: industrial ventilation machine commonly used, domestic fan etc., only need to use the first half section of opening auspicious curve just passable, can play spinoff on the contrary if add the second half section.Here need benly to be: industrial ventilation machine commonly used, domestic fan etc. are out very huge, a very broad application market of auspicious curve.Should be energetically and powerful promotion and application.Open auspicious curve and can also be applied to the design that pipe section changes the planform change procedure of section.

On engineering in the widely used pipeline, no matter be water pipe, tracheae, oil pipe etc., the change procedure in its cross section all is the structure of sudden change formula basically, all will produce fluid impact in process fluid flow, produce eddy current and cause a large amount of consumption, loss and the waste of energy.Employing is opened auspicious curved surface and just can be addressed these problems.On the automobile fan testing table, the structural design that duct cross-section changes section also is mutation structure, has both produced impact, increases energy consumption, has influence on the accuracy of data again, uses and opens auspicious curved surface, can improve precision and the level of fan test stand.

Description of drawings

Accompanying drawing 1 vias inner walls surface ideal curve and desirable accelerating curve;

Accompanying drawing 2 acceleration plots;

Accompanying drawing 3 speed curve diagrams;

Accompanying drawing 4 is opened auspicious curve data figure;

Accompanying drawing 5 dull and stereotyped wind-lead-cover structure figure;

Accompanying drawing 6 automobile cooling system general arrangements;

Accompanying drawing 7 desirable wind-lead-cover structure figure;

Accompanying drawing 8 combination accelerating curves;

Accompanying drawing 9 huge floral part cloth water conservancy diversion surface models.

Among Fig. 5 and Fig. 7,1 is wind scooper.(suggestion deletion this journey, illustration is placed on below the picture specification routinely, adds)

Embodiment

The invention will be further described below in conjunction with accompanying drawing and embodiment.

The wind scooper that this example is used take automobile cooling system is as example.

Commonly use dull and stereotyped wind-lead-cover structure figure as shown in Figure 5, its principal feature is that there is an angle on the windstream and the wind scooper plane that produce owing to running car, such as 30 °.When therefore windstream contacts with the plane wind scooper, will produce impact, this loss of impacting to air current flow kinetic energy is very serious.Powerful kinetic energy is consumed, and be not used for impacting or brushing water tank, play cooling effect.This is a greatly waste.

Now, need to reduce and impact, the flowed energy that slatterns is used, the strong water tank that brushes plays cooling effect.

For the flow state of tissue fluid, desirable gas channel of this routine Technical Design, the place that allows shock-free, smooth and easy, level and smooth the flowing to of air-flow need it to go.Facilitate the wind scooper of this desirable gas channel, in this example, this wind scooper is called " desirable wind scooper ", and the curve of this ideal air current flow is called " desirable wind scooper curve ".The methods analyst of seeking desirable wind scooper curve is as follows:

Interaction between fluid and the wind scooper mainly contains three phases:

1, fluid and wind scooper begin contact phase

This stage should make the impact of air-flow and wind scooper curved surface as much as possible little, thereby noise reduction, reduces energy loss, improves energy conversion efficiency.The key of accomplishing this point is, makes the energy exchange between air-flow and the wind scooper minimum, perhaps is zero.

The parameter of the wind scooper curve the initial segment of sign energy exchange is the second derivative d of curve ²Y/dx ²If the second derivative d of starting point ²Y/dx ²Equal zero, and smoothly increase by linear relation, such as the AB of Fig. 1 " shown in the section, just can make the work quality in this stage the most desirable.

2, fluid continues the mobile stage on the wind scooper surface

This stage should make the impact of air-flow and wind scooper curved surface as much as possible little, thereby noise reduction, reduces energy loss.The method of accomplishing this point is, allows the second derivative d of wind scooper parameter of curve of sign energy exchange ²Y/dx ²Equal a constant, shown in B " C " section of Fig. 1.

3, stage of reducing of fluid acceleration

Two stages of the requirement in this stage and front are identical, but this stage just in time is the reverse procedure of first stage, namely allow the second derivative d of curve ²Y/dx ²Descend by linear relation and to equal zero at last, such as the C of Fig. 1 " shown in the F section.

4, by above-mentioned three phases, accelerating curve AB " C " F can find out that it is not round and smooth from Fig. 1, and the change procedure of this accelerating curve has two sudden changes, two cusps.See it also is undesirable from the angle of energy conversion.For this reason, with two quafric curve B ' C ' and D ' E ' with they round and smooth coupling together.So accelerating curve AB ' C ' D ' E ' F just becomes desirable accelerating curve.

The wind scooper curve that designs according to above-mentioned steps 1～4 is shown in Fig. 1 first half section.

Although the air current flow process is very desirable,, when air-flow left wind scooper, airflow direction rushed at oblique upper, and designing requirement is, air-flow should be that along continuous straight runs rushes at the water tank dead ahead., top step 1～4, utilize once in the other direction more for this reason, obtain whole accelerating curve as shown in Figure 1, just can satisfactorily reach designing requirement.

Obtain last desirable accelerating curve, be depicted as such as Fig. 1 bottom: AB ' C ' D ' E ' FG ' H ' I ' J ' K.Accordingly, desirable wind scooper curve is shown in Fig. 1 middle and upper part.

As can be seen from Figure 1: desirable accelerating curve can be divided into ten intervals, corresponding to ten intervals of X-axle is: AB, BC, CD, DE, EF, FG, GH, HI, IJ, JK.

In order to carry out engineering calculation, the magnitude numerical value in ten intervals is allocated as follows:

Make that AF=D, AK=2D are the sizes that the automobile cooling system global design determines,

Gather and tentative calculation order: AB=BC=DE=EF=FG=GH=IJ=JK=0.15D CD=HI=0.4D through examination

Above the subregion in ten intervals and the title of each subregion point and the numerical value of coordinate points, be indicated in respectively among Fig. 1, on the X coordinate axis.The acceleration equation in these ten intervals is as follows:

A-B d ²y/dx ²＝a ₁₁x BC d ²y/dx ²＝a ₂₀+a ₂₁+a ₂₂x ² C-D d ²y/dx ²＝a ₃

D-E d ²y/dx ²＝a ₄₀+a ₄₁x+a ₄₂x ² E-F d ²y/dx ²＝a ₅₀+a ₅₁x F-G d ²y/dx ²＝a ₅₀+a ₅₁x

G-H d ²y/dx ²＝a ₆₀+a ₆₁x+a ₆₂x ² H-I d ²y/dx ²＝-a3 I-J d ²y/dx ²＝a ₈₀+a ₈₁x+a ₈₂x ²

J-K d ²y/dx ²＝a ₉₀+a ₉₁x

Two equations in top E-F and F-G interval can be merged into an equation, are actually nine equations.

With top nine acceleration equation integrations once, just obtain speed (the being the curvilinear motion rate) equation of desirable wind scooper curve.

A-B?dy/dx＝0.5a ₁₁x ²+C ₁₁ BC dy/dx＝a ₂₀x+0.5a ₂₁x ²+1/3*a ₂₂x ³+C ₂₁

C-D?dy/dx＝a ₃x+C ₃₁ D-E?dy/dx＝a ₄₀x+0.5a ₄₁x ²+1/3*a ₄₂x ³+C ₄₁

E-G?dy/dx＝a ₅₀x+0.5a ₅₁x ²+C ₅₁ G-H?dy/dx＝a ₆₀x+0.5a ₆₁x ²+1/3*a ₆₂x ³+C ₆₁

H-I?dy/dx＝-a ₃x+C ₇₁ I-J?dy/dx＝a ₈₀x+0.5a ₈₁x ²+1/3*a ₈₂x ³+C ₈₁

J-K?dy/dx＝a ₉₀x+0.5a ₉₁x ²+C ₉₁

Integration once just obtains nine curvilinear equations of desirable wind scooper curve again, writes out simultaneously the interval of function.

A-B y＝1/6*a ₁₁x ³+C ₁₁x+C ₁₂ 0.000≤x≤0.15D

B-C y＝0.5a ₂₀x ²+1/6*a ₂₁x ³+1/12*a ₂₂x ⁴+C21x+C ₂₂ 0.15D≤x≤0.30D

C-D y＝0.5a ₃x2+C ₃₁x+C ₃₂ 0.30D≤x≤0.70D

D-E y＝0.5a ₄₀x+1/6*a ₄₁x ³+1/12*a ₄₂x ⁴+C ₄₁x+C ₄₂ 0.70D≤x≤0.85D

E-G y＝0.5a ₅₀x ²+1/6*a ₅₁x ³+C ₅₁x+C ₅₂ 0.85D≤x≤1.15D

G-H y＝0.5a ₆₀x ²+1/6*a ₆₁x ³+1/12*a ₆₂x ⁴+C ₆₁x+C ₆₂ 1.15D≤x≤1.30D

H-I y＝-0.5a ₃x ²+C ₇₁x+C ₇₂ 1.30D≤x≤1.70D

I-J y＝0.5a ₈₀x+1/6*a ₈₁x ³+1/12*a ₈₂x ⁴+C ₈₁x+C ₈₂ 1.70D≤x≤1.85D

J-K y＝0.5a ₉₀x ²+1/6*a ₉₁x ³+C ₉₁x+C ₉₂ 1.85D≤x≤2.00D

Solve the ideal curve that top nine equations just obtain this wind scooper.

In this example, the method for solving of above-mentioned nine equations is:

Obtain 36 unknown numbers in nine equations, as follows:

a ₁₁?C ₁₁?C ₁₂?a ₂₀?a ₂₁?a ₂₂?C ₂₁?C ₂₂?a ₃?C ₃₁?C ₃₂?a ₄₀?a ₄₁?a ₄₂?C ₄₁?C ₄₂?a ₅₀?a ₅₁?C ₅₁

C ₅₂?a ₆₀?a ₆₁?a ₆₂?C ₆₁?C ₆₂?C ₇₁?C ₇₂?a ₈₀?a ₈₁?a ₈₂?C ₈₁?C ₈₂?a ₉₀?a ₉₁?C ₉₁?C ₉₂

Want to ask 36 unknown numbers, need 36 equations.Above the characteristics of nine equations be at middle point symmetry, so minutes two sections find the solution.

The first step is asked first 20 unknown numbers of five curves in front, needs to seek 20 equations, and the process of seeking 20 equations is as follows:

Determine 10 unknowm coefficient a by five acceleration equations ₁₁a ₂₀a ₂₁a ₂₂a ₃a ₄₀a ₄₁a ₄₂a ₅₀a ₅₁

By the continuous and shock-free boundary condition of accelerating curve, it is as follows to set up nine equations: referring to the bottom of Fig. 1.

B ' the condition of continuity is two curvilinear equations about B ', equates at B ' acceleration, is expressed as with mathematical expression:

0.15Da ₁₁=a ₂₀+ 0.15Da ₂₁+ (0.15D) ²a ₂₂1. slope equates a ₁₁=a ₂₁+ 2*0.15Da ₂₂2.

C ' continuous a ₂₀+ 0.3Da ₂₁+ (0.3D) ²a ₂₂=a ₃3. slope equates a ₂₁+ 2*0.3Da ₂₂=0 ... 4.

D ' continuous a ₃=a ₄₀+ 0.7Da ₄₁+ (0.7D) ²a ₄₂5. slope equates a ₄₁+ 2*0.7Da ₄₂=0 ... 6.

E ' continuous a ₄₀+ 0.85Da ₄₁+ (0.85D) ²a ₄₂=a ₅₀+ 0.85Da ₅₁7.

Slope equates a ₄₁+ 2*0.85Da ₄₂=a ₅₁8.

F point acceleration is zero a ₅₀+ Da ₅₁=0 ... 9.

As seen, 10 unknown numbers only have 9 solution of equations not out.Set first the coefficient a an of the unknown for this reason ₃Just can solve other nine unknown numbers.On engineering concept, preset exactly the acceleration of a maximum, the problem that solution party's number of passes amount is inadequate.In the practical operation, select an acceleration a ₃, after all equation solves, calculate height overall H.If from designing requirement height overall H different, then, select again an acceleration a ₃, the overall process above repeating, until the height overall that calculates equates with the height overall of designing requirement or error within the scope of our regulation, then calculating end.

On mathematical method, a ₃It is an object that examination is gathered.This method of dealing with problems is called method of trial and error.This method of trial and error is easy to realize with computing machine.Concrete computation process is as follows.

After making a3=0.01 substitution equation 3., 5. put in order:

Separate this Simultaneous Equations with the method for matrix.For simplifying computation process, minute two groups of simultaneous solutions.

Equation is simultaneous 1.-4., order

$K=\left(\begin{array}{cccc}1& 0& -1& 0.3D\\ -0.15\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="HDA0000072698200000011.png,HDA0000072698200000021.png"\; state="\{\{state\}\}">D</figure-callout>}& 1& 0.15D& {\left(0.15D\right)}^2\\ 0& 1& 0.3D& {\left(0.3D\right)}^2\\ 0& 0& 1& 0.6D\end{array}\right)$ $A=\left(\begin{array}{c}{a}_{11}\\ a_{20}\\ a_{21}\\ a_{22}\end{array}\right)$ $B=\left(\begin{array}{c}0\\ 0\\ 0.01\\ 0\end{array}\right)$

1.-4. substitution gets: KA=B A=K ^-1B has just solved unknown number a ₁₁a ₂₀a ₂₁a ₂₂

Equation is simultaneous 5.-9., order

$J=\left(\begin{array}{ccccc}1& 0.7D& {\left(0.7D\right)}^2& 0& 0\\ 0& 1& 1.4\mathrm{<figure-callout\; id="0"\; label="D"\; filenames="HDA0000072698200000011.png,HDA0000072698200000012.png"\; state="\{\{state\}\}">D</figure-callout>}& 0& 0\\ 1& 0.85D& {\left(0.85D\right)}^2& -1& -0.85\mathrm{<figure-callout\; id="0"\; label="D"\; filenames="HDA0000072698200000011.png,HDA0000072698200000012.png"\; state="\{\{state\}\}">D</figure-callout>}\\ 0& 1& 1.7D& 0& -1\\ 0& 0& 0& 1& D\end{array}\right)$ $P=\left(\begin{array}{c}{a}_{40}\\ a_{41}\\ a_{42}\\ a_{50}\\ a_{51}\end{array}\right)$ $Q=\left(\begin{array}{c}0.01\\ 0\\ 0\\ 0\\ 0\end{array}\right)$

5.-9. substitution gets: JP=Q P=J-1Q has just solved unknown number a ₄₀a ₄₁a ₄₂a ₅₀a ₅₁

So far, add a selected unknown number a ₃, all solution is out for the coefficient of 10 the unknowns.

Determine now 10 remaining unknown numbers of curvilinear equation, namely 10 integration constants.Source or the boundary condition of finding the solution the equation of 10 integration constants remains continuously (functional value of subregion point left and right sides curvilinear equation equate) and without impacting (slope of subregion point left and right sides curvilinear equation is equal).

The A point is by y=1/6*a ₁₁x ³+ C ₁₁X+C ₁₂The y=0 substitution gets C during with starting point boundary condition x=0 ₁₂=0

By dy/dx=0.5a ₁₁x ²+ C ₁₁Dy/dx=V during with starting point boundary condition x=0 ₀Substitution gets C ₁₁=0

V wherein ₀Be initial velocity, i.e. the air-flow initial deflection speed of air-flow and wind scooper contact point.According to smooth-going, shock-free requirement, choosing air-flow initial deflection speed is 0, i.e. V ₀=0.

The below continues to ask remaining 8 integration constant.

B point slope equates 0.5a ₁₁x ²+ C ₁₁=a ₂₀X+0.5a ₂₁x ²+ 1/3*a ₂₂x ³+ C ₂₁X=0.15D

Transformation equation is tried to achieve C ₂₁=0.5a ₁₁x ²+ C ₁₁-a ₂₀X-0.5a ₂₁x ²-1/3*a ₂₂x ³X=0.15D

Continuous 1/6*a ₁₁x ³+ C ₁₁X+C ₁₂=0.5a ₂₀x ²+ 1/6*a ₂₁x ³+ 1/12*a ₂₂x ⁴+ C ₂₁X+C ₂₂X=0.15D

C is tried to achieve in conversion ₂₂=1/6*a ₁₁x ³+ C ₁₁X+C ₁₂-0.5a ₂₀x ²-1/6*a ₂₁x ³-1/12*a ₂₂x ⁴-C ₂₁X x=0.15D

C point slope equates a ₂₀X+0.5a ₂₁x ²+ 1/3*a ₂₂x ³+ C ₂₁=a ₃X+C ₃₁X=0.3D

C is tried to achieve in conversion ₃₁=a ₂₀X+0.5a ₂₁x ²+ 1/3*a ₂₂x ³+ C ₂₁-a ₃X x=0.3D

Continuous 0.5a ₂₀x ²+ 1/6*a ₂₁x ³+ 1/12*a ₂₂x ⁴+ C ₂₁X+C ₂₂=0.5a ₃x ²+ C ₃₁X+C ₃₂X=0.3D

C is tried to achieve in conversion ₃₂=0.5a ₂₀x ²+ 1/6*a ₂₁x ³+ 1/12*a ₂₂x ⁴+ C ₂₁X+C ₂₂-0.5a ₃x ²-C ₃₁X x=0.3D

D point slope equates a ₃X+C ₃₁=a ₄₀X+0.5a ₄₁x ²+ 1/3*a ₄₂x ³+ C ₄₁X=0.7D

C is tried to achieve in conversion ₄₁=a ₃X+C ₃₁-a ₄₀X-0.5a ₄₁x ²-1/3*a ₄₂x ³X=0.7D

Continuous 0.5a ₃x ²+ C ₃₁X+C ₃₂=0.5a ₄₀x ²+ 1/6*a ₄₁x ³+ 1/12*a ₄₂x ⁴+ C ₄₁X+C ₄₂X=0.7D

C is tried to achieve in conversion ₄₂=0.5a ₃x ²+ C ₃₁X+C ₃₂-0.5a ₄₀x ²-1/6*a ₄₁x ³-1/12*a ₄₂x ⁴-C ₄₁X x=0.7D

E point slope equates a ₄₀X+0.5a ₄₁x ²+ 1/3*a ₄₂x ³+ C ₄₁=a ₅₀X+0.5a ₅₁x ²+ C ₅₁X=0.85D

C is tried to achieve in conversion ₅₁=a ₄₀X+0.5a ₄₁x ²+ 1/3*a ₄₂x ³-a ₅₀X-0.5a ₅₁x ²X=0.85D

Continuous 0.5a ₄₀x ²+ 1/6*a ₄₁x ³+ 1/12*a ₄₂x ⁴+ C ₄₁X+C ₄₂=0.5a ₅₀x ²+ 1/6*a ₅₁x ³+ C ₅₁X+C ₅₂X=0.85D

C is tried to achieve in conversion ₅₂=0.5a ₄₀X+1/6*a ₄₁x ³+ 1/12*a ₄₂x ⁴+ C ₄₁X+C ₄₂-0.5a ₅₀x ²-1/6*a ₅₁x ³-C ₅₁X x=0.85D

So far, 20 unknowm coefficients and integration constant have all been obtained.20 coefficients and the integration constant that is to say 5 curvilinear equations of desirable wind-guiding curve previous section have been known numbers all.

Second step is obtained 16 unknown numbers of four remaining equations.Its mathematical procedure of finding the solution is similar to the mathematical procedure of finding the solution of top 20 unknown numbers, therefore, and Palingraphia here not just.

Hereto, 36 coefficients and the integration constant of nine curvilinear equations of desirable wind-guiding curve have all been found the solution out, all are known numbers.The x (can get an x numerical value every 2mm or 3mm in the practical operation) of the corresponding interval whole points of nine curvilinear equations of substitution again, just can obtain y value corresponding to all x, level and smooth coupling together of point (x, y) all just consisted of desirable wind-guiding curve.

The below calculates acceleration plots, speed curve diagram, the curve data figure of desirable wind scooper curve, shown in Fig. 2,3,4 take the structural parameters of certain vehicle as example.

The vertical direction of desirable wind-guiding curve along Calculation Plane, move up and down needed width again, just consisted of desirable wind-guiding curved surface.

The above has illustrated the wind scooper of gas channel lower surface, and to the guiding of windstream and mobile organizational process.The following describes the air current composition of two sides of wind scooper.

Under the prerequisite that the global design of automobile face shield is allowed, the leader of front portion, wind scooper side should be wider as far as possible, so that head-on incoming air area is large as much as possible, the air quantity that enters is some more as much as possible, in guided procedure, progressively diminish, become at last the same width of heating radiator.The same employing of this guided procedure is opened auspicious curved surface and is finished.

Therefore whole desirable wind scooper is made of three desirable wind-guiding curved surfaces altogether.Adopt the larger excessive R15-R20 of fillet in side and bottom surface intersection.

Above-mentioned desirable wind scooper curve is " opening auspicious curve ", desirable wind scooper curved surface and is that " opening auspicious curved surface ", desirable wind scooper are called " opening auspicious wind scooper ", nine equations and combination thereof and corresponding integral equation is called " opening auspicious equation ".

Does the below describes with regard to the flow field problem of curve negative pressure direction: how negative acceleration obtain? can obtain? because air-flow is the larger fluid of a kind of degree of freedom, give its positive acceleration, it is easy forcing it to flow to some directions.But the physical concept of negative acceleration is exactly: by the design of shape, produce vacuum tightness, airstream suction is come on designed curvilinear path and path.This thinking? can be all right?

Answer as follows:

1, attract air-flow with vacuum tightness, the application on engineering is that non-constant width is wide.Such as; The fluid of the breathing process of internal combustion engine, all air pumps, liquid pump advances the pump process until production process of nature wind etc. all is by vacuum tightness fluid to be attracted to come, thereby produces the continuously course of work.

2, open the vacuum tightness that auspicious curved surface produces, it is very little beginning, and then be progressively slowly to increase, and the speed of increase is smaller, and fluid ratio is easier to adapt to, than the curvilinear motion that is easier to by design.

3, take this wind scooper as example, air-flow is from the process of following upward guiding, to push with the air-flow that another top strand come in from air inlet, this extruding force just in time promotes air-flow to the negative pressure direction of opening auspicious curved surface generation, so air-flow just can flow by the streamline of opening auspicious curved design very smoothly.

From the reason explanation of above three aspects:, the motion of opening auspicious curve negative pressure direction is rational, establishment, normal.

By the desirable wind scooper that this method design obtains, its curve form guarantees that the energy and the impulsive force that maximally utilise windstream come cooling water tank, and the energy of windstream and impulsive force have been applied to ultimate limit state.Existing energy has been used optimum condition, from another perspective, saved exactly energy resource consumption, so this is again invention and the patent of a low-carbon (LC) life.Therefore opening auspicious equation is the low-carbon (LC) equation.

Open auspicious equation and can also be applied in other more widely technical field.For example: design, the artificial tourist sight of " sand washing gate " correlation surface of hydraulic and electric engineering department, for example: Huangguoshu Waterfall adds one such as the structure of Fig. 9, flying to flow and under waterfall, become the huge colored waterfall landscape of various styles design, change present stiff state.Become rich and varied so that scenery is more graceful.The cost increase is also few simultaneously.Because it is very high manually to make various fountain costs, uses the ideal surface drainage, only need a small amount of investment, just can reach desirable effect.

Be a complete cyclic process because open auspicious curved surface, the air-flow in a place, the high efficiency another place that directs into goes.For example the horizontal gas flow below the bumper, cooling effect has been gone on the high efficiency water tank plane that directs into.

Open auspicious curve and can also be applied to the design that pipe section changes the planform variation of section.Automobile fan testing table particularly, duct cross-section changes on the structural design of section.The pipe section that adopts in the present whole world changes the planform of section, no matter is water pipe, oil pipe and tracheae, is mutation structure basically.This structure causes the flow state of fluid to undergo mutation, and produces impact, eddy current, mixed flow etc., causes energy loss and energy dissipation.Employing is opened after the auspicious curved surface, can save a large amount of energy, is the design of a worth spread really.

In automobile wind tunnel test, the construction of wind tunnel that national standard is used, the variation of the direction of gas velocity and size also is a kind of structure of sudden change, and test accuracy is had certain harmful effect, adopts and opens after the auspicious curved surface, can improve test accuracy.Will be helpful to improving the test level.

And so on, open auspicious equation and will be applied in numerous fields such as very broad technology, life and test.

Claims (3)

1. the design of a fluid passage, computing method is characterized in that, according to the form arrangement of the interaction force between fluid and the passage with the best, a minute three phases designs respectively:

1) design of fluid and vias inner walls surface beginning contact phase:

The derivative d of vias inner walls surface curve ⁿY/dx ⁿParameter as the vias inner walls surface; Described derivative is second derivative or higher derivative;

If the derivative d of vias inner walls surface curve starting point ⁿY/dx ⁿEqual zero, and smoothly increase by linear relation, so that the work quality in this stage is the most desirable;

2) fluid continues the design in mobile stage on the vias inner walls surface:

If should the stage, described derivative d ⁿY/dx ⁿBe a constant, make the impact of air-flow and working curved surface as much as possible little;

3) the derivative d that fluid is corresponding ⁿY/dx ⁿReduce the design in stage:

This stage is the reverse procedure of the design of step 1) fluid and vias inner walls surface beginning contact phase, namely allows derivative d ⁿY/dx ⁿEqual zero at last by linear relation decline;

4) obtain derivative d by above-mentioned three phases ⁿY/dx ⁿCorresponding curve uses n curve with this derivative d again ⁿY/dx ⁿNot round and smooth junction smooth connection is got up in the corresponding curve, obtains at last the ideal operation curve;

5) corresponding above-mentioned four steps of ideal operation curve are divided into five intervals;

6) ideal operation curve shape obtained above along the symmetrical projection of X-axis, obtain the negative curve of ideal operation curve, again this negative curve integrated moving forward, and end to end with the ideal operation curve, with regard to the ideal operation curve of complete; This complete ideal operation curve is made of ten intervals, ten function curves altogether;

7) functional equation that each is interval carries out integration n time, obtains each interval curvilinear equation of complete ideal operation curve;

8) at the interval of each curvilinear equation function, input a series of x numerical value, each interval curvilinear equation of substitution just obtains vias inner walls surface ideal curve;

9) ideal curve on the direction perpendicular to coordinate plane, move up and down needed width, perhaps ideal curve is rotated around some turning axles, obtain the round surface of a fan-shaped curved surface or sealing, just obtained needed ideal surface.

2. the design of fluid passage as claimed in claim 1, computing method is characterized in that described derivative d ⁿY/dx ⁿSecond derivative d ²Y/dx ², i.e. n=2;

In the step 1), second derivative is the parameter on the vias inner walls surface of sign energy exchange;

Step 2) in, second derivative is a constant, makes the impact of air-flow and working curved surface as much as possible little, thereby noise reduction, reduces energy loss.

3. the design of fluid passage as claimed in claim 1, computing method, it is characterized in that: in the described step 6), the source of ten functions and according to being, from the optimal job requirement of serviceability, efficient and energy conversion, and ten functional equations that write out.

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