CN104537234A - One-dimensional high-low-pressure turbine transition flow channel optimization design method - Google Patents

Abstract

The invention discloses a one-dimensional high-low-pressure turbine transition flow channel optimization design method. The method aims to solve the technical problem that an existing method is poor in practicability. According to the technical scheme, an end wall profile equation meeting the transition flow channel geometric constraint is built by the adoption of a Bezier curve; the disturbance quantity meeting the orthogonal polynomials is generated afterwards, and correction is conducted on the generated extremely large disturbance quantity to prevent deformation of a disturbed flow channel; a new high-low-pressure turbine transition flow channel profile equation is generated based on the existing transition flow channel geometric profile equation; a flow field performance parameter is solved through a flow control equation on the high-low-pressure turbine transition flow channel center line; a total pressure recovery coefficient serves as an optimization objective function, and a complex method is adopted till an iteration result meets the accuracy requirement. According to the method, the high-low-pressure turbine transition flow channel profile equation is built based on the Bezier curve to optimize the high-low-pressure turbine transition flow channel, the defect that the existing method is not suitable for an urgently-expanded flow channel with the larger expansion angle is overcome, and practicability is high.

Description

High and low pressure turbine transition runner one dimension Optimization Design

Technical field

The present invention relates to a kind of high and low pressure turbine transition runner method for designing, particularly relate to a kind of high and low pressure turbine transition runner one dimension Optimization Design.

Background technology

The turbine transition runner connecting high-pressure turbine and low-pressure turbine is the vitals of large duct gas-turbine unit, and air-flow needs experience deceleration diffusion process in turbine transition runner.From classical diffuser theory, air-flow is very easily separated in diffusion passage, causing flow losses, must increase passage axial length to alleviate diffusion degree, and increasing the increase that axial length must bring turbine weight and cost in order to avoid being separated.

For a long time, turbine transition runner design problem is not given sufficient attention, it is theoretical that method for designing stops at classical diffuser, but along with the development of aero engine technology, core engine size constantly reduces, turbine material tolerable temperature improves constantly, turbine cooling technology tremendous development, and classical transition runner method for designing can not meet the demand of Aeroengine Design instantly.

Document " turbine transition runner optimal design " Push Technology " the 2nd phase in 2012 the 179 to 184 page based on one-dimensional model " discloses a kind of one dimension turbine transition runner performance prediction method.The geometric condition that first the method should clearly design, completes transition runner initial designs according to known conditions; Then with the runner of initial designs for benchmark, the given disturbance basis function meeting orthogonality condition, carries out disturbance to original design curve; Then with the weighted mean of pressure-recovery factor and total pressure recovery coefficient for objective function, adopt simplicial method optimization, iteration for several times until reach required precision, then completes the one dimension optimal design of transition runner.

Existing method can not be used for the larger urgency expansion type runner design of expansion angle, and the scope of application is narrower.

Summary of the invention

In order to overcome the deficiency of existing method poor practicability, the invention provides a kind of high and low pressure turbine transition runner one dimension Optimization Design.The method adopts Bezier to build the end wall profile equation meeting transition runner geometrical constraint.Then generate and meet the disturbance quantity of orthogonal polynomial, and excessive person in generation disturbance quantity is revised, to prevent runner deformity after disturbance.And based on existing transition runner geometry curved dies, generate new high and low pressure turbine transition runner curved dies.Then, Flow Field Performance parameter is solved by the Fluid Control Equation on high and low pressure turbine transition runner center line.Finally, take total pressure recovery coefficient as optimization object function, adopt complex method till iteration result meets accuracy requirement.The present invention adopts the curved dies constructing high and low pressure turbine transition runner based on Bezier, adopts the complex method of belt restraining, is optimized high and low pressure turbine transition runner.Overcome the problem that background technology method is not suitable for the larger urgency expansion type runner of expansion angle, practical.

The technical solution adopted for the present invention to solve the technical problems is: a kind of high and low pressure turbine transition runner one dimension Optimization Design, is characterized in adopting following steps:

Import and export size and geometric configuration according to known runner, calculate θ according to formula (1) _cand determine L _m.θ _cit is equivalent conical expander angle; L _mtransition runner meridian length; A ₁it is transition runner import normal direction area; A ₂it is transition runner outlet normal direction area.

${\mathrm{\θ}}_c=2\arctan \left(\frac{\sqrt{A_2}-\sqrt{A_1}}{L_m\sqrt{\mathrm{\π}}}\right)---\left(1\right)$

The casing of turbine transition runner and wheel hub molded line built with two 4 rank Beziers with 5 reference mark respectively, the parametrization equation of every bar curve is formula (2). it is Bernstein polynomial expression; M is polynomial exponent number; T is the controling parameters of curve, and its span is 0 to 1; N _iit is reference mark coordinate.

$\left\{\begin{array}{c}x\left(t\right)=\underset{i=0}{\overset{4}{\mathrm{\Σ}}}{C}_4^i{t}^i{(1-t)}^{4-i}\left(t\right)x_i\\ y\left(t\right)=\underset{i=0}{\overset{4}{\mathrm{\Σ}}}{C}_4^i{t}^i{(1-t)}^{4-i}\left(t\right)y_i\end{array}\right.---\left(2\right)$

By radius and the slope of geometrical constraint known runner import and export center line, the value of second derivative at import and export place presetting center line is 0, tries to achieve curve initial design equation.

Disturbance basis function adopts the orthogonal polynomial meeting following condition.I is basis function order; L is transition runner axial length.

As x=0.0 or L, $P_i\left(x\right)=\frac{{\mathrm{dP}}_i}{\mathrm{dx}}=\frac{d^2{P}_i}{{\mathrm{dx}}^2}=0---\left(3\right)$

First basis function is the minimum polynomial expression of the order that meets formula (3), and the basis function of higher order both should meet formula (3), should meet formula (4) simultaneously.

${\∫}_0^L{P}_i\left(x\right)P_j\left(x\right)\mathrm{dx}=\left\{\begin{array}{c}=0,i\≠j\\ \≠0,i=j\end{array}\right.---\left(4\right)$

Disturbance is the linear superposition of orthogonal polynomial basis function.

By gained disturbance maximal value compared with 0.05h (0).If disturbance maximal value is greater than 0.05h (0), gained disturbance quantity etc. is contracted to maximal value equal with 0.05h (0).H (0) is tunnel inlets height.

Nondimensionalization is carried out by function 2 norm shown in formula (5).

P ₁(x)＝x ³(L-x) ³

$P_2\left(x\right)=x^3{(L-x)}^3(\frac{L}{2}-x)---\left(5\right)$

The reference data of disturbance is current turbine transition runner molded line.

Solution formula (6), (7), (8) and (9), i.e. One-Dimensional flows governing equation, solve the performance parameter of runner.

$2\mathrm{\πrb\ρ}{C}_m(1-B)=\stackrel{\·}{m}---\left(6\right)$

$b{C}_m\frac{d\left(r{C}_{\mathrm{\θ}}\right)}{\mathrm{dm}}=-r{\mathrm{CC}}_{\mathrm{\θ}}{c}_f---\left(7\right)$

$\frac{1}{\mathrm{\ρ}}\frac{\mathrm{dp}}{\mathrm{dm}}=\frac{C_{\mathrm{\θ}}^2\sin \mathrm{\φ}}{r}-C_m\frac{{\mathrm{dC}}_m}{\mathrm{dm}}-\frac{{\mathrm{CC}}_m{c}_f}{b}-\frac{{\mathrm{dI}}_D}{\mathrm{dm}}-I_C---\left(8\right)$

$H=h+\frac{1}{2}{C}^2---\left(9\right)$

In formula, r is F-L curve radius; B is perpendicular to the width of flow path of center line; C _mmeridian speed; ρ is density; B is the plugging factor considered boundary-layer and be separated impact; it is mass rate; C is full speed degree; M is meridional stream line direction; P is static pressure; C _θit is tangential velocity; φ is the angle of meridional stream line and axis; c _fit is skin-friction coefficient; IC is curvature loss item; ID is diffusion loss item; H is total enthalpy; H is quiet enthalpy.

Optimization object function is formula 10.σ is total pressure recovery coefficient.

maxobj＝σ (10)

The complex method optimization of belt restraining is adopted to try to achieve new profile equation.

Approach distance with each summit of complex to meet given accuracy for standard and judge whether convergence, convergence then optimizes end, does not restrain, generates new disturbance quantity, repeats self-generating disturbance basis function and starts new optimizing process.

The invention has the beneficial effects as follows: the method adopts Bezier to build the end wall profile equation meeting transition runner geometrical constraint.Then generate and meet the disturbance quantity of orthogonal polynomial, and excessive person in generation disturbance quantity is revised, to prevent runner deformity after disturbance.And based on existing transition runner geometry curved dies, generate new high and low pressure turbine transition runner curved dies.Then, Flow Field Performance parameter is solved by the Fluid Control Equation on high and low pressure turbine transition runner center line.Finally, take total pressure recovery coefficient as optimization object function, adopt complex method till iteration result meets accuracy requirement.The present invention adopts the curved dies constructing high and low pressure turbine transition runner based on Bezier, adopts the complex method of belt restraining, is optimized high and low pressure turbine transition runner.Overcome the problem that background technology method is not suitable for the larger urgency expansion type runner of expansion angle, practical.

Below in conjunction with the drawings and specific embodiments, the present invention is elaborated.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of high and low pressure turbine transition runner one dimension Optimization Design of the present invention.

Fig. 2 is the runner-type line figure that the inventive method obtains, and dotted line is for before optimization, and solid line is for after optimization.

Embodiment

With reference to Fig. 1-2.High and low pressure turbine transition runner one dimension Optimization Design concrete steps of the present invention are as follows:

Import and export size and geometric configuration according to known runner, the given initializing constraint of this example is as following table:

Then calculate θ according to formula (1) _cand determine L _m.Equivalent divergent angle θ is tried to achieve according to formula 1 _c=17.6895 °, this runner is that a urgency expands runner.

θ _cit is equivalent conical expander angle; L _mtransition runner meridian length; A ₁it is transition runner import normal direction area; A ₂it is transition runner outlet normal direction area.

${\mathrm{\θ}}_c=2\arctan \left(\frac{\sqrt{A_2}-\sqrt{A_1}}{L_m\sqrt{\mathrm{\π}}}\right)---\left(1\right)$

The casing of turbine transition runner and wheel hub molded line built with two 4 rank Beziers with 5 reference mark respectively, the parametrization equation of every bar curve is formula (2). it is Bernstein polynomial expression; M is polynomial exponent number; T is the controling parameters of curve, and its span is 0 to 1; N _iit is reference mark coordinate.

$\left\{\begin{array}{c}x\left(t\right)=\underset{i=0}{\overset{4}{\mathrm{\Σ}}}{C}_4^i{t}^i{(1-t)}^{4-i}\left(t\right)x_i\\ y\left(t\right)=\underset{i=0}{\overset{4}{\mathrm{\Σ}}}{C}_4^i{t}^i{(1-t)}^{4-i}\left(t\right)y_i\end{array}\right.---\left(2\right)$

By radius and the slope of geometrical constraint known runner import and export center line, the value of second derivative at import and export place presetting center line is 0, tries to achieve curve initial design equation.

Disturbance basis function adopts the orthogonal polynomial meeting following condition.I is basis function order; L is transition runner axial length.

As x=0.0 or L, $P_i\left(x\right)=\frac{{\mathrm{dP}}_i}{\mathrm{dx}}=\frac{d^2{P}_i}{{\mathrm{dx}}^2}=0---\left(3\right)$

First basis function is the minimum polynomial expression of the order that meets formula (3), and the basis function of higher order both should meet formula (3), should meet formula (4) simultaneously.

${\∫}_0^L{P}_i\left(x\right)P_j\left(x\right)\mathrm{dx}=\left\{\begin{array}{c}=0,i\≠j\\ \≠0,i=j\end{array}\right.---\left(4\right)$

Disturbance is the linear superposition of orthogonal polynomial basis function.

By gained disturbance maximal value compared with 0.05h (0).If disturbance maximal value is greater than 0.05h (0), gained disturbance quantity etc. is contracted to maximal value equal with 0.05h (0).H (0) is tunnel inlets height.

Nondimensionalization is carried out by function 2 norm shown in formula (5).

P ₁(x) _＝x ³(L-x) ³

$P_2\left(x\right)=x^3{(L-x)}^3(\frac{L}{2}-x)---\left(5\right)$

The reference data of disturbance is current turbine transition runner molded line.

Solution formula (6), (7), (8) and (9), i.e. One-Dimensional flows governing equation, solve the performance parameter of runner.

$2\mathrm{\πrb\ρ}{C}_m(1-B)=\stackrel{\·}{m}---\left(6\right)$

$b{C}_m\frac{d\left(r{C}_{\mathrm{\θ}}\right)}{\mathrm{dm}}=-r{\mathrm{CC}}_{\mathrm{\θ}}{c}_f---\left(7\right)$

$\frac{1}{\mathrm{\ρ}}\frac{\mathrm{dp}}{\mathrm{dm}}=\frac{C_{\mathrm{\θ}}^2\sin \mathrm{\φ}}{r}-C_m\frac{{\mathrm{dC}}_m}{\mathrm{dm}}-\frac{{\mathrm{CC}}_m{c}_f}{b}-\frac{{\mathrm{dI}}_D}{\mathrm{dm}}-I_C---\left(8\right)$

$H=h+\frac{1}{2}{C}^2---\left(9\right)$

In formula, r is F-L curve radius; B is perpendicular to the width of flow path of center line; C _mmeridian speed; ρ is density; B is the plugging factor considered boundary-layer and be separated impact; it is mass rate; C is full speed degree; M is meridional stream line direction; P is static pressure; C _θit is tangential velocity; φ is the angle of meridional stream line and axis; c _fit is skin-friction coefficient; IC is curvature loss item; ID is diffusion loss item; H is total enthalpy; H is quiet enthalpy.

Optimization object function is formula 10.σ is total pressure recovery coefficient.

maxobj＝σ (10)

The complex method optimization of belt restraining is adopted to try to achieve new profile equation.

Approach distance with each summit of complex to meet given accuracy for standard and judge whether convergence, convergence then optimizes end, does not restrain, generates new disturbance quantity, repeats self-generating disturbance basis function and starts new optimizing process.

The given aerodynamic parameter for solving governing equation of the present embodiment, as following table:

With reference to Fig. 1, reach after 273 step iteration accuracy requirement optimize after runner shape line.

With reference to Fig. 2, comparison diagram before and after visible improving cavity, in figure, dotted line is for optimizing front high and low pressure turbine transition runner molded line, and solid line is high and low pressure turbine transition runner molded line after optimizing.

This example calculates an anxious expansion type transition runner, and before optimizing, pressure-recovery factor Cp is 0.561, and total pressure loss coefficient ω is 0.0135, and after optimizing, pressure-recovery factor Cp is 0.585, and total pressure loss coefficient is ω is 0.0109, and total pressure loss coefficient reduction reaches 19.3%.。

From this example, suddenly expand runner to the one dimension that existing method cannot be optimized, this method effect of optimization is still better.

Claims (1)

1. a high and low pressure turbine transition runner one dimension Optimization Design, is characterized in that comprising the following steps:

Import and export size and geometric configuration according to known runner, calculate θ according to formula (1) _cand determine L _m; θ _cit is equivalent conical expander angle; L _mtransition runner meridian length; A ₁it is transition runner import normal direction area; A ₂it is transition runner outlet normal direction area;

${\mathrm{\θ}}_c=2\arctan \left(\frac{\sqrt{A_2}-\sqrt{A_1}}{L_m\sqrt{\mathrm{\π}}}\right)---\left(1\right)$

The casing of turbine transition runner and wheel hub molded line built with two 4 rank Beziers with 5 reference mark respectively, the parametrization equation of every bar curve is formula (2); it is Bernstein polynomial expression; M is polynomial exponent number; T is the controling parameters of curve, and its span is 0 to 1; N _iit is reference mark coordinate;

$\left\{\begin{array}{c}x\left(t\right)=\underset{i=0}{\overset{4}{\mathrm{\Σ}}}{C}_4^i{t}^i{(1-t)}^{4-i}\left(t\right)x_i\\ y\left(t\right)=\underset{i=0}{\overset{4}{\mathrm{\Σ}}}{C}_4^i{t}^i{(1-t)}^{4-i}\left(t\right)y_i\end{array}\right.---\left(2\right)$

By radius and the slope of geometrical constraint known runner import and export center line, the value of second derivative at import and export place presetting center line is 0, tries to achieve curve initial design equation;

Disturbance basis function adopts the orthogonal polynomial meeting following condition; I is basis function order; L is transition runner axial length;

As x=0.0 or L, $P_i\left(x\right)=\frac{d{P}_i}{\mathrm{dx}}=\frac{d^2{P}_i}{d{x}^2}=0---\left(3\right)$

First basis function is the minimum polynomial expression of the order that meets formula (3), and the basis function of higher order both should meet formula (3), should meet formula (4) simultaneously;

${\∫}_0^L{P}_i\left(x\right)P_i\left(x\right)\mathrm{dx}=\left\{\begin{array}{c}=0,i\≠j\\ \≠0,i=j\end{array}\right.---\left(4\right)$

Disturbance is the linear superposition of orthogonal polynomial basis function;

By gained disturbance maximal value compared with 0.05h (0); If disturbance maximal value is greater than 0.05h (0), gained disturbance quantity etc. is contracted to maximal value equal with 0.05h (0); H (0) is tunnel inlets height;

Nondimensionalization is carried out by function 2 norm shown in formula (5);

P ₁(x)＝x ³(L-x) ³

$P_2\left(x\right)=x^3{(L-x)}^3(\frac{L}{2}-x)---\left(5\right)$

The reference data of disturbance is current turbine transition runner molded line;

Solution formula (6), (7), (8) and (9), i.e. One-Dimensional flows governing equation, solve the performance parameter of runner;

$2\mathrm{\πrb\ρ}{C}_m(1-B)=\stackrel{.}{m}---\left(6\right)$

$b{C}_m\frac{d\left(r{C}_{\mathrm{\θ}}\right)}{\mathrm{dm}}=-\mathrm{rC}{C}_{\mathrm{\θ}}{c}_f---\left(7\right)$

$\frac{1}{\mathrm{\ρ}}\frac{\mathrm{dp}}{\mathrm{dm}}=\frac{C_{\mathrm{\θ}}^2\sin \mathrm{\φ}}{r}-C_m\frac{d{C}_m}{\mathrm{dm}}-\frac{C{C}_m{c}_f}{b}-\frac{d{I}_d}{\mathrm{dm}}-I_C---\left(8\right)$

$H=h+\frac{1}{2}{C}^2---\left(9\right)$

In formula, r is F-L curve radius; B is perpendicular to the width of flow path of center line; C _mmeridian speed; ρ is density; B is the plugging factor considered boundary-layer and be separated impact; it is mass rate; C is full speed degree; M is meridional stream line direction; P is static pressure; C _θit is tangential velocity; φ is the angle of meridional stream line and axis; c _fit is skin-friction coefficient; IC is curvature loss item; ID is diffusion loss item; H is total enthalpy; H is quiet enthalpy;

Optimization object function is formula 10; σ is total pressure recovery coefficient;

max obj＝σ (10)

The complex method optimization of belt restraining is adopted to try to achieve new profile equation;

Approach distance with each summit of complex to meet given accuracy for standard and judge whether convergence, convergence then optimizes end, does not restrain, generates new disturbance quantity, repeats self-generating disturbance basis function and starts new optimizing process.