DE3346579A1 - METHOD AND DEVICE FOR DETERMINING AN INSTATIONAL TEMPERATURE PROFILE ABOVE THE WALL THICKNESS OF A COMPONENT - Google Patents

Abstract

Method and device for detecting the temperatures through the wall thickness of a building element, particularly a thick plate or pipe. Such a method is intended to determine an instationary temperature profile throughout the wall thickness of a building element, particularly a steam generator pipe. The whole temperature profile caused by the heat transport process is thus determined from the chronological order of temperature measurement values of a thermoelement at a single measuring point at the vicinity of inner fibres of the building element on the basis of a given balance equation.

Description

33 ^ 6579

Method and device for determining an unsteady temperature profile over the wall thickness

of a component

The invention relates to a method and a device for detecting temperatures above the wall thickness of a component, in particular a thick-walled plate or a thick-walled pipe. Such a method is used to determine a transient Temperature profile over the wall thickness of a component, in particular a pipe in steam generators.

The temperature of a thick-walled one through which a hot medium flows When the medium temperature changes, Rohres does not adjust to the new temperature as quickly as desired. Rather, it fits the temperature of the inner fiber adapts to the new temperature more quickly than the temperature averaged over the cross-section . , ·

The inner fiber is at the rapid temperature adaptation, however hindered in their thermal expansion by the surrounding material. This creates strong stresses that lead to material fatigue lead (low cycle fatique).

According to the supervision regulations of the Technical Supervision Association for steam generators, to avoid accidents bursting pipes the material fatigue of pipes can be recalculated from measured values. The recalculation has been carried out so far so that the temperatures of the inner fiber and the center of the wall of a pipe were measured and from this using the following formula

= α.

1-v

Δ-θ

the thermal stress was calculated;

-2-

= the shape number for the thermal stress,

ß _L = the differential linear expansion,

= the modulus of elasticity,

Δθ = the temperature difference,

and

ν = the number of cross contacts.

It turned out that the measurement made in this way is very imprecise for the following reasons:

- If electrically isolated thermocouples are used, the temperature difference can be achieved by direct counter-switching can be determined, but this determination is imprecise because these thermocouples themselves have a time behavior have and the geometric position of the thermocouple tip can only be precisely determined by X-rays, wherein the properties of the insulating material of the thermocouples are mostly unknown.

- If non-isolated thermocouples are used, each of the two thermocouples must first be made potential-free with a transmitter before the temperature difference can be established; this creates a non-negligible error due to the phase shift of the transducers.

-3-

- The temperature of the inner fiber is in practice not without it further measurable; instead, three to five millimeters away from the inner fiber is measured through a hole from the outside, so that there is an inaccuracy due to the spatial shift that the integral mean Wall temperature is measured through an offset thermal sleeve in wall rails.

The invention is based on the object of specifying a method and a device, with which the temperatures above the The thickness of a component can be precisely recorded, 'grounded.

According to the invention, the object is achieved with the features of the main claim solved. Advantageous refinements of the invention are specified in the subclaims. It is special It is advantageous that only one thermocouple is to be used in order to determine from the time sequence of measured values of this thermocouple to determine the complete temperature profile over the wall thickness of the corresponding component at its measuring point.

Further details and advantages of the invention are based on the description and German? Drawing explained in more detail. Show it

1 shows a section through an arrangement of a thermocouple in a component according to the invention

and

2 shows a section of a component with a measuring point of a thermocouple according to the invention.

According to FIG. 1, a thermocouple 10 is arranged in the vicinity of the inner fiber of a component 12. The thermocouple is placed in a holder 14.

-A-

With such an arrangement of a thermocouple nearby the inner fiber of a component can be the complete temperature profile over the wall thickness of the component according to the following Record the procedure precisely. The computational determination is made using microprocessors and the electronic Carry out data processing in the usual way.

The procedure used to determine the full temperature profile over the wall thickness of a component from the chronological sequence of temperature readings of a thermocouple on its The balance equation underlying the measuring point near the inner fiber of the component is found as follows.

The heat transport processes causing the three-dimensional temperature profile can basically be described by the following Fourier differential equation:

Θχ ² 3y ² 3z ²

a (- &) = the thermal diffusivity of the component,

Cp Xp

λ = the coefficient of thermal conductivity of the component,

= the specific heat capacity of the component,

-5-

p = the density of the component material, θ _(τχγζ) = the temperature τ = the time
xyz = the space coordinates.

Since the direction of the heat flow is largely related to a coordinate direction agrees, only the one-dimensional is of interest here Temperature profile given by the following balance equation is described:

3ΐ

(21,

where, according to Fig. 2, the following boundary conditions apply:

= ^f C *> ^{for x} = ^r _me

= 0 for x = r. (4)

3x

(Insulation)

The initial condition also applies (for the unsteady case)

-Ö- _(TX) = g (t) for x = 0 (5),

• V · ·

-6-

a unique solution of the differential equation for the determination of the temperature profile between the measuring point (x = r) and the outer fiber (x = r).

To determine the full temperature profile, i. H. from the inner fiber (x = r.) to the outer fiber, there is a third To meet boundary condition, namely

= h (x)

for χ = r.

(6)

which describes the temperature profile over time on the fluid side of the inner fiber.

In order to maintain the boundary condition on the inner fiber, a considered analytical solution for the differential equation (2) given by

ⁱ to

_X li-i

(7)

m = entier (—75—).

For every η this series represents a solution.

j- r »« a ssii

"β« · Cf *

-7-

In the present case, the accuracy of the solution for η = 2 proves to be sufficient. Hence, one after the other η = 2 canceled. Then is obtained

^ (τ, χ) ~ ° o ^{+ 0} ^ JC ⁺⁰ ? (τ- + ^τ J ( ^s )

For three given support points χ. ₁ χ. χ. ₁ reduced

the problem of determining the coefficients is based on a system of equations made up of three equations with three unknowns, that is clearly solvable. By analogous consideration in the direction of time the coefficient a »can be eliminated so that a free unknown in the system of equations is replaced by the Edge temperature on the inner fiber can be occupied.

This also gives rise to a boundary condition on the inner fiber, so that the complete temperature profile corresponds to the known one implicit difference method according to Crank-Nicolson can be determined with sufficient accuracy. With that this way certain temperature profile can be determined by well-known Quarirant method is the integral mean wall temperature determine.

Further characterization of the specified method is given by the fact that the specific material parameters are determined in each discretization point as a function of temperature (see tables in the FDBR manual (Fachverband Dampfkessel-, _Behältungs- und Rohrleitungsbau), "Strength calculation ¹ ", Vulkan Verlag, Essen, edition 1976, under 3. Material properties).

-8th-

The accuracy of the temperature profile to be determined by the specified method can be increased by further influencing variables can be taken into account through the function of a certain factor.

The specified method can advantageously be used in the computer-aided, computational determination of the total degree of exhaustion of components subject to pressure and temperature, the temperature profile over ^{1 of} the wall thickness being an important course. The decisive temperature difference Δθ is derived from the integral mean wall temperature xT _m and that on the inner fiber of the component

present temperature θ, - to form, thus

with Ά -

^ m _v

where V = volume of the component.

When determining the total degree of exhaustion, such components are recorded at defined time intervals the measured values pressure, temperature and temperature profile. According to the rate of change of a control measuring point the polling cycle is controlled. These are required to determine the static and dynamic stress on the components Measured values are checked for plausibility and either the creep and alternating strain is determined or if there is no plausibility, substitute functions are activated for determination.

-9-

With the exhaustion recalculation system, the p, degree of creep as a result of creep damage as well as the Determine and display the degree of exhaustion caused by alternating expansion stress at any point in time.

Claims (1)

Claims /1. ) Method for recording temperatures above the wall thickness of a component, in particular a thick-walled plate or a thick-walled pipe, characterized in that it is achieved by heat transfer processes Complete temperature profile produced from the chronological sequence of temperature readings from a thermocouple _ at only one measuring point near the inner fiber of the component is determined on the basis of the following balance equation: 3τ 3x ² whereby α (θ) = —i— the thermal diffusivity ^c p P of the component, = Thermal conductivity of the component, specific heat capacity of the component, Density of the material of the component, = the temperature τ - the time x = the path coordinate ....... . . .-SS-,. . . γ ν X ^k x x <'- ^2k ) t that the series (7) for η = 2 with "" 334S579 Ji * · * · with m - entier (- ^ -, x ²
"" (τ, χ) "" ^a o ^{+ a} l » ^{+ a} 2 2 ⁺ 2- The method according to claim 1, characterized g e the determination of the temperature profile -2- η e 1. and the following conditions apply: = O (5), θ _{τχ) = g (τ) for τ for = r _me (3), wire . .iT. ' ^x ^ - ο for x οχ mark h— ,,., pretty accurate Device for recording temperatures above the wall f thickness of a component for a method according to claim 1, \ characterized in that a single. ^ Thermocouple (10) near the inner fiber of a construction * partly (12) is arranged. | Device according to claim 3, characterized in that the thermocouple (10) in one
Bracket (14) is introduced.