CN103838961A - Method for monitoring three-dimensional temperature and thermal stress of ultra-supercritical steam turbine rotor in real time - Google Patents

Abstract

The invention discloses a method for monitoring the three-dimensional temperature and thermal stress of an ultra-supercritical steam turbine rotor in real time. The method comprises the steps that a calculation formula for the temperature and the thermal stress of a monitoring point of the steam turbine rotor is expressed in a Green function mode according to the characteristics of heating of an ultra-supercritical steam turbine in the running process and an equation for heat conduction in a three-dimensional object, the Green function is calculated in an off-line mode by using a finite element method, and after the actual structure shape of the steam turbine and the cooling steam working state of the steam turbine are accurately simulated and are processed through various precision improvement methods, the temperature and thermal stress distribution are rapidly and accurately calculated by using the Green function. The obtained calculation result is quite close to the finite element calculation result, ideal calculation accuracy is achieved, a model is simple, calculation is rapid, information of changes of the temperature and information of changes of the thermal stress at any positions in the ultra-supercritical steam turbine rotor can be accurately monitored in real time, the overstressing phenomenon is avoided, safety of the steam turbine in the running process is protected, starting, shutdown and variable-load running of the steam turbine are guided, and economy of the steam turbine in the running process is improved.

Description

The three-dimensional temperature of supercritical turbine rotor and thermal stress method of real-time

Technical field

The present invention relates to a kind of temperature and method for measuring stress of steam turbine in thermal power plant rotor, specifically refer to the three-dimensional temperature of supercritical turbine rotor and thermal stress method of real-time.

Background technology

Development of Ultra-Supercritical unit is the inexorable trend that cost of electricity-generating is saved the energy, improves environmental protection and improved generating efficiency, reduces in thermal power generation.Along with scientific and technical progress and the development of material technology, the main steam temperature of supercritical turbine and reheat steam temperature are the trend of growth.Along with the rising of vapor (steam) temperature, the mechanical property of material declines to some extent, in order to ensure that the parts of supercritical turbine have enough intensity and life-span, except adopting the steel that elevated temperature strength is good, also should adopt steam cooling technology and cooling structure design.Steam is cooling is to adopt the steam (as steam after high pressure steam discharge, high pressure extraction or movable vane) that temperature is lower to carry out cooling supercritical turbine high-temperature component, to reduce the working temperature of supercritical turbine high-temperature component.By the research of advanced steam cooling technology, realize the decline of supercritical turbine parts high temperature position working temperature, be one of important technical ensureing supercritical turbine safe operation.

Due to the introducing of steam cooling technology, the worst high temperature key component of condition of work in steam turbine, as parts such as governing stage and the middle pressure first order, it is no longer the heating and cooling effect of the steam of two-dimensional axial symmetric, but complicated distributed in three dimensions.For accurately monitoring the supercritical turbine thermal stress that critical component bears in the process of startup, shutdown and load change; must carry out Three-dimensional Thermal-elastic analysis to steam turbine; Three Dimensional Thermal monitoring model and related system are proposed; thereby monitor accurately and real-time the heating status in rotor operation process, improve security of operation and economy.

For realizing the cooling of supercritical turbine rotor key component, typical cooling system structure and vapor flow are as depicted in figs. 1 and 2, wherein Fig. 1 illustrates high pressure rotor cooling system composition, principal feature for offering cooling inclined hole on impeller, after governing stage, sub-fraction steam is after half-turn, due to the effect of vane rotary generation centrifugal pump, governing stage outlet fraction steam is inhaled and come, flow through the chamber between nozzle box and rotor, chamber between cooling inclined hole and nozzle box's outside surface and the rotor of flowing through on governing stage impeller, the middle aperture in double flowing nozzle chamber of flowing through again turns back to after governing stage.In this flow process, the outside surface of cooling high temperature nozzle chamber and high pressure rotor.

Fig. 2 illustrates middle pressure rotor cooling system composition, the space of the import guide ring bottom of high-pressure turbine steam discharge or 350 DEG C of following introducing middle-pressure steam turbines that draw gas, in this cooling steam, fraction flows into main steam flow by the packing between first order movable vane and stator blade: before most of cooling steam flows into second level stator blade by the vertical tree-like blade root bottom gap of first order movable vane and the second level is quiet, between movable vane, make middle pressure rotor high temperature position obtain cooling.Clearly, no matter be high-pressure section or low-pressure section, owing to Cooling Holes or gap being along the circumferential direction interrupted distribution, flowing of steam is no longer axisymmetric two-dimensional flow, the structure of steam turbine can not be reduced to two-dimensional approach, for accurately calculating rotor key component temperature and thermal stress, need to adopt Three-dimensional Thermal-elastic theory to analyze.

It is to be all based upon on the basis that heat conduction in hypothesis steam turbine is one dimension or TWO-DIMENSIONAL CIRCULAR CYLINDER to suppose that Rotor Physical Property parameter is normal physical property that existing turbine rotor temperature and thermal stress are calculated model and system, is considering to become the achievement in research of carrying out modeling under physical property condition and setting up thermal monitoring system at present there are no the three-dimensional steam turbine structure for having a complicated shape.

Summary of the invention

The object of this invention is to provide the three-dimensional temperature of supercritical turbine rotor and thermal stress method of real-time; this monitoring method detects for supercritical turbine rotor key position; the method can provide temperature and stress information to supercritical turbine rotor optional position; can process the change coefficient of heat transfer that startup, shutdown and variable load operation bring and the physical parameter problem of temperature correlation; the result of calculation obtaining and result of finite element are very approaching; there is desirable computational accuracy; model is simple simultaneously; calculate rapidly, be very suitable for Real-Time Monitoring.

Above-mentioned purpose of the present invention realizes by following technical solution: the three-dimensional temperature of supercritical turbine rotor and thermal stress method of real-time, the method comprises the steps:

Step (1): build the three-dimensional temperature of supercritical turbine rotor and thermal stress monitoring model

Structure and the derivation of the three-dimensional temperature of described supercritical turbine rotor and thermal stress monitoring model are as follows:

The differential equation of the non-linear transient state Heat Conduction Problems of turbine rotor in the time considering physical parameter to the dependence of temperature below meeting during as three-dimensional structure:

$\mathrm{\ρc}\frac{\∂T}{\∂t}=\frac{\∂}{\∂x}\left(\mathrm{\λ}\frac{\∂T}{\∂x}\right)+\frac{\∂}{\∂y}\left(\mathrm{\λ}\frac{\∂T}{\∂y}\right)+\frac{\∂}{\∂z}\left(\mathrm{\λ}\frac{\∂T}{\∂z}\right)=\▿\·(\mathrm{\λ}\▿T)\·---\left(1\right)$

In formula, T is turbine rotor in-vivo metal temperature, and λ is turbine rotor Thermal Conductivity by Using, and ρ is turbine rotor density metal, and c is that turbine rotor metal specific heat holds, and t is the time, x, and y, z is coordinate variable, ▽, ▽ is three-dimensional divergence and gradient operator;

Initial temperature is assumed to be evenly, adopts the 3rd class Transfer Boundary Condition:

$\mathrm{\λ}\frac{\∂T}{\∂r}{|}_{\mathrm{boi}}={\mathrm{\α}}_{\mathrm{boi}}(T_{\mathrm{boi}}-T)---\left(2\right)$

In formula, boi represents i surface of turbine rotor metal, T _boirepresent i surface vapor (steam) temperature of turbine rotor metal, in this temperature engineering, the general temperature sensor that adopts is directly measured, and can be used as the function into time t;

When temperature variation is not very acutely, the calculating of stress field can be carried out after temperature field analysis; By thermoelastic theory, the intrametallic stress of three-dimensional turbine rotor, strain and displacement meet constitutive equation below:

$\left.\begin{array}{c}{\mathrm{\σ}}_x=\frac{E}{(1-2v)(1+v)}[(1-v){\mathrm{\ϵ}}_x+v({\mathrm{\ϵ}}_y+{\mathrm{\ϵ}}_z)]-\frac{\mathrm{E\β}}{1-2v}T\\ {\mathrm{\σ}}_y=\frac{E}{(1-2v)(1+v)}[(1-v){\mathrm{\ϵ}}_y+v({\mathrm{\ϵ}}_x+{\mathrm{\ϵ}}_z)]-\frac{\mathrm{E\β}}{1-2v}T\\ {\mathrm{\σ}}_z=\frac{E}{(1-2v)(1+v)}[(1-v){\mathrm{\ϵ}}_z+v({\mathrm{\ϵ}}_x+{\mathrm{\ϵ}}_y)]-\frac{\mathrm{E\β}}{1-2v}T,\end{array}\right\}---\left(3\right)$

In formula, E is turbine rotor Elastic Modulus for Metals, and β is turbine rotor expansion coefficients of metal wire, and ν is turbine rotor metal Poisson ratio, σ _x, σ _yand σ _zfor thermal stress component in turbine rotor metal;

In turbine rotor metal, each physical parameter can adopt the physical parameter formula of temperature second order function to represent, that is:

P＝P ₀(1+P ₁T+P ₂T ²)

(4)

P in formula ₀, P ₁and P ₂it is turbine rotor metal material constant;

The physical parameter of turbine rotor Thermal Conductivity by Using and linear expansion coefficient can be expressed as:

λ＝λ ₀(1+λ ₁T+λ ₂T ²)，β＝β ₀(1+β ₁T+β ₂T ²) (5)

Other the physical parameter such as elastic modulus and specific heat capacity can be adopted the correlativity that uses the same method to process itself and temperature; Conventionally-1<< λ ₁and β ₁<<1, supposes ε=λ ₁and ξ=β ₁for small parameter:

$\mathrm{\&lambda;}={\mathrm{\&lambda;}}_0(1+\mathrm{\&epsiv;T}+{\mathrm{m\&epsiv;T}}^2),\mathrm{\&beta;}={\mathrm{\&beta;}}_0(1+\mathrm{\&xi;T}+{\mathrm{n\&xi;T}}^2),m=\frac{{\mathrm{\&lambda;}}_2}{{\mathrm{\&lambda;}}_1},n=\frac{{\mathrm{\&beta;}}_2}{{\mathrm{\&beta;}}_1}---\left(6\right)$

The polynomial form that temperature, stress and strain in turbine rotor metal is launched into small parameter ε and ξ, has:

$T={\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0+\mathrm{\&epsiv;}{T}_{10}+\mathrm{\&xi;}{T}_{01}+...=\underset{i,j=0}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{\mathrm{\&epsiv;}}^i{\mathrm{\&xi;}}^j{T}_{\mathrm{ij}},\mathrm{\&sigma;}={\mathrm{\&sigma;}}_0+\mathrm{\&epsiv;}{\mathrm{\&sigma;}}_{10}+\mathrm{\&xi;}{\mathrm{\&sigma;}}_{01}+...=\underset{i,j=0}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{\mathrm{\&epsiv;}}^i{\mathrm{\&xi;}}^j{\mathrm{\&sigma;}}_{\mathrm{ij}}---\left(7\right)$

Be updated to formula (2) and formula (3), the homogeneous item of merger ε and ξ, can obtain:

ε ⁰ξ ⁰： $\mathrm{\&rho;c}\frac{\&PartialD;{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}{\&PartialD;t}={\mathrm{\&lambda;}}_0{\&dtri;}^2{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0$ Boundary condition ${\mathrm{\&lambda;}}_0\frac{\&PartialD;{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}{\&PartialD;n_i}{|}_{\mathrm{boi}}={\mathrm{\&alpha;}}_{\mathrm{boi}}(T_{\mathrm{boi}}-T_0),$

$\left.\begin{array}{c}{\mathrm{\&sigma;}}_{x0}=\frac{E}{(1-2v)(1+v)}[(1-v){\mathrm{\&epsiv;}}_{x0}+v({\mathrm{\&epsiv;}}_{\mathrm{yo}}+{\mathrm{\&epsiv;}}_{z0})]-\frac{E{\mathrm{\&beta;}}_0}{1-2v}{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0,\\ {\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">y</figure-callout>}0}=\frac{E}{(1-2v)(1+v)}[(1-v){\mathrm{\&epsiv;}}_{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">y</figure-callout>}0}+v({\mathrm{\&epsiv;}}_{x0}+{\mathrm{\&epsiv;}}_{z0})]-\frac{E{\mathrm{\&beta;}}_0}{1-2v}{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0,\\ {\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="0"\; label="Z"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">Z</figure-callout>}0}=\frac{E}{(1-2v)(1+v)}[(1-v){\mathrm{\&epsiv;}}_{z0}+v({\mathrm{\&epsiv;}}_{x0}+{\mathrm{\&epsiv;}}_{y0})]-\frac{E{\mathrm{\&beta;}}_0}{1-2v}{T}_0\end{array}\right\}---\left(8\right)$

ε ¹ξ ⁰:

$\mathrm{\&rho;c}\frac{\&PartialD;T_{10}}{\&PartialD;t}={\mathrm{\&lambda;}}_0{\&dtri;}^2{T}_{10}+{\mathrm{\&lambda;}}_0{\&dtri;}^2(\frac{{{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}^2}{2}+\frac{{{\mathrm{<figure-callout\; id="0"\; label="mT"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">mT</figure-callout>}}_0}^3}{3})---\left(9\right)$

Corresponding boundary condition is: ${\mathrm{\&lambda;}}_0\frac{{\&PartialD;T}_{10}}{{\&PartialD;n}_i}{|}_{\mathrm{boi}}={\mathrm{\&alpha;}}_{\mathrm{boi}}[-T_{10}+({\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0+\mathrm{<figure-callout\; id="0"\; label="m\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">m</figure-callout>}{T}_{}^{}{}_0^2)(T_0-T_{\mathrm{boi}})],$

$\left.\begin{array}{c}{\mathrm{\&sigma;}}_{x10}=\frac{E}{(1-2v)(1+v)}[(1-v){\mathrm{\&epsiv;}}_{x10}+v({\mathrm{\&epsiv;}}_{y10}+{\mathrm{\&epsiv;}}_{z10})]-\frac{E{\mathrm{\&beta;}}_0}{1-2v}{T}_{10}\\ {\mathrm{\&sigma;}}_{y10}=\frac{E}{(1-2v)(1+v)}[(1-v){\mathrm{\&epsiv;}}_{y10}+v({\mathrm{\&epsiv;}}_{x10}+{\mathrm{\&epsiv;}}_{z10})]-\frac{\mathrm{E\&beta;}}{1-2v}{T}_{10};\\ {\mathrm{\&sigma;}}_{z10}=\frac{E}{(1-2v)(1+v)}[(1-v){\mathrm{\&epsiv;}}_{z10}+v({\mathrm{\&epsiv;}}_{x10}+{\mathrm{\&epsiv;}}_{y10})]-\frac{E{\mathrm{\&beta;}}_0}{1-2v}{T}_{10}\end{array}\right\}---\left(10\right)$

ε ⁰ξ ¹:

$\mathrm{\&rho;c}\frac{\&PartialD;T_{01}}{\&PartialD;t}={\mathrm{\&lambda;}}_0{\&dtri;}^2{T}_{01},$ Corresponding boundary condition is ${\mathrm{\&lambda;}}_0\frac{\&PartialD;T_{01}}{\&PartialD;n_i}{|}_{\mathrm{boi}}={\mathrm{\&alpha;}}_{\mathrm{boi}}(0-T_{01})---\left(11\right)$

$\left.\begin{array}{c}{\mathrm{\&sigma;}}_{x01}=\frac{E}{(1-2v)(1+v)}[(1-v){\mathrm{\&epsiv;}}_{x01}+v({\mathrm{\&epsiv;}}_{{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">y</figure-callout>}0}_1}+{\mathrm{\&epsiv;}}_{\mathrm{<figure-callout\; id="0"\; label="z"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">z</figure-callout>}{0}_1})]-\frac{E{\mathrm{\&beta;}}_0}{1-2v}(T_{01}+{{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}^2+\mathrm{<figure-callout\; id="0"\; label="n\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">n</figure-callout>}{T_{}}^{}{{}_0}^3),\\ {\mathrm{\&sigma;}}_{{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">y</figure-callout>}0}_1}=\frac{E}{(1-2v)(1+v)}[(1-v){\mathrm{\&epsiv;}}_{y01}+v({\mathrm{\&epsiv;}}_{x01}+{\mathrm{\&epsiv;}}_{z01})]-\frac{\mathrm{E\&beta;}}{1-2v}(T_{01}+{{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}^2+\mathrm{<figure-callout\; id="0"\; label="n\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">n</figure-callout>}{T_{}}^{}{{}_0}^3),\\ {\mathrm{\&sigma;}}_{z01}=\frac{E}{(1-2v)(1+v)}[(1-v){\mathrm{\&epsiv;}}_{z01}+v({\mathrm{\&epsiv;}}_{{\mathrm{<figure-callout\; id="1"\; label="yo"\; filenames="HDA0000452730040000041.png"\; state="\{\{state\}\}">yo</figure-callout>}}_1}+{\mathrm{\&epsiv;}}_{x01})]-\frac{E{\mathrm{\&beta;}}_0}{1-2v}(T_{01}+{{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}^2+\mathrm{<figure-callout\; id="0"\; label="n\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">n</figure-callout>}{T_{}}^{}{{}_0}^3)\end{array}\right\}---\left(12\right)$

……………………………

First solve the corresponding Thermoelastic Problems of formula (8); In the time of startup, shutdown or varying load, the vapor (steam) temperature of turbine rotor metal surface changes, optional position X in turbine rotor _cr(x ₀,, y ₀,, z ₀) can be calculated by following formula in temperature and the thermal stress of moment t:

$\left.\begin{array}{c}{T}_0(X_{\mathrm{cr}},t)=\underset{i}{\mathrm{\&Sigma;}}\underset{\mathrm{\&tau;}=0}{\overset{t}{\mathrm{\&Sigma;}}}\left[{G^{\&prime;}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{T}_{\mathrm{boi}}\left(\mathrm{\&tau;}\right)\right]\\ {\mathrm{\&sigma;}}_0(X_{\mathrm{cr}},t)=\underset{i}{\mathrm{\&Sigma;}}\underset{\mathrm{\&tau;}=0}{\overset{t}{\mathrm{\&Sigma;}}}\left[G{G^{\&prime;}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{T}_{\mathrm{boi}}\left(\mathrm{\&tau;}\right)\right]\end{array}\right\}---\left(13\right)$

T in formula _boi(t) be the vapor (steam) temperature at i level place of turbine rotor metal, Δ T _boi(t) be the variable quantity of vapor (steam) temperature, G' _boi(X _cr, t) and GG' _boi(X _cr, t) be the vapor (steam) temperature at i, turbine rotor metal level place position X in rotor while occurring that step changes _crin temperature and the THERMAL STRESS RESPONSE value of moment t;

Next solve formula (9) and (10) corresponding Thermoelastic Problems; By (T ₀+ mT ₀ ²) (T ₀-T _boi) and

at position X _cr(x ₀, y ₀, z ₀) locate to be launched into Taylor series, ignore second order and high order item, have:

$\left.\begin{array}{c}({\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0+\mathrm{<figure-callout\; id="0"\; label="m\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">m</figure-callout>}{T}_{}^{}{}_0^2)(T_0-T_{\mathrm{boi}})={\mathrm{\&eta;}}_1\left(t\right)+{\mathrm{\&eta;}}_2\left(t\right)x+{\mathrm{\&eta;}}_3\left(t\right)y+{\mathrm{\&eta;}}_4\left(t\right)z,\\ {\mathrm{\&lambda;}}_0{\&dtri;}^2(\frac{{{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}^2}{2}+\frac{\mathrm{<figure-callout\; id="0"\; label="m\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">m</figure-callout>}{T_{}}^{}{{}_0}^3}{3})={{\mathrm{\&eta;}}_1}^{\&prime;}\left(t\right)+{{\mathrm{\&eta;}}_2}^{\&prime;}\left(t\right)x+{{\mathrm{\&eta;}}_3}^{\&prime;}\left(t\right)y+{{\mathrm{\&eta;}}_4}^{\&prime;}\left(t\right)z\end{array}\right)---\left(14\right)$

In formula:

$\left.\begin{array}{c}{\mathrm{\&eta;}}_1\left(t\right)=({\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0+\mathrm{<figure-callout\; id="0"\; label="m\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">m</figure-callout>}{T_{}}^{}{{}_0}^2)(T_0-T_{\mathrm{boi}}){|}_{\mathrm{Xcr}}-\frac{\&PartialD;[({\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0+\mathrm{<figure-callout\; id="0"\; label="m\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">m</figure-callout>}{T_{}}^{}{{}_0}^2)(T_0-T_{\mathrm{boi}})}{\&PartialD;x}{|}_{X_{\mathrm{cr}}}{x}_0\\ -\frac{\&PartialD;[({\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0+\mathrm{<figure-callout\; id="0"\; label="m\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">m</figure-callout>}{T_{}}^{}{{}_0}^2)(T_0-T_{\mathrm{boi}})}{\&PartialD;y}{|}_{X_{\mathrm{cr}}}{y}_0-\frac{\&PartialD;\left[({\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0+\mathrm{<figure-callout\; id="0"\; label="m\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">m</figure-callout>}{T_{}}^{}{{}_0}^2)(T_0-T_{\mathrm{boi}})\right]}{\&PartialD;z}{|}_{X_{\mathrm{cr}}}{z}_0\end{array}\right\}---\left(15\right)$

${\mathrm{\&eta;}}_2\left(t\right)=\frac{\&PartialD;[({\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0+\mathrm{<figure-callout\; id="0"\; label="m\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">m</figure-callout>}{T}_{}^{}{}_0^2)(T_0-T_{\mathrm{boi}})}{\&PartialD;x}{|}_{X_{\mathrm{cr}}},{\mathrm{\&eta;}}_3\left(t\right)=\frac{\&PartialD;[({\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0+\mathrm{<figure-callout\; id="0"\; label="m\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">m</figure-callout>}{T}_{}^{}{}_0^2)(T_0-T_{\mathrm{boi}})}{\&PartialD;y}{|}_{X_{\mathrm{cr}},}{\mathrm{\&eta;}}_4\left(t\right)=\frac{\&PartialD;[({\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0+\mathrm{<figure-callout\; id="0"\; label="m\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">m</figure-callout>}{T}_{}^{}{}_0^2)(T_0-T_{\mathrm{boi}})}{\&PartialD;z}{|}_{X_{\mathrm{cr}},}---\left(16\right)$

$\left.\begin{array}{c}{{\mathrm{\&eta;}}_1}^{\&prime;}\left(t\right)=\left[{\mathrm{\&lambda;}}_0{\&dtri;}^2({{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}^2/2+\mathrm{<figure-callout\; id="0"\; label="m\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">m</figure-callout>}{T}_{}^{}{}_0^3/3)\right]{|}_{X_{\mathrm{cr}}}-\frac{\&PartialD;\left[{\mathrm{\&lambda;}}_0{\&dtri;}^2({{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}^2/2+\mathrm{<figure-callout\; id="0"\; label="m\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">m</figure-callout>}{T}_{}^{}{}_0^3/3)\right]}{\&PartialD;x}{|}_{X_{\mathrm{cr}}}{x}_0\\ -\frac{\&PartialD;\left[{\mathrm{\&lambda;}}_0{\&dtri;}^2({{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}^2/2+\mathrm{<figure-callout\; id="0"\; label="m\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">m</figure-callout>}{T}_{}^{}{}_0^3/3)\right]}{\&PartialD;y}{|}_{X_{\mathrm{cr}}}{y}_0-\frac{\&PartialD;\left[{\mathrm{\&lambda;}}_0{\&dtri;}^2({{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}^2/2+\mathrm{<figure-callout\; id="0"\; label="m\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">m</figure-callout>}{T_{}}^{}{{}_0}^3)\right]}{\&PartialD;z}{|}_{{\mathrm{<figure-callout\; id="0"\; label="X\; cr\; z"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">X</figure-callout>}}_{\mathrm{cr}}}{z}_{}{}_0\\ {{\mathrm{\&eta;}}_2}^{\&prime;}\left(t\right)=\frac{\&PartialD;\left[{\mathrm{\&lambda;}}_0{\&dtri;}^2({{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}^2/2+\mathrm{<figure-callout\; id="0"\; label="m\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">m</figure-callout>}{T_{}}^{}{{}_0}^3/3)\right]}{\&PartialD;x}{|}_{X_{\mathrm{cr}}}\\ {{\mathrm{\&eta;}}_3}^{\&prime;}\left(t\right)=\frac{\&PartialD;\left[{\mathrm{\&lambda;}}_0{\&dtri;}^2({{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}^2/2+\mathrm{<figure-callout\; id="0"\; label="m\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">m</figure-callout>}{T_{}}^{}{{}_0}^3/3)\right]}{\&PartialD;y}{|}_{X_{\mathrm{cr}}}\\ {{\mathrm{\&eta;}}_4}^{\&prime;}\left(t\right)=\frac{\&PartialD;\left[{\mathrm{\&lambda;}}_0{\&dtri;}^2({{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}^2/2+\mathrm{<figure-callout\; id="0"\; label="m\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">m</figure-callout>}{T_{}}^{}{{}_0}^3/3)\right]}{\&PartialD;z}{|}_{X_{\mathrm{cr}}};\end{array}\right\}---\left(17\right)$

By the vapor (steam) temperature substitution of turbine rotor surface, by formula (9) and the interior position X of turbine rotor corresponding to (10) defined Thermoelastic Problems _crtemperature and stress in the time of moment t can be expressed as:

The solution in temperature field can be expressed as:

$T_{10}=\underset{0}{\overset{t}{\text{\&Integral;}}}\underset{\mathrm{\&Gamma;}}{\&Integral;}G({\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0+\mathrm{<figure-callout\; id="0"\; label="m\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">m</figure-callout>}{T_{}}^{}{{}_0}^2)(T_0-T_{\mathrm{boi}})\mathrm{d\&Gamma;d\&tau;}+\underset{0}{\overset{t}{\&Integral;}}\underset{\mathrm{\&Omega;}}{\&Integral;}G{\mathrm{\&lambda;}}_0{\&dtri;}^2(\frac{{{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}^2}{2}+\frac{\mathrm{<figure-callout\; id="0"\; label="m\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">m</figure-callout>}{T_{}}^{}{{}_0}^3}{3})\mathrm{d\&Omega;d\&tau;}$

In formula, G is formula (9) and Green function corresponding to (10) corresponding Thermoelastic Problems, the outer boundary that Γ is turbine rotor, and Ω is turbine rotor volume;

For ease of computing machine processing, write formula (18) as discrete form in time domain:

$\begin{array}{c}{T}_{10}(X_{\mathrm{cr}},t)=\underset{i}{\mathrm{\&Sigma;}}\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[G_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{\mathrm{\&eta;}}_1\left(\mathrm{\&tau;}\right)\right]+\underset{i}{\mathrm{\&Sigma;}}\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{Gx}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{\mathrm{\&eta;}}_2\left(\mathrm{\&tau;}\right)\right]\\ +\underset{i}{\mathrm{\&Sigma;}}\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{Gy}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{\mathrm{\&eta;}}_3\left(\mathrm{\&tau;}\right)\right]+\underset{i}{\mathrm{\&Sigma;}}\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GZ}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{\mathrm{\&eta;}}_4\left(\mathrm{\&tau;}\right)\right]\\ +\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GV}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{{\mathrm{\&eta;}}_1}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]+\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GVx}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{{\mathrm{\&eta;}}_2}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]\\ +\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GV}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{{\mathrm{\&eta;}}_3}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]+\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GVy}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{{\mathrm{\&eta;}}_4}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]\end{array}---\left(19\right)$

$\begin{array}{c}{\mathrm{\&sigma;}}_{10}(X_{\mathrm{cr}},t)=\underset{i}{\mathrm{\&Sigma;}}\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GG}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{\mathrm{\&eta;}}_1\left(\mathrm{\&tau;}\right)\right]+\underset{i}{\mathrm{\&Sigma;}}\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GGx}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{\mathrm{\&eta;}}_2\left(\mathrm{\&tau;}\right)\right]\\ +\underset{i}{\mathrm{\&Sigma;}}\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GGy}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{\mathrm{\&eta;}}_3\left(\mathrm{\&tau;}\right)\right]+\underset{i}{\mathrm{\&Sigma;}}\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GGZ}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{\mathrm{\&eta;}}_4\left(\mathrm{\&tau;}\right)\right]\\ +\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GGV}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{{\mathrm{\&eta;}}_1}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]+\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[G{\mathrm{GVx}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{{\mathrm{\&eta;}}_2}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]\\ +\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[G{\mathrm{GV}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{{\mathrm{\&eta;}}_3}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]+\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GGVz}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{{\mathrm{\&eta;}}_4}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]\end{array}---\left(20\right)$

Gx in formula _boi(X _cr, t) andGGx _boi(X _cr, t) in the time that vapor (steam) temperature input signal is ux (x, t), X in turbine rotor metal construction _crtemperature and the stress response value of position in the time of moment t, Gy _boi(X _cr, t) and GGy _boi(X _cr, t) in the time that vapor (steam) temperature input signal is uy (y, t), X in turbine rotor structure _crtemperature and the stress response value of position in the time of moment t, GZ _boi(X _cr, t) and GGZ _boi(X _cr, t) in the time that vapor (steam) temperature input signal is uz (z, t), X in steam turbine structure _crtemperature and the stress response value of position in the time of moment t, GV _boi(X _cr, t) and GGV _boi(X _cr, t) in the time that turbine rotor endogenous pyrogen intensity generation step changes, X in steam turbine structure _crtemperature and the stress response value of position in the time of moment t, GVx _boi(X _cr, t) and GGVx _boi(X _cr, t) in the time that turbine rotor endogenous pyrogen intensity input signal is ux (x, t), X in rotor structure _crtemperature and the stress response value of position in the time of moment t, GVy _boi(X _cr, t) and GGVy _boi(X _cr, t) in the time that turbine rotor endogenous pyrogen intensity input signal is uy (y, t), X in rotor structure _crtemperature and the stress response value of position in the time of moment t, GVZ _boi(X _cr, t) and GGVZ _boi(X _cr, t) in the time that turbine rotor endogenous pyrogen intensity input signal is uz (z, t), X in rotor structure _crtemperature and the stress response value of position in the time of moment t, the input signal definition is here respectively:

$\mathrm{ux}(x,t)=\left\{\begin{array}{c}x,t>0\\ 0,t=0\end{array}\right.,\mathrm{uy}(z,t)=\left\{\begin{array}{c}y,t>0\\ 0,t=0\end{array}\right.,\mathrm{uz}(z,t)=\left\{\begin{array}{c}z,t>0\\ 0,t=0\end{array}\right.;$

For solving by formula (11) and (12) corresponding Thermoelastic Problems, establish T ₁₀=T ₁₀'+T ₀ ²+ nT ₀ ³, by formula (9), can obtain

Can obtain:

$\begin{array}{c}{T_{10}}^{\&prime;}=G\underset{0}{\overset{t}{\&Integral;}}\underset{\mathrm{\&Gamma;}}{\&Integral;}[({\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0+\mathrm{<figure-callout\; id="0"\; label="m\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">m</figure-callout>}{T_{}}^{}{{}_0}^2)(T_0-T_{\mathrm{boi}})-({{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}^2+\mathrm{<figure-callout\; id="0"\; label="n\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">n</figure-callout>}{T_{}}^{}{{}_0}^3)+(2{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0+3\mathrm{<figure-callout\; id="0"\; label="n\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">n</figure-callout>}{T_{}}^{}{{}_0}^2)(T_0-T_{\mathrm{boi}})]\mathrm{d\&Gamma;d\&tau;}\\ +\underset{0}{\overset{t}{\&Integral;}}\underset{\mathrm{\&Omega;}}{\text{\&Integral;}}G[{\mathrm{\&lambda;}}_0{\&dtri;}^2(\frac{{{3\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}^2}{2}+\mathrm{<figure-callout\; id="0"\; label="m\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">m</figure-callout>}\frac{{T_{}}^{}}{}\frac{{{}_0}^3}{3}+\mathrm{<figure-callout\; id="0"\; label="n\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">n</figure-callout>}{T_{}}^{}{{}_0}^3)-\mathrm{\&rho;c}\frac{\&PartialD;({{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}^2+\mathrm{<figure-callout\; id="0"\; label="n\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">n</figure-callout>}{T_{}}^{}{{}_0}^3)}{\&PartialD;t}]\mathrm{d\&Omega;d\&tau;}\end{array}---\left(22\right)$

Thermal stress component is:

$\begin{array}{c}{\mathrm{\&sigma;}}_{x{0}_1}=\frac{E}{(1-2v)(1+v)}[(1-v){\mathrm{\&epsiv;}}_{x01}+v({\mathrm{\&epsiv;}}_{y01}+{\mathrm{\&epsiv;}}_{z01})]+\underset{0}{\overset{t}{\&Integral;}}\underset{\mathrm{\&Omega;}}{\&Integral;}G[\mathrm{\&rho;c}\frac{\&PartialD;({{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}^2+\mathrm{<figure-callout\; id="0"\; label="n\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">n</figure-callout>}{T_{}}^{}{{}_0}^3)}{\&PartialD;t}-{\mathrm{\&lambda;}}_0{\&dtri;}^2({{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}^2+\mathrm{<figure-callout\; id="0"\; label="n\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">n</figure-callout>}{T_{}}^{}{{}_0}^3)]\mathrm{d\&Omega;d\&tau;}\\ -\frac{E{\mathrm{\&beta;}}_0}{1-2v}\left\{\underset{0}{\overset{t}{\&Integral;}}\underset{\mathrm{\&Gamma;}}{\&Integral;}G\right[({{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}^2+\mathrm{<figure-callout\; id="0"\; label="n\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">n</figure-callout>}{T_{}}^{}{{}_0}^3)-(2{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0+3\mathrm{<figure-callout\; id="0"\; label="n\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">n</figure-callout>}{T_{}}^{}{{}_0}^2)(T_0-T_{\mathrm{boi}})\left]\mathrm{d\&Gamma;d\&tau;}\right\},\end{array}---\left(24\right)$

Will $\left.\begin{array}{c}\mathrm{\&rho;c}\frac{\&PartialD;({{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}^2+\mathrm{<figure-callout\; id="0"\; label="n\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">n</figure-callout>}{T}_{}^{}{}_0^3)}{\&PartialD;t}-{\mathrm{\&lambda;}}_0{\&dtri;}^2({{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}^2+\mathrm{<figure-callout\; id="0"\; label="n\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">n</figure-callout>}{T_{}}^{}{{}_0}^3)\\ ({{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}^2+\mathrm{<figure-callout\; id="0"\; label="n\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">n</figure-callout>}{T_{}}^{}{{}_0}^3)-(2{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0+3\mathrm{<figure-callout\; id="0"\; label="n\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">n</figure-callout>}{T_{}}^{}{{}_0}^2)(T_0-T_{\mathrm{boi}})\end{array}\right\}---\left(25\right)$

At turbine rotor surface monitoring point position X _cr(x ₀, y ₀, z ₀) be launched into Taylor series, neglect second order and higher order term, can obtain:

$({{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}^2+\mathrm{<figure-callout\; id="0"\; label="n\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">n</figure-callout>}{T_{}}^{}{{}_0}^3)-(2{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0+3\mathrm{<figure-callout\; id="0"\; label="n\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">n</figure-callout>}{T_{}}^{}{{}_0}^2)(T_0-T_{\mathrm{boi}})={\mathrm{\&phi;}}_1\left(t\right)+{\mathrm{\&phi;}}_2\left(t\right)x+{\mathrm{\&phi;}}_3\left(t\right)x+{\mathrm{\&phi;}}_4\left(t\right)z---\left(26\right)$

$\mathrm{\&rho;c}\frac{\&PartialD;({{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}^2+\mathrm{<figure-callout\; id="0"\; label="n\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">n</figure-callout>}{T_{}}^{}{{}_0}^3)}{\&PartialD;t}-{\mathrm{\&lambda;}}_0{\&dtri;}^2({{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}^2+\mathrm{<figure-callout\; id="0"\; label="n\; T"\; filenames="HDA0000452730040000031.png,HDA0000452730040000051.png"\; state="\{\{state\}\}">n</figure-callout>}{T_{}}^{}{{}_0}^3)={{\mathrm{\&phi;}}_1}^{\&prime;}\left(t\right)+{{\mathrm{\&phi;}}_2}^{\&prime;}\left(t\right)x+{{\mathrm{\&phi;}}_3}^{\&prime;}\left(t\right)y+{{\mathrm{\&phi;}}_4}^{\&prime;}\left(t\right)z---\left(27\right)$

In formula:

By formula (22) to (26), position, turbine rotor monitoring point X _cr(x ₀, _y0,, z ₀) temperature and the thermal stress of moment t can be expressed as under by formula (11) and (12) defined Thermoelastic Problems:

T ₀₁＝0

(29)

$\begin{array}{c}{\mathrm{\&sigma;}}_{01}(X_{\mathrm{cr}},t)=\underset{i}{\mathrm{\&Sigma;}}\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GG}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{\mathrm{\&phi;}}_1\left(\mathrm{\&tau;}\right)\right]+\underset{i}{\mathrm{\&Sigma;}}\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GGx}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{\mathrm{\&phi;}}_2\left(\mathrm{\&tau;}\right)\right]\\ +\underset{i}{\mathrm{\&Sigma;}}\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GGy}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{\mathrm{\&phi;}}_3\left(\mathrm{\&tau;}\right)\right]+\underset{i}{\mathrm{\&Sigma;}}\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GGZ}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{\mathrm{\&phi;}}_4\left(\mathrm{\&tau;}\right)\right]\\ +\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GGV}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{{\mathrm{\&phi;}}_1}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]+\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[G{\mathrm{GVx}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{{\mathrm{\&phi;}}_2}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]\\ +\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[G{\mathrm{GV}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{{\mathrm{\&phi;}}_3}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]+\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GGVy}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{{\mathrm{\&phi;}}_4}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]\end{array}---\left(30\right)$

Wushu (13), (19), (20), (29) and (30) substitution formulas (7) can obtain three-dimensional structure monitoring point position temperature and thermal stress analytical calculation model:

Temperature field: T=T ₀+ ε T ₁₀, (31)

Wherein, $T_0(X_{\mathrm{cr}},t)=\underset{i}{\mathrm{\&Sigma;}}\underset{\mathrm{\&tau;}=0}{\overset{t}{\mathrm{\&Sigma;}}}\left[{G^{\&prime;}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{T}_{\mathrm{boi}}\left(\mathrm{\&tau;}\right)\right],$

$\begin{array}{c}{T}_{10}(X_{\mathrm{cr}},t)=\underset{i}{\mathrm{\&Sigma;}}\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[G_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{\mathrm{\&eta;}}_1\left(\mathrm{\&tau;}\right)\right]+\underset{i}{\mathrm{\&Sigma;}}\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{Gx}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{\mathrm{\&eta;}}_2\left(\mathrm{\&tau;}\right)\right]\\ +\underset{i}{\mathrm{\&Sigma;}}\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{Gy}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{\mathrm{\&eta;}}_3\left(\mathrm{\&tau;}\right)\right]+\underset{i}{\mathrm{\&Sigma;}}\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GZ}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{\mathrm{\&eta;}}_4\left(\mathrm{\&tau;}\right)\right]\\ +\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GV}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{{\mathrm{\&eta;}}_1}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]+\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GVx}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{{\mathrm{\&eta;}}_2}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]\\ +\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GV}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{{\mathrm{\&eta;}}_3}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]+\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GVz}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{{\mathrm{\&eta;}}_4}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]\end{array}$

Stress field: σ=σ ₀+ ε σ ₁₀+ ξ σ ₀₁(32)

Wherein, ${\mathrm{\&sigma;}}_0(X_{\mathrm{cr}},t)=\underset{i}{\mathrm{\&Sigma;}}\underset{\mathrm{\&tau;}=0}{\overset{t}{\mathrm{\&Sigma;}}}\left[{{\mathrm{GG}}^{\&prime;}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{T}_{\mathrm{boi}}\left(\mathrm{\&tau;}\right)\right],$

$\begin{array}{c}{\mathrm{\&sigma;}}_{10}(X_{\mathrm{cr}},t)=\underset{i}{\mathrm{\&Sigma;}}\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[G{G}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{\mathrm{\&eta;}}_1\left(\mathrm{\&tau;}\right)\right]+\underset{i}{\mathrm{\&Sigma;}}\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GGx}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{\mathrm{\&eta;}}_2\left(\mathrm{\&tau;}\right)\right]\\ +\underset{i}{\mathrm{\&Sigma;}}\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GGy}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{\mathrm{\&eta;}}_3\left(\mathrm{\&tau;}\right)\right]+\underset{i}{\mathrm{\&Sigma;}}\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GGZ}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{\mathrm{\&eta;}}_4\left(\mathrm{\&tau;}\right)\right]\\ +\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[G{\mathrm{GV}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{{\mathrm{\&eta;}}_1}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]+\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GGVx}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{{\mathrm{\&eta;}}_2}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]\\ +\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[G{\mathrm{GV}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{{\mathrm{\&eta;}}_3}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]+\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GGVz}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{{\mathrm{\&eta;}}_4}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]\end{array},$

$\begin{array}{c}{\mathrm{\&sigma;}}_{01}(X_{\mathrm{cr}},t)=\underset{i}{\mathrm{\&Sigma;}}\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GG}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{\mathrm{\&phi;}}_1\left(\mathrm{\&tau;}\right)\right]+\underset{i}{\mathrm{\&Sigma;}}\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GGx}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{\mathrm{\&phi;}}_2\left(\mathrm{\&tau;}\right)\right]\\ +\underset{i}{\mathrm{\&Sigma;}}\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GGy}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{\mathrm{\&phi;}}_3\left(\mathrm{\&tau;}\right)\right]+\underset{i}{\mathrm{\&Sigma;}}\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GGZ}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{\mathrm{\&phi;}}_4\left(\mathrm{\&tau;}\right)\right]\\ +\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GGV}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{{\mathrm{\&phi;}}_1}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]+\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[G{\mathrm{GVx}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{{\mathrm{\&phi;}}_2}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]\\ +\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[G{\mathrm{GV}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{{\mathrm{\&phi;}}_3}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]+\underset{\mathrm{\&tau;}=t_D}{\overset{t}{\mathrm{\&Sigma;}}}\left[{\mathrm{GGVy}}_{\mathrm{boi}}(X_{\mathrm{cr}},t-\mathrm{\&tau;})\mathrm{\&Delta;}{{\mathrm{\&phi;}}_4}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]\end{array}$

In formula, each variable-definition is shown in formula (7), (13), (19), (20), (29) and (30);

Step (2): the three-dimensional temperature and the thermal stress monitoring model that build according to step (1), obtain the three-dimensional temperature of optional position in supercritical turbine rotor and the change information of thermal stress, thereby three-dimensional temperature and thermal stress to optional position in supercritical turbine rotor are carried out Real-Time Monitoring, avoid turbine rotor overstressing, thereby ensure steam turbine operation safety, instruct steam turbine start and stop and variable load operation.

Compared with prior art, the present invention's feature of being heated while operation according to supercritical turbine, set out by Three-dimensional Thermal-elastic equation, the computing formula of temperature and thermal stress is expressed by the form of Green function, utilize Finite Element Method calculated off-line Green function, for improving model computational accuracy, utilize the physical parameter problem that multiparameter perturbation method treatment temperature is relevant, process by the method for design Green's function database the problem that becomes the coefficient of heat transfer.The method can provide very high computational accuracy, can calculate optional position temperature simultaneously, in the time of line computation, need not carry out grid division, and computing velocity is fast, is suitable for on-line monitoring.

Brief description of the drawings

Below in conjunction with the drawings and specific embodiments, the present invention is further described most.

Fig. 1 is typical ultra supercritical unit high pressure rotor impeller cooling system;

Fig. 2 presses impeller of rotor cooling system in typical ultra supercritical unit;

Fig. 3 is the local structural graph of three-dimensional pressure container of the present invention;

Fig. 4 is that unit vapor (steam) temperature of the present invention changes course;

Fig. 5 a be in Fig. 3 A point position taking observed temperature result as standard, the temperature deviation curve between the model calculation and the standard results being proposed by normal physical property Green Function Method result of calculation and the present invention;

Fig. 5 b be in Fig. 3 B point position taking observed temperature result as standard, the temperature deviation curve between the model calculation and the standard results being proposed by normal physical property Green Function Method result of calculation and the present invention;

Fig. 5 c be in Fig. 3 C point position taking observed temperature result as standard, the temperature deviation curve between the model calculation and the standard results being proposed by normal physical property Green Function Method result of calculation and the present invention;

Fig. 6 a is by the correlation curve that measures A point position equivalent speed stress calculating results in the Fig. 3 calculating with model of the present invention;

Fig. 6 b is by the correlation curve that measures B point position equivalent speed stress calculating results in the Fig. 3 calculating with model of the present invention;

Fig. 6 c is by the correlation curve that measures C point position equivalent speed stress calculating results in the Fig. 3 calculating with model of the present invention;

Fig. 7 is high pressure cylinder vapor (steam) temperature measuring point of the present invention installation site schematic diagram;

Fig. 8 is intermediate pressure cylinder vapor (steam) temperature measuring point of the present invention installation site schematic diagram;

Fig. 9 is the block diagram of the three-dimensional temperature of supercritical turbine rotor of the present invention and thermal stress method of real-time.

Embodiment

It while operation because of turbine rotor, is High Rotation Speed state, cannot directly measure rotor metal temperature and stress, below taking a three-dimensional pressure container as object, adopt respectively invention modeling calculate and measurement method to obtain position, monitoring point temperature and stress result under given operating mode, thereby checking propose the computational accuracy of model.When this pressure vessel operation, its inside surface contacts with steam and carries out convection heat transfer, outside surface thermal insulation, there is complicated three-dimensional structure, closely similar with supercritical turbine operation characteristic, the computation model that this patent proposes is applicable to being applied to this pressure vessel equally, but does not need rotation when the operation of this pressure vessel, can measuring point be set at pressure vessel wall and directly measure wall surface temperature and stress.

The profile of pressure vessel and main physical dimension are shown in Fig. 3, consider the symmetry of structure, choose the section of 45o as shown in the figure as analytic target.

Consider the dependent physical parameter of temperature in table 1.Inside surface and steam carry out convection heat transfer, heat up 150 minutes since 0 degree with the temperature rise rates of 2 degrees/min, then remain on 300 degree 180 minutes, finally in 120 minutes, are reduced to 0 degree.Outside surface is assumed to be thermal insulation.The variation of measuring this monitoring point place temperature and thermal stress at A, B and the C point sensor installation of container respectively.

Table 1 reactor pressure vessel physical parameter

Fig. 5 a, Fig. 5 b, Fig. 5 c have provided respectively taking observed temperature result as standard, by normal physical property Green Function Method result of calculation and propose the temperature deviation curve between the model calculation and standard results herein, A, B in figure, 3 positions of C indicate in Fig. 3.

Fig. 6 a, Fig. 6 b, Fig. 6 c have provided respectively respectively by the A, the B that measure and model calculates herein, the correlation curve of 3 equivalent speed stress calculating results of C.

Can see equally from Fig. 5 a, Fig. 5 b, Fig. 5 c and Fig. 6 a, Fig. 6 b, Fig. 6 c, while considering temperature on the affecting of physical parameter, when the interior temperature of pressure vessel and stress and normal physical property, there is significant difference, model in this paper can address this problem preferably, and herein the result of finite element degree of agreement of model when considering temperature on the affecting of physical parameter is very good.

For complicated three-dimensional structure, for improving computational accuracy, its Green function can carry out numerical evaluation by finite element, then result of calculation is fitted to the form of sum of series.For operating modes such as startup, shutdown and varying loaies, between steam and rotor, convection transfer rate is relevant with temperature with vapor pressure, in the time of unit operation, is time dependent.In the time that the coefficient of heat transfer is the numerical value changing, Green function need adopt finite element method to recalculate in principle, very consuming time, can not meet the requirement of on-line monitoring.For this problem, this patent proposes to adopt the Green's function database with certain Density Distribution of calculated off-line corresponding to various heat exchange coefficient, when on-line monitoring, by vapor pressure and the temperature of actual measurement, from Green's function database, choose immediate Green function, then the Green function selecting is carried out to linear interpolation, thereby obtain fast the Green function corresponding with the vapor pressure of surveying and temperature, obtain high-precision result of calculation.

Supercritical turbine temperature of rotor and thermal stress monitoring model online that this patent proposes, computational accuracy is high, computing velocity is fast, required vapor (steam) temperature as shown in Figures 7 and 8, for high pressure rotor, need install and measure at governing stage impeller exhaust casing position the temperature sensor of cooling steam temperature real-time information, installation position as shown in Figure 7, because cooling steam is steam after governing stage, if thermocouple temperature sensor has been established at this position, without other hypothesis, for middle pressure rotor, need install and measure at cylinder and dividing plate position the temperature sensor of cooling steam temperature real-time information, installation position as shown in Figure 8, shown in whole temperature and thermal stress real-time monitoring system composition diagram 9.

The feature of being heated when the method is moved according to supercritical turbine, set out by heat conduction equation in three-dimensional body, the computing formula of turbine rotor monitoring point position place temperature and thermal stress is expressed by the form of Green function, utilize Finite Element Method calculated off-line Green function, warp is to steam turbine practical structures shape, after the accurate simulation of cooling steam duty and multiple raising precision methods are processed, utilize finally accounting temperature and thermal stress distribution fast and accurately of Green function, the result of calculation obtaining and result of finite element are very approaching, there is desirable computational accuracy, model is simple simultaneously, calculate rapidly, can be accurately and optional position temperature and thermal stress change information in Real-Time Monitoring supercritical turbine rotor, avoid overstressing, thereby the safety while having protected steam turbine operation, instruct steam turbine start and stop and variable load operation, economy while improving operation.

Claims (1)

1. the three-dimensional temperature of supercritical turbine rotor and thermal stress method of real-time, the method comprises the steps:

Step (1): build the three-dimensional temperature of supercritical turbine rotor and thermal stress monitoring model

Structure and the derivation of the three-dimensional temperature of described supercritical turbine rotor and thermal stress monitoring model are as follows:

The differential equation of the non-linear transient state Heat Conduction Problems of turbine rotor in the time considering physical parameter to the dependence of temperature below meeting during as three-dimensional structure:

In formula, T is turbine rotor in-vivo metal temperature, and λ is turbine rotor Thermal Conductivity by Using, and ρ is turbine rotor density metal, and c is that turbine rotor metal specific heat holds, and t is the time, x, and y, z is coordinate variable, ▽, ▽ is three-dimensional divergence and gradient operator;

Initial temperature is assumed to be evenly, adopts the 3rd class Transfer Boundary Condition:

In formula, boi represents i surface of turbine rotor metal, T _boirepresent i surface vapor (steam) temperature of turbine rotor metal, in this temperature engineering, the general temperature sensor that adopts is directly measured, and can be used as the function into time t;

When temperature variation is not very acutely, the calculating of stress field can be carried out after temperature field analysis; By thermoelastic theory, the intrametallic stress of three-dimensional turbine rotor, strain and displacement meet constitutive equation below:

In formula, E is turbine rotor Elastic Modulus for Metals, and β is turbine rotor expansion coefficients of metal wire, and ν is turbine rotor metal Poisson ratio, σ _x, σ _yand σ _zfor thermal stress component in turbine rotor metal;

In turbine rotor metal, each physical parameter can adopt the physical parameter formula of temperature second order function to represent,

That is:

P＝P ₀(1+P ₁T+P ₂T ²) (4)

P in formula ₀, P ₁and P ₂it is turbine rotor metal material constant;

The physical parameter of turbine rotor Thermal Conductivity by Using and linear expansion coefficient can be expressed as:

λ＝λ ₀(1+λ ₁T+λ ₂T ²)，β＝β ₀(1+β ₁T+β ₂T ²) (5)

Other the physical parameter such as elastic modulus and specific heat capacity can be adopted the correlativity that uses the same method to process itself and temperature; Conventionally-1<< λ ₁and β ₁<<1, supposes ε=λ ₁and ξ=β ₁for small parameter:

The polynomial form that temperature, stress and strain in turbine rotor metal is launched into small parameter ε and ξ, has:

Be updated to formula (2) and formula (3), the homogeneous item of merger ε and ξ, can obtain:

ε ⁰ξ 0 ^:

boundary condition

ε1ξ0：

Corresponding boundary condition is:

ε ⁰ξ ¹：

corresponding boundary condition is

………………………………

First solve the corresponding Thermoelastic Problems of formula (8); In the time of startup, shutdown or varying load, the vapor (steam) temperature of turbine rotor metal surface changes, optional position X in turbine rotor _cr(x ₀,, y ₀,, z ₀) can be calculated by following formula in temperature and the thermal stress of moment t:

Tboi in formula (t) is the vapor (steam) temperature at i level place of turbine rotor metal, Δ T _boi(t) be the variable quantity of vapor (steam) temperature, G' _boi(X _cr, t) and GG' _boi(X _cr, t) be the vapor (steam) temperature at i, turbine rotor metal level place position X in rotor while occurring that step changes _crin temperature and the THERMAL STRESS RESPONSE value of moment t;

Next solve formula (9) and (10) corresponding Thermoelastic Problems; Will

with at position X _cr(x ₀, y ₀, z ₀) locate to be launched into Taylor series, ignore second order and high order item, have:

In formula:

By the vapor (steam) temperature substitution of turbine rotor surface, by position Xcr in formula (9) and turbine rotor corresponding to (10) defined Thermoelastic Problems, temperature and the stress when the moment t can be expressed as:

The solution in temperature field can be expressed as:

In formula, G is formula (9) and Green function corresponding to (10) corresponding Thermoelastic Problems, the outer boundary that Γ is turbine rotor, and Ω is turbine rotor volume;

For ease of computing machine processing, write formula (18) as discrete form in time domain:

Gx in formula _boi(X _cr, t) andGGx _boi(X _cr, t) in the time that vapor (steam) temperature input signal is ux (x, t), X in turbine rotor metal construction _crtemperature and the stress response value of position in the time of moment t, Gy _boi(X _cr, t) and GGy _boi(X _cr, t) in the time that vapor (steam) temperature input signal is uy (y, t), X in turbine rotor structure _crtemperature and the stress response value of position in the time of moment t, GZ _boi(X _cr, t) and GGZ _boi(X _cr, t) in the time that vapor (steam) temperature input signal is uz (z, t), X in steam turbine structure _crtemperature and the stress response value of position in the time of moment t, GV _boi(X _cr, t) and GGV _boi(X _cr, t) in the time that turbine rotor endogenous pyrogen intensity generation step changes, X in steam turbine structure _crtemperature and the stress response value of position in the time of moment t, GVx _boi(X _cr, t) and GGVx _boi(X _cr, t) in the time that turbine rotor endogenous pyrogen intensity input signal is ux (x, t), X in rotor structure _crtemperature and the stress response value of position in the time of moment t, GVy _boi(X _cr, t) and GGVy _boi(X _cr, t) in the time that turbine rotor endogenous pyrogen intensity input signal is uy (y, t), X in rotor structure _crtemperature and the stress response value of position in the time of moment t, GVZ _boi(X _cr, t) and GGVZ _boi(X _cr, t) in the time that turbine rotor endogenous pyrogen intensity input signal is uz (z, t), X in rotor structure _crtemperature and the stress response value of position in the time of moment t, the input signal definition is here respectively:

For solving by formula (11) and (12) corresponding Thermoelastic Problems, establish

By formula (9), can obtain

Can obtain:

Thermal stress component is:

Will

At turbine rotor surface monitoring point position X _cr(x ₀, y ₀, z ₀) be launched into Taylor series, neglect second order and higher order term, can obtain:

(T ₀ ²+nT ₀ ³)-(2T ₀+3nT ₀ ²)(T ₀-T _boi)＝φ ₁(t)+φ ₂(t)x+φ ₃(t)x+φ ₄(t)z (26)

In formula:

By formula (22) to (26), position, turbine rotor monitoring point X _cr(x ₀, y ₀,, z ₀) temperature and the thermal stress of moment t can be expressed as under by formula (11) and (12) defined Thermoelastic Problems:

T ₀₁＝0(29)

Wushu (13), (19), (20), (29) and (30) substitution formulas (7) can obtain three-dimensional

Structure monitoring point position temperature and thermal stress analytical calculation model:

Temperature field: T=T ₀+ ε T ₁₀, (31)

Wherein,

Stress field: σ=σ ₀+ ε σ ₁₀+ ξ σ ₀₁(32)

Wherein,

In formula, each variable-definition is shown in formula (7), (13), (19), (20), (29) and (30);

Step (2): the three-dimensional temperature and the thermal stress monitoring model that build according to step (1), obtain the three-dimensional temperature of optional position in supercritical turbine rotor and the change information of thermal stress, thereby three-dimensional temperature and thermal stress to optional position in supercritical turbine rotor are carried out Real-Time Monitoring, avoid turbine rotor overstressing, thereby ensure steam turbine operation safety, instruct steam turbine start and stop and variable load operation.

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