CN103870626A - Type line design and check method for impeller meridian plane of radial-axial turbine expander - Google Patents

Abstract

The invention discloses a type line design and check method for an impeller meridian plane of a radial-axial turbine expander. The type line design and check method comprises the following main steps of reading in basic parameters of the impeller meridian plane; selecting a two-dimensional coordinate system of the meridian plane; calculating point coordinates of an input and an exit of a hub and shroud curve; giving an initial equation index value by adopting a generalized elliptic equation according to known parameters and solving a hub and shroud curvilinear equation; solving the arc length of the curve from the input to the output, dividing the arc length of the curve into N equal parts, solving the coordinates of equal diversion points according to the curvilinear equation, thus calculating the through-flow area at constant current contour position, and drawing with the flow line position as a horizontal coordinate and the through-flow area of the flow line position as a longitudinal coordinate; judging whether a flow channel meets the requirement or not, if so, outputting the point coordinates of the hub and shroud curve of the meridian plane, and if not, adjusting curvilinear equation indexes ph and qh or ps and qs and recalculating. According to the method provided by the invention, the design process is simpler, more convenient and quicker; the reference for checking smoothing changes of the flow channel is more visual and reliable; in addition, the processing and the manufacturing of subsequent impellers are facilitated.

Description

The axial-flow expansion turbine impeller meridian surface shape design of a kind of footpath and check method

Technical field

The present invention relates to the design of turbomachinery impeller meridian ellipse, particularly relate to the axial-flow expansion turbine impeller meridian surface shape design of a kind of footpath and check method.

Background technology

Impeller is the main flow passage component of turbomachinery, its performance has decisive role to overall performance, meridian surface shape directly affects the fluidal texture of impeller inside, in the axial-flow expansion turbine of footpath, the method that tradition adopts is that meridian ellipse curve is regarded as by circular arc and straight-line segment and formed, on the basis of empirical data, be estimated to take arc radius, build meridian ellipse, after then meridian ellipse runner being launched with mapping software, check with a series of envelope circles, be progressively modified to the runner that fairing changes.Such geometric modeling method, there is the shortcoming of three aspects:: the one, traditional design method is drawing method of trial and error, if envelope circle has a condition that can not meet fairing, need to revise flow channel shape, restarting to do envelope circle from import checks, or in the time there is a large amount of candidate's impeller, need these impeller meridian ellipses to design one by one and the check of envelope circle, this makes workload larger; The 2nd, whether the tangent line of the envelope circle both sides after runner launches of the check in traditional design method approaches the foundation that straight line changes as fairing, this method is confined in two dimension judgement, do not calculate the flow area of three-dimensional lower flow channel, basis for estimation does not have enough cogencyes; The 3rd, traditional design and check method need to be realized by drawing, and there is no digitizing, be not easy to integral wheel three-dimensionally shaped with the follow-up work such as processing and runner numerical simulation.

Summary of the invention

The problem existing in order to solve prior art, the object of the present invention is to provide the axial-flow expansion turbine impeller meridian surface shape design of a kind of footpath and check method, this method utilization programming is according to the mathematic(al) representation of meridian ellipse Parameter Calculation meridian ellipse runner molded line and calculate the variation tendency of flow area with streamline position, it is characterized in that one is by programming, meridian surface shape mathematical expression to be expressed, design process is easier, quick, and can draw soon the variation of meridian surface shape when a certain basic parameter of meridian ellipse changes; The 2nd, by calculate three-dimensional lower flow channel flow area check runner whether fairing change, more directly with there is cogency; The 3rd, by meridian ellipse design and check digitizing, facilitate integral wheel three-dimensionally shaped with the follow-up work such as processing and runner numerical simulation.

In order to address the above problem, the present invention adopts following technical scheme:

The axial-flow expansion turbine impeller meridian surface shape design of a kind of footpath and check method, comprise the steps:

Illustrate: following " subscript 1 " represents import, " subscript 2 " represents outlet, and " subscript h " represents hub curve, i.e. wheel disc baseline, and " subscript s " represents shroud curve, i.e. wheel cap baseline or leaf top line;

Step 1, read in impeller meridian ellipse basic parameter: inlet diameter D ₁, the high L of leaf ₁, outlet outer diameter D ' ₂and outlet inner diameter D " ₂, axially overall width B _t, hub curve is imported and exported cone angle beta _1hand β _2h(a certain angle of pointing out tangent line and axis on wheel disc baseline), shroud curve is imported and exported cone angle β _1sand β _{β s}(a certain angle of pointing out tangent line and axis on wheel cap baseline or leaf top line);

Step 2, selected meridian ellipse two-dimensional coordinate system, taking impeller axis and against airflow direction as Z axis forward, vertical axis and be R axle forward from blade root to leaf top direction, taking impeller meridian ellipse egress line elongated segment line and Z axis intersection point as initial point, impeller meridian ellipse hub and shroud curve ingress-egress point coordinate are respectively:

$\left\{\begin{array}{c}{z}_{1h}=B_t,r_{1h}={\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="HDA0000432210210000011.png,HDA0000432210210000022.png"\; state="\{\{state\}\}">D</figure-callout>}}_1/2\\ z_{1s}=B_t-{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="HDA0000432210210000011.png,HDA0000432210210000022.png"\; state="\{\{state\}\}">L</figure-callout>}}_1,r_{1s}={\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="HDA0000432210210000011.png,HDA0000432210210000022.png"\; state="\{\{state\}\}">D</figure-callout>}}_1/2\\ z_{2h}={0,r}_{2h}={{\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="HDA0000432210210000011.png,HDA0000432210210000022.png"\; state="\{\{state\}\}">D</figure-callout>}}_2^{\&prime;\&prime;}}_{}/2\\ z_{2s}={0,r}_{2h}={\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="HDA0000432210210000011.png,HDA0000432210210000022.png"\; state="\{\{state\}\}">D</figure-callout>}}_2^{\&prime;}/2\end{array}\right.$

Step 3, according to known parameters, adopt broad sense elliptic equation general expression:

${\left(\frac{z+a}{b}\right)}^p+{\left(\frac{r+c}{d}\right)}^q=1---\left(1\right)$

R to the first order derivative of z is:

$\tan \mathrm{\&beta;}=r^{\&prime;}=\frac{\mathrm{dr}}{\mathrm{dz}}=-\frac{p}{q}\frac{d}{b}{\left(\frac{z+a}{b}\right)}^{p-1}{\left(\frac{r+c}{d}\right)}^{1-q}---\left(2\right)$

Solve respectively hub curve and shroud curvilinear equation:

Step 3.1, solve hub curvilinear equation, the value of the initial index p of given equation and q is p _hand q _h; Make z ₁=z _1h, r ₁=r _1hand z ₂=z _2h, r ₂=r _2hrespectively in substitution equation (1); Make β ₁=β _1h, β ₂=β _2hrespectively in substitution equation (2).This shows, have four unknown numbers of four equations, according to turbo-expander actual conditions, solving equation group is discussed:

1), when radial air inlet, while axially giving vent to anger, i.e. β ₁=90 ° and β ₂=0 °, r ₁' → ∞ and r ₂'=0, try to achieve:

a _h=-z ₂，b _h=z ₁-z ₂，c _h=-r ₁，d _h=r ₂-r ₁ （3）

2), when inducer have certain pitch angle, while axially giving vent to anger, r ₁' be a finite value and r ₂'=0, try to achieve:

$\left\{\begin{array}{c}\frac{{\mathrm{<figure-callout\; id="1"\; label="p\; h\; r"\; filenames="HDA0000432210210000011.png,HDA0000432210210000022.png"\; state="\{\{state\}\}">p</figure-callout>}}_h}{{r_{}}^{}}[1-{\left(\frac{{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA0000432210210000011.png,HDA0000432210210000022.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="c\; h\; r"\; filenames="HDA0000432210210000011.png,HDA0000432210210000022.png"\; state="\{\{state\}\}">c</figure-callout>}}_h}{r_{}}\right)}^{q_h}]+\frac{{\mathrm{<figure-callout\; id="2"\; label="q\; h\; r"\; filenames="HDA0000432210210000011.png,HDA0000432210210000022.png"\; state="\{\{state\}\}">q</figure-callout>}}_h}{r_{}}{\left(\frac{{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA0000432210210000011.png,HDA0000432210210000022.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="c\; h\; r"\; filenames="HDA0000432210210000011.png,HDA0000432210210000022.png"\; state="\{\{state\}\}">c</figure-callout>}}_h}{r_{}}\right)}^{q_h-1}=0\\ a_h=-z_2\\ d_h=r_2+c_h\\ b_h=(z_1-z_2){[1-{\left(\frac{{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA0000432210210000011.png,HDA0000432210210000022.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="c\; h\; r"\; filenames="HDA0000432210210000011.png,HDA0000432210210000022.png"\; state="\{\{state\}\}">c</figure-callout>}}_h}{r_{}}\right)}^{q_h}]}^{-1/p_h}\end{array}\right.---\left(4\right)$

3), in the time that inducer has certain pitch angle, outlet section also to have certain pitch angle, i.e. r ₁' and r ₂' be finite value, by being rotated counterclockwise coordinate system β ₂, making curve outlet section pitch angle is 0, this kind of situation becomes 2), then carry out the equation solution of curvilinear equation, then calculate by coordinate conversion:

z _R=zcosβ ₂+rsinβ ₂ （5）

r _R=-zsinβ ₂+rcosβ ₂

Can obtain the coordinate of former coordinate system lower curve;

Step 3.2, solve shroud curvilinear equation, the value of given original equation index p and q is p _sand q _s, make z ₁=z _1s, r ₁=r _1s, z ₂=z _2s, r ₂=r _2sand β ₁=β _1s, β ₂=β _2s, other obtains shroud curvilinear equation as follows with step 3.1:

1), when radial air inlet, while axially giving vent to anger, i.e. β ₁=90 ° and β ₂=0 °, r ₁' → ∞ and r ₂'=0, try to achieve:

a _s=-z ₂，b _s=z ₁-z ₂，c _s=-r ₁，d _s=r ₂-r ₁ （6）

2), when inducer have certain pitch angle, while axially giving vent to anger, r ₁' be a finite value and r ₂'=0, try to achieve:

$\left\{\begin{array}{c}\frac{{\mathrm{<figure-callout\; id="1"\; label="p\; s\; r"\; filenames="HDA0000432210210000011.png,HDA0000432210210000022.png"\; state="\{\{state\}\}">p</figure-callout>}}_s}{{r_{}}^{}}[1-{\left(\frac{{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA0000432210210000011.png,HDA0000432210210000022.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="c\; s\; r"\; filenames="HDA0000432210210000011.png,HDA0000432210210000022.png"\; state="\{\{state\}\}">c</figure-callout>}}_s}{r_{}}\right)}^{q_s}]+\frac{{\mathrm{<figure-callout\; id="2"\; label="q\; s\; r"\; filenames="HDA0000432210210000011.png,HDA0000432210210000022.png"\; state="\{\{state\}\}">q</figure-callout>}}_s}{r_{}}{\left(\frac{{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA0000432210210000011.png,HDA0000432210210000022.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="c\; s\; r"\; filenames="HDA0000432210210000011.png,HDA0000432210210000022.png"\; state="\{\{state\}\}">c</figure-callout>}}_s}{r_{}}\right)}^{q_s-1}=0\\ a_s=-z_2\\ d_s={\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HDA0000432210210000011.png,HDA0000432210210000022.png"\; state="\{\{state\}\}">r</figure-callout>}}_2+c_s\\ b_s=(z_1-z_2){[1-{\left(\frac{{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA0000432210210000011.png,HDA0000432210210000022.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="c\; s\; r"\; filenames="HDA0000432210210000011.png,HDA0000432210210000022.png"\; state="\{\{state\}\}">c</figure-callout>}}_s}{r_{}}\right)}^{q_s}]}^{-1/p_s}\end{array}\right.---\left(7\right)$

3), in the time that inducer has certain pitch angle, outlet section also to have certain pitch angle, i.e. r ₁' and r ₂' be finite value, by being rotated counterclockwise coordinate system β ₂, making curve outlet section pitch angle is 0, this kind of situation becomes 2), then carry out the equation solution of curvilinear equation, then calculate by coordinate conversion:

z _R=zcosβ ₂+rsinβ ₂ （8）

r _R=-zsinβ ₂+rcosβ ₂

Can obtain the coordinate of former coordinate system lower curve;

Step 4, solve the flow area at constant current contour sectional position place:

Step 4.1, according to hub curve and bent shroud line curvilinear equation, the arc length of calculated curve from import to outlet section respectively, method is: curve Z coordinate is divided into N section, and described N gets the degree of accuracy of calculating to improve arc length greatly as far as possible, obtains N+1 Z coordinate zz including ingress-egress point ₁, zz ₂..., zz _k..., zz _n+1, in substitution formula (1), try to achieve corresponding R coordinate rr respectively ₁, rr ₂..., rr _k..., rr _n+1, the distance of calculating between adjacent 2 is sued for peace and just can be obtained out the arc length L of curve all distances again;

The flow area of step 4.2, calculating constant current contour position, does not consider the thick impact on flow area of leaf, and its method is: curve arc long L is divided into N section, and the length of each section is L/N, and utilizing dichotomy to try to achieve on the coordinate hub curve of Along ent is (zh ₁, rh ₁), (zh ₂, rh ₂) ..., (zh _k, rh _k) ..., (zh _n+1, rh _n+1), on shroud curve, be (zs ₁, rs ₁), (zs ₂, rs ₂) ..., (zs _k, rs _k) ..., (zs _n+1, rs _n+1), connecting K point and shroud curve K point on hub curve, the area that gained line segment rotates gained around axis is the flow area that streamline position 1/ (K-1) is located, and its calculating formula of deriving is:

$S_K=\mathrm{\&pi;}{[1+{\left(\frac{{\mathrm{zs}}_K-{\mathrm{zh}}_K}{{\mathrm{rs}}_K-{\mathrm{rh}}_K}\right)}^2]}^{0.5}({{\mathrm{rs}}_K}^2-{{\mathrm{rh}}_K}^2)---\left(9\right)$

Step 4.3, note inflow point's streamline position are 0, and streamline position, exit is 1, K point (zh of hub curve _k, rh _k) or K point (zs of shroud curve _k, rs _k) the streamline position located is 1/(K-1), taking streamline position as horizontal ordinate, the flow area of this streamline position is that ordinate is drawn, and can obtain the change curve of flow area with streamline position;

Step 5, can judge the whether smooth or whether realistic requirement of design of meridian ellipse runner according to flow area with the change curve of streamline position; If so, export the point coordinate of meridian ellipse hub curve and shroud curve, if not, revise equation index p _hand q _hor p _sand q _s, then return to step 3 and recalculate.

Step 1 of the present invention, step 2 and step 3 are method for designing, by programming, meridian ellipse shape are expressed by mathematical expression, and design process is easier, quick, and can draw soon the variation of meridian ellipse shape when a certain basic parameter of meridian ellipse changes; Step 4 and step 5 are check method, by calculate three-dimensional lower flow channel flow area check runner whether fairing change, more directly with there is cogency; Two parts content is by meridian ellipse design and check digitizing, facilitate integral wheel three-dimensionally shaped with the follow-up work such as processing and runner numerical simulation.

Brief description of the drawings

Fig. 1 is the schematic flow sheet of footpath of the present invention axial-flow expansion turbine meridian ellipse design and check method;

Fig. 2 is the selected schematic diagram of meridian ellipse basic parameter of the present invention and two-dimensional coordinate system;

Fig. 3 is that the present invention solves curvilinear equation coordinate system conversion schematic diagram;

Fig. 4 is the schematic diagram that the present invention calculates constant current contour position flow area;

Fig. 5 is the variation diagram of the flow area that calculates of the present invention with streamline position;

Fig. 6 is meridian ellipse hub and the shroud curve map of twice calculating of Fig. 5, wherein: Fig. 6 a calculates meridian ellipse hub and the shroud curve map that I obtains, and Fig. 6 b calculates meridian ellipse hub and the shroud curve map that II obtains.

embodiment

Taking the supporting turbo-expander of the empty point flow process of certain mesohigh as embodiment, turbo-expander design parameter and impeller structural dimensions be as table 1, and for axially giving vent to anger.

Table 1 turbo-expander design parameter and impeller structural dimensions

Design according to the following steps (represent import with " subscript 1 ", " subscript 2 " represents outlet, and " subscript h " represents hub curve, i.e. wheel disc baseline, " subscript s " represents shroud curve, i.e. wheel cap baseline or leaf top line):

Step 1, read in impeller meridian ellipse basic parameter: inlet diameter D ₁the high L of=206mm and leaf ₁=10mm, outlet outer diameter D ' ₂=140mm and outlet inner diameter D " ₂=42mm, axially overall width, hub curve is imported and exported cone angle beta _1h=90 ° and β _2h=0 °, shroud curve is imported and exported cone angle beta _1s=90-37=53 ° and β _2s=0 °;

Step 2, selected meridian ellipse two-dimensional coordinate system, as shown in Figure 2, taking impeller axis and against airflow direction as Z axis forward, vertical axis and be R axle forward from blade root to leaf top direction, taking impeller meridian ellipse egress line elongated segment line and Z axis intersection point as initial point, impeller meridian ellipse hub and shroud curve ingress-egress point coordinate are respectively:

z _1h=B _t=72，r _1h=D ₁/2=103；z _1s=B _t-L ₁=62，r _1s=D ₁/2=103；

z _2h=0，r _2h=D″ ₂/2=21；z _2s=0，r _2s=D′ ₂/2=70；

Step 3, according to known parameters, adopt broad sense elliptic equation general expression:

${\left(\frac{z+a}{b}\right)}^p+{\left(\frac{r+c}{d}\right)}^q=1$

R to the first order derivative of z is:

$\tan \mathrm{\&beta;}=r^{\&prime;}=\frac{\mathrm{dr}}{\mathrm{dz}}=-\frac{p}{q}\frac{d}{b}{\left(\frac{z+a}{b}\right)}^{p-1}{\left(\frac{r+c}{d}\right)}^{1-q}$

Solve respectively hub and shroud curvilinear equation, will calculate for the first time and be designated as calculating I:

Step 3.1, solve hub curvilinear equation, the value of the initial index p of given equation and q is p _h=2 and q _h=2; Make z ₁=z _1h, r ₁=r _1hand z ₂=z _2h, r ₂=r _2hsubstitution equation respectively

in; Make β ₁=β _1hand β ₂=β _2hsubstitution equation respectively $\tan \mathrm{\&beta;}=r^{\&prime;}=\frac{\mathrm{dr}}{\mathrm{dz}}=-\frac{p}{q}\frac{d}{b}{\left(\frac{z+a}{b}\right)}^{p-1}{\left(\frac{r+c}{d}\right)}^{1-q}$ In.This shows, have four unknown numbers of four equations, due to hub curve radial air inlet, import coning angle is β ₁=90 °, export as axially giving vent to anger outlet cone angle beta ₂=0 °, solution of equations is:

a=-z ₂=0；b=z ₁-z ₂=72;c=-r ₁=-103;d=r ₂-r ₁=-82;

Hub curvilinear equation is:

${\left(\frac{z}{72}\right)}^2+{\left(\frac{r-103}{-82}\right)}^2=1,z\&Element;\left[\mathrm{0,72}\right],r\&Element;\left[\mathrm{21,103}\right]$

Step 3.2, solve shroud curvilinear equation, the value of given original equation index p and q is p _s=2 and q _s=2, similar with step 3.1, difference is that the import of shroud curve has one section of pitch angle, exports as axially giving vent to anger, should be according to the 2nd) kind situation solves, and solves to such an extent that shroud curvilinear equation is:

${\left(\frac{z}{83.4855}\right)}^2+{\left(\frac{r-169.9051}{-99.9051}\right)}^2=1,z\&Element;\left[\mathrm{0,62}\right],r\&Element;\left[\mathrm{70,103}\right]$

Note: in the time that inducer has certain pitch angle, outlet section also to have certain pitch angle, i.e. r ₁' and r ₂' be finite value, can be by being rotated counterclockwise coordinate system β ₂, making curve outlet section pitch angle is 0, as shown in Figure 3, this kind of situation becomes 2), then carry out the equation solution of curvilinear equation, then calculate by coordinate conversion:

z _R=zcosβ ₂+rsinβ ₂

r _R=-zsinβ ₂+rcosβ ₂；

Can obtain the coordinate of former coordinate system lower curve, just no longer give an example here;

Step 4, solve the flow area at constant current contour sectional position place:

Step 4.1, according to hub curve and shroud curvilinear equation, the arc length of calculated curve from import to outlet section respectively, method is: curve Z coordinate is divided into N section (N gets the degree of accuracy of calculating to improve arc length greatly as far as possible), obtains N+1 Z coordinate zz including ingress-egress point ₁, zz ₂..., zz _k..., zz _n+1, in substitution formula (1), try to achieve corresponding R coordinate rr respectively ₁, rr ₂..., rr _k..., rr _n+1, the distance of calculating between adjacent 2 is sued for peace and just can be obtained out the arc length L of curve all distances again;

The flow area of step 4.2, calculating constant current contour position, does not consider the thick impact on flow area of leaf, and its method is: curve arc long L is divided into N section, and the length of each section is L/N, and utilizing dichotomy to try to achieve on the coordinate hub curve of Along ent is (zh ₁, rh ₁), (zh ₂, rh ₂) ..., (zh _k, rh _k) ..., (zh _n+1, rh _n+1), on shroud curve, be (zs ₁, rs ₁), (zs ₂, rs ₂) ..., (zs _k, rs _k) ..., (zs _n+1, rs _n+1), connect K point and shroud curve K point on hub curve, as shown in Figure 4, the area that gained line segment rotates gained around axis is the flow area that streamline position 1/ (K-1) is located, and its calculating formula that is easy to derive is:

$S_K=\mathrm{\&pi;}{[1+{\left(\frac{{\mathrm{zs}}_K-{\mathrm{zh}}_K}{{\mathrm{rs}}_K-{\mathrm{rh}}_K}\right)}^2]}^{0.5}({{\mathrm{rs}}_K}^2-{{\mathrm{rh}}_K}^2)$

Step 4.3, note inflow point's streamline position are 0, and streamline position, exit is 1, K point (zh of hub curve _k, rh _k) or K point (zs of shroud curve _k, rs _k) the streamline position located is 1/(K-1), taking streamline position as horizontal ordinate, the flow area of this streamline position is that ordinate is drawn, and can obtain the variation diagram of flow area with streamline position, as calculated in Fig. 5 as shown in I;

Step 5, can find out according to Fig. 5, be not monotone increasing trend from import to outlet flow area, but in the decline of living in of streamline position, and be tending towards straight near outlet, consider from geometric angle, this explanation meridian ellipse runner molded line is not that fairing changes; Revising equation index is p _h=1.5, q _h=2, shroud curvilinear equation index is constant, this calculating is designated as calculating II, turn back to step 3 and recalculate, obtain hub and shroud curvilinear equation, flow area is with the variation diagram of streamline position, as Fig. 5 calculates as shown in II, can find out that flow area is monotone increasing trend, satisfy condition, select this kind of curve.The meridian ellipse hub of twice calculating and shroud curve are as shown in Figure 6.

In sum, these are only preferred embodiment of the present invention, be not intended to limit protection scope of the present invention.Within the spirit and principles in the present invention all, any amendment of doing, be equal to replacement, improvement etc., within all should being included in protection scope of the present invention.

Claims (1)

1. the design of footpath axial-flow expansion turbine impeller meridian surface shape and a check method, is characterized in that: comprise the steps:

Illustrate: following " subscript 1 " represents import, " subscript 2 " represents outlet, and " subscript h " represents hub curve, i.e. wheel disc baseline, and " subscript s " represents shroud curve, i.e. wheel cap baseline or leaf top line;

Step 1, read in impeller meridian ellipse basic parameter: inlet diameter D ₁, the high L of leaf ₁, outlet outer diameter D ' ₂and outlet inner diameter D " ₂, axially overall width B _t, hub curve is imported and exported cone angle beta _1hand β _2h, shroud curve is imported and exported cone angle β _1sand β _2s;

Step 2, selected meridian ellipse two-dimensional coordinate system, taking impeller axis and contrary airflow direction as Z axis forward, vertical axis and be R axle forward from blade root to leaf top direction, taking impeller meridian ellipse egress line elongated segment line and Z axis intersection point as initial point, z _1h, z _1s, z _2hand z _2sthe import and export coordinate that is respectively impeller meridian ellipse hub and shroud curve, its expression formula is:

$\left\{\begin{array}{c}{z}_{1h}=B_t,r_{1h}=D_1/2\\ z_{1s}=B_t-L_1,r_{1s}=D_1/2\\ z_{2h}={0,r}_{2h}={D_2^{\&prime;\&prime;}}_{}/2\\ z_{2s}={0,r}_{2h}=D_2^{\&prime;}/2\end{array}\right.$

Step 3, according to known parameters, adopt broad sense elliptic equation general expression:

${\left(\frac{z+a}{b}\right)}^p+{\left(\frac{r+c}{d}\right)}^q=1---\left(1\right)$

R to the first order derivative of z is:

$\tan \mathrm{\&beta;}=r^{\&prime;}=\frac{\mathrm{dr}}{\mathrm{dz}}=-\frac{p}{q}\frac{d}{b}{\left(\frac{z+a}{b}\right)}^{p-1}{\left(\frac{r+c}{d}\right)}^{1-q}---\left(2\right)$

Solve respectively hub and shroud curvilinear equation:

Step 3.1, solve hub curvilinear equation, the value of the initial index p of given equation and q is p _hand q _h; Make z ₁=z _1h, r ₁=r _1hand z ₂=z _2h, r ₂=r _2hrespectively in substitution equation (1); Make β ₁=β _1h, β ₂=β _2hrespectively in substitution equation (2); Find out thus, have four unknown numbers of four equations, according to turbo-expander actual conditions, solving equation group is discussed:

1), when radial air inlet, while axially giving vent to anger, i.e. β ₁=90 ° and β ₂=0 °, r ₁' → ∞ and r ₂'=0, try to achieve:

a _h=-z ₂，b _h=z ₁-z ₂，c _h=-r ₁，d _h=r ₂-r ₁ （3）

2), when inducer have certain pitch angle, while axially giving vent to anger, r ₁' be a finite value and r ₂'=0, try to achieve:

$\left\{\begin{array}{c}\frac{p_h}{{r_1}^{\&prime;}(z_1-z_2)}[1-{\left(\frac{r_1+c_h}{r_2+c_h}\right)}^{q_h}]+\frac{q_h}{r_2+c_h}{\left(\frac{r_1+c_h}{r_2+c_h}\right)}^{q_h-1}=0\\ a_h=-z_2\\ d_h=r_2+c_h\\ b_h=(z_1-z_2){[1-{\left(\frac{r_1+c_h}{r_2+c_h}\right)}^{q_h}]}^{-1/p_h}\end{array}\right.---\left(4\right)$

3), in the time that inducer has certain pitch angle, outlet section also to have certain pitch angle, i.e. r ₁' and r ₂' be finite value, by being rotated counterclockwise coordinate system β ₂, making curve outlet section pitch angle is 0, this kind of situation becomes 2), then carry out the equation solution of curvilinear equation, then calculate by coordinate conversion:

z _R=zcosβ ₂+rsinβ ₂ （5）

r _R=-zsinβ ₂+rcosβ ₂

Can obtain the coordinate of former coordinate system lower curve;

Step 3.2, solve shroud curvilinear equation, the value of given original equation index p and q is p _sand q _s, make z ₁=z _1s, r ₁=r _1s, z ₂=z _2s, r ₂=r _2sand β ₁=β _1s, β ₂=β _2s, other obtains shroud curvilinear equation as follows with step 3.1:

1), when radial air inlet, while axially giving vent to anger, i.e. β ₁=90 ° and β ₂=0 °, r ₁' → ∞ and r ₂'=0, try to achieve:

a _s=-z ₂，b _s=z ₁-z ₂，c _s=-r ₁，d _s=r ₂-r ₁ （6）

2), when inducer have certain pitch angle, while axially giving vent to anger, r ₁' be a finite value and r ₂'=0, try to achieve:

$\left\{\begin{array}{c}\frac{p_s}{{r_1}^{\&prime;}(z_1-z_2)}[1-{\left(\frac{r_1+c_s}{r_2+c_s}\right)}^{q_s}]+\frac{q_s}{r_2+c_h}{\left(\frac{r_1+c_s}{r_2+c_s}\right)}^{q_s-1}=0\\ a_s=-z_2\\ d_s=r_2+c_s\\ b_s=(z_1-z_2){[1-{\left(\frac{r_1+c_s}{r_2+c_s}\right)}^{q_s}]}^{-1/p_s}\end{array}\right.---\left(7\right)$

3), in the time that inducer has certain pitch angle, outlet section also to have certain pitch angle, i.e. r ₁' and r ₂' be finite value, by being rotated counterclockwise coordinate system β ₂, making curve outlet section pitch angle is 0, this kind of situation becomes 2), then carry out the equation solution of curvilinear equation, then calculate by coordinate conversion:

z _R=zcosβ ₂+rsinβ ₂ （8）

r _R=-zsinβ ₂+rcosβ ₂

Can obtain the coordinate of former coordinate system lower curve;

Step 4, solve the flow area at constant current contour sectional position place:

Step 4.1, according to hub curve and shroud curve curvilinear equation, the arc length of calculated curve from import to outlet section respectively, method is: curve Z coordinate is divided into N section, and described N gets the degree of accuracy of calculating to improve arc length greatly as far as possible, obtains N+1 Z coordinate zz including ingress-egress point ₁, zz ₂..., zz _k..., zz _n+1, in substitution formula (1), try to achieve corresponding R coordinate rr respectively ₁, rr ₂..., rr _k..., rr _n+1, the distance of calculating between adjacent 2 is sued for peace and just can be obtained out the arc length L of curve all distances again;

The flow area of step 4.2, calculating constant current contour position, does not consider the thick impact on flow area of leaf, and its method is: curve arc long L is divided into N section, and the length of each section is L/N, and utilizing dichotomy to try to achieve on the coordinate hub curve of Along ent is (zh ₁, rh ₁), (zh ₂, rh ₂) ..., (zh _k, rh _k) ..., (zh _n+1, rh _n+1), on shroud curve, be (zs ₁, rs ₁), (zs ₂, rs ₂) ..., (zs _k, rs _k) ..., (zs _n+1, rs _n+1), connecting K point and shroud curve K point on hub curve, the area that gained line segment rotates gained around axis is the flow area that streamline position 1/ (K-1) is located, and its calculating formula of deriving is:

$S_K=\mathrm{\&pi;}{[1+{\left(\frac{{\mathrm{zs}}_K-{\mathrm{zh}}_K}{{\mathrm{rs}}_K-{\mathrm{rh}}_K}\right)}^2]}^{0.5}({{\mathrm{rs}}_K}^2-{{\mathrm{rh}}_K}^2)---\left(9\right)$

Step 4.3, note inflow point's streamline position are 0, and streamline position, exit is 1, K point (zh of hub curve _k, rh _k) or K point (zs of shroud curve _k, rs _k) the streamline position located is 1/(K-1), taking streamline position as horizontal ordinate, the flow area of this streamline position is that ordinate is drawn, and can obtain the change curve of flow area with streamline position;

Step 5, can judge the whether smooth or whether realistic requirement of design of meridian ellipse runner according to flow area with the change curve of streamline position; If so, export the point coordinate of meridian ellipse hub curve and shroud curve, if not, revise equation index p _hand q _hor p _sand q _s, then return to step 3 and recalculate.

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