CN117647334A - Temperature measuring crystal measurement high-temperature gas temperature correction and error evaluation method - Google Patents
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Abstract
A temperature measuring crystal measuring high-temperature fuel gas temperature correction and error evaluation method belongs to the field of aeroengine temperature field test. Firstly, a heat transfer model of a crystal measurement high-temperature gas temperature support rod is established, and influence factors of a crystal measurement high-temperature gas temperature error are obtained, such as increasing the length L of the support rod, a heat convection coefficient h, the outer diameter R of the support rod, a heat conduction coefficient k of a support rod material and the like; the temperature of a gas strut, a crystal and gas in a turbine channel under different flow conditions is simulated by using the existing commercial computational fluid dynamics software, and a high-temperature gas temperature correction and error evaluation method is constructed by combining the results obtained by a theoretical model with simulation data. Compared with the design problem of the support rod when the temperature measuring crystal measures high-temperature fuel gas in the current stage, the reliable theoretical support rod design method is provided. And a high-temperature gas temperature correction and error evaluation method is constructed, so that the measurement error of a crystal temperature measurement result is reduced. The measuring error generated when the temperature measuring crystal measures high-temperature fuel gas is effectively reduced.
Description
Technical Field
The invention belongs to the field of aeroengine temperature field test, and particularly relates to a method for correcting and evaluating the temperature of high-temperature fuel gas measured by a temperature measuring crystal, which is used for measuring the temperature of air flow in a hot end component channel such as a turbine blade and the like.
Background
The temperature measuring crystal can be used for measuring the highest temperature of near-surface airflow of the aero-engine, and particularly can be used for measuring positions of air film holes, tenons and the like where temperature measuring sensors are difficult to arrange. However, the preparation process of the temperature measuring crystal is strictly required, and the temperature measuring crystal is required to be tested and analyzed after the test to obtain the measured temperature value. At present, the foreign temperature measuring crystal technology is developed and mature, and is put into practical engineering application of aeroengines. Compared with abroad, the domestic temperature measurement crystal technology is relatively slow to develop, research such as exploratory tests and temperature measurement crystal material preparation is concentrated, and partial advanced research technological results pass the test verification stage and are applied to aeroengine research and development tests. Further researches are required to be carried out in the future aiming at various aspects such as preparation and use standards of the temperature measuring crystal.
In the development process of the aero-engine in China, the process of design and research of the aero-engine in China is seriously hindered due to the serious lack of basic data such as the surface of the hot end parts such as the turbine blades and the air flow temperature in the channels, and the research of accurate test methods of the surface of the hot end parts such as the turbine blades of the aero-engine, the air flow temperature and the distribution thereof is urgently needed to be developed. The advantages of wide temperature measuring range, no wire, less flow field interference, high precision, easy installation, good survival rate, good economy and the like of the microcrystal temperature measuring technology are widely concerned in the field of aeroengine temperature measurement, the temperature measuring crystal can only obtain the highest temperature of the contact part of the installation support rod, the relation between the temperature measuring crystal and the air flow near the turbine blade also needs to be deeply analyzed, and the law of the influence of heat load, installation mode, support rod (geometric dimension, material and the like) on the gas temperature is obtained, so that a correction method for measuring high-temperature gas by the microcrystal is established.
In the test of the existing method for measuring the high-temperature fuel gas by the crystal, the accuracy of measuring the high-temperature fuel gas by the crystal is affected by reasons such as heat flow and heat convection of the support rod, heat conduction between the support rod and the thermosetting adhesive, heat radiation of the metal sheet and the like.
The invention carries out theoretical deduction aiming at the problem, compares the theoretical solution with the numerical solution and considers whether the heat radiation problem exists or not, and obtains a feasible temperature correction method for measuring the high-temperature fuel gas by the crystal.
Disclosure of Invention
The invention aims to provide a crystal temperature measurement correction and error evaluation method for measuring the air flow temperature in a hot end component channel such as a turbine blade. In the process of measuring high-temperature fuel gas by using the crystal, the inaccurate measurement result can be caused by the phenomena of convection heat exchange, heat conduction and heat radiation of the supporting rod, the thermosetting glue and the like. Research is carried out aiming at the problem, and the estimation of the convective heat transfer coefficient is carried out by establishing a simple crystal measurement heat transfer model of high-temperature fuel gas. And correcting the results obtained by the numerical simulation method in the subsequent process, thereby verifying the reliability of the method.
Firstly, establishing a heat transfer model of a crystal measurement high-temperature gas temperature strut to obtain influencing factors of a crystal measurement high-temperature gas temperature error; and constructing a high-temperature fuel gas temperature correction and error evaluation method by combining a theoretical model with simulation data.
The invention comprises the following steps:
1) Establishing a heat transfer model of a crystal measurement high-temperature fuel gas temperature supporting rod: and respectively considering a convection heat transfer model and a heat transfer model of convection heat transfer, heat radiation heat transfer and heat transfer, and obtaining a corresponding correction equation based on theoretical deduction of the two models. Meanwhile, the convective heat transfer coefficient is estimated, and an empirical formula for estimating the convective heat transfer coefficient is obtained;
2) Providing a crystal measurement high-temperature gas temperature error analysis method to obtain the influencing factors of the crystal measurement high-temperature gas temperature error: and carrying out theoretical deduction on the error analysis method to obtain a conclusion. The difference between the temperature of the temperature measuring crystal arranged in the support rod and the incoming flow temperature is greatly influenced by the temperature of the bottom of the support rod, and when the crystal is closer to the top, the closer the crystal is to the incoming flow temperature, the smaller the measurement error is; the influence factors of the temperature errors of the high-temperature fuel gas measured by the crystal are increased, the length L of the support rod is increased under the condition that other parameters are consistent, the convective heat transfer coefficient h is improved, the outer diameter R of the support rod is reduced, and the support rod is made of a material with a small heat transfer coefficient k, so that the measurement accuracy is improved;
3) And (3) correcting the calculation result obtained by the numerical simulation method, and verifying the accuracy of the correction equation obtained in the step 1).
Compared with the traditional crystal for measuring the temperature of high-temperature fuel gas, the invention has the following advantages:
1) According to the established heat transfer model of the high-temperature gas temperature supporting rod for measuring the high-temperature gas, influence factors of the high-temperature gas temperature error of the crystal are theoretically obtained, such as increasing the length L of the supporting rod, reducing the outer diameter R of the supporting rod, reducing the heat conduction coefficient k of the supporting rod material and the like. Compared with the design problem of the support rod when the temperature measuring crystal measures high-temperature fuel gas in the current stage, the reliable theoretical support rod design method is provided.
2) And the temperature measurement precision analysis and correction are carried out on the crystal measurement high-temperature gas temperature strut by utilizing a theoretical model in combination with simulation software, so that a high-temperature gas temperature correction and error evaluation method is constructed, and the measurement error of a crystal temperature measurement result is reduced. Based on the temperature correction algorithm, the measurement error generated when the temperature measuring crystal measures high-temperature fuel gas at the present stage can be effectively reduced.
Drawings
FIG. 1 is a schematic diagram of a strut heat transfer model for measuring high temperature gas temperature.
FIG. 2 is a schematic illustration of a thermoset adhesive and struts.
FIG. 3 is a calculation model of a three-dimensional temperature measurement crystal for measuring high temperature fuel gas.
FIG. 4 is a cross-sectional view of a temperature measuring crystal for measuring high temperature fuel gas.
Fig. 5 is a computational meshing of a three-dimensional steady-state heat transfer numerical computation.
Fig. 6 is a temperature distribution cloud of a three-dimensional steady-state heat transfer numerical simulation.
FIG. 7 is a flow chart of the method of the present invention, in which the result of the crystal temperature measurement is improved by the correction method.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described with reference to the following examples. It should be understood that the specific examples described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
1. Heat transfer model for crystal measuring high-temperature fuel gas temperature supporting rod
FIG. 1 is a schematic view of a temperature sensing strut. In order to deduce the heat transfer model of the temperature measuring support rod, firstly, the change of the temperature (T) on the cross section of the cylindrical support rod is far smaller than the change along the x direction, namely, the temperature on any cross section is uniformly distributed, and only the temperature along x is changed, so that the heat transfer model of the temperature measuring support rod can be assumed to be a quasi-one-dimensional heat transfer model. The cylindrical struts are composed of 2 materials as shown in fig. 2. In FIG. 2, 1 is a thermosetting adhesive having a thermal conductivity of k 1 Cross-sectional area in x-direction is A 1 The method comprises the steps of carrying out a first treatment on the surface of the 2 is a ceramic tube with a heat conduction coefficient k 2 Cross-sectional area in x-direction is A 2 The method comprises the steps of carrying out a first treatment on the surface of the The convective heat transfer coefficient of the surrounding fluid and the support rod is a constant h.
1.1 Heat transfer model considering convection and Heat conduction
To derive a quasi-one-dimensional heat transfer model of the temperature sensing strut, consider the portion between the two cross sections separated by dx in fig. 1, and study the energy balance problem. The sum of the heat introduced by heat conduction at x and the heat introduced to the inflow surface by the fluid is equal to the heat extracted at x+dx, namely:
q k,x +dq c ＝q k,x+dx (1)
wherein q is k,x Represents the heat introduced at x by thermal conduction, dq c Represents the heat flow through the fluid to the inflow surface, q k,x+dx Representing the amount of heat extracted at x+dx.
Or alternatively, the first and second heat exchangers may be,
wherein A is 1 Is the cross-sectional area of the thermosetting adhesive along the x direction, k 1 Is thermosetCoefficient of thermal conductivity of adhesive, A 2 For the cross-sectional area of the ceramic tube in the x-direction, k 2 Is the thermal conductivity coefficient of the ceramic tube;for the temperature gradient at the length x of the strut, +.>Is the temperature gradient at a strut length of x+dx. T (T) ∞ For the incoming flow temperature, P is the perimeter of the cross section of the cylindrical support rod, h is the convective heat transfer coefficient, and Pdx is the surface area of the support rod between x and x+dx; if ka=k 1 A 1 +k 2 A 2 A is the area of the cross section of the support rod, k is the uniform heat conductivity coefficient of the whole thermosetting adhesive and the ceramic tube, and then the equation (2) can be simplified as follows:
introducing excessive temperature θ (x) =t (x) -T ∞ (F.Kreith and Bohn M.,Principles of Heat Transfer,[M]The fifth edition, 1993) and takeThe above can be written as:
the above is a second order linear homogeneous ordinary differential equation, since m is a constant value, its general solution is:
θ(x)＝C 1 e mx +C 2 e -mx (5)
C 1 ，C 2 represents an integral constant, e is a natural constant
Integral constant C 1 And C 2 Determined by boundary conditions:
θ(0)＝T s -T ∞ ≡θ s when x=0
When x=l
Wherein T is s The temperature of the bottom of the support rod is L, the length of the support rod along the x direction is theta s Indicating excess temperature, θ, at the bottom of the rod L The excess temperature at the top of the strut is shown, h is the convective heat transfer coefficient, T L Representing the temperature at the top of the strut, T ∞ Represents the incoming flow temperature, k represents the uniform heat conductivity of the whole of the thermosetting adhesive and the ceramic tube,representing the derivative of excess temperature at the top of the strut. Substituting the boundary condition into equation (5) to obtain the integral constant C 1 And C 2 And substituting the original process to obtain the temperature distribution of the support rod along the x direction:
where the hyperbolic function is defined as:
when the temperature measuring crystal is arranged at x=x c At a temperature of T c Substituting into equation (6) can obtain an equation for calculating the incoming flow temperature, namely a temperature correction equation:
wherein, dash and sinh represent hyperbolic functions, L is the length of the support rod, x c The temperature measuring crystal is positioned at the supporting rod; taking outWherein h is a convection heat transfer coefficient, k is a uniform heat transfer coefficient of the thermosetting adhesive and the ceramic tube support rod, A is the area of the cross section of the support rod, P is the perimeter of the cross section of the cylindrical support rod, and C is a correction parameter. T (T) ∞ For incoming flow temperature, T s T is the temperature of the bottom of the supporting rod c The temperature at the measuring point of the temperature measuring crystal is measured.
The equation (7) can obtain the correction parameters, the result of the correction parameters C is obtained by calculation, and the result is substituted into the temperature correction equation, namely, the equation (8), so that the corrected result can be obtained.
1.2 Heat transfer model considering convection, heat radiation and Heat conduction
If the heat radiation heat transfer is considered in the quasi-one-dimensional heat transfer model of the temperature measurement strut, then equation (2) can be rewritten as:
wherein ε is the surface emissivity (blackness), σ≡5.67×10 -8 W/m 3 The temperature is Stefan-Boltzman constant. After finishing, equation (9) can be rewritten as:
equation (10) is a second order nonlinear very differential equation for temperature, whose boundary conditions at the x=l end can be written as:
wherein,representing the temperature gradient at the top of the strut, T L Indicating the temperature at the top of the strut.
Equation (10) does not give a theoretical solution as in equation (2), where the temperature distribution along the thermometric support is calculated only by means of a numerical solution, given the boundary conditions.
1.3 estimation of Heat convection coefficients
In the quasi-one-dimensional heat transfer model, when the formulas (2) and (10) calculate the temperature distribution of the temperature measuring support rod, the convective heat transfer coefficient h needs to be given. Because it is difficult to obtain accurate values in advance in the actual temperature measurement process, the convective heat transfer coefficient is estimated.
For fluid flow around a cylinder, the dimensionless Nusselt number is defined as:
wherein D is the diameter of the temperature measuring support rod, lambda is the heat conduction coefficient of incoming gas, h is the convective heat transfer coefficient, nusselt number Nu is the function of incoming gas Reynolds number Re and Plantain number Pr, and the function definitions of incoming gas Reynolds number Re and Plantain number Pr are respectively:
in the above, ρ, U ∞ Mu and c p Density, speed, dynamic viscosity coefficient and constant pressure specific heat capacity of incoming gas. The empirical formula for solving Nu given by experimentation (ref. English: J.DeVoe, A.Thomas, R.DeVoe and e. Ginzburst, gas Temperature Measurment in Engine Conditions Using Uniform Crystal Temperature Sensors (UCTS). Proceedings of ASME Turbo Expo 2018 GT2018-76890) is as follows:
where α is the angle between the incoming flow and each point on the cylinder, and α=0 for the standing point. Empirical formula for estimating convective heat transfer coefficient:
2. crystal measurement high-temperature gas error analysis method
As can be seen from the quasi-one-dimensional heat transfer model of the temperature measuring support rod, the temperature distribution along the x direction on the support rod mainly depends on the temperature of the bottom of the support rod, namely, the temperature of the temperature measuring crystal installed in the support rod and the incoming flow temperature are greatly influenced by the temperature of the bottom of the support rod, and under the condition that other parameters are consistent, the closer the installation is to the bottom of the support rod, the larger the difference between the temperature of the crystal and the incoming flow temperature is. As the strut increases gradually in the x-direction, the temperature across the strut cross-section is less affected by the base, the heat conducted forward decreases gradually, slowly tending to 0, i.e. gradually meeting the adiabatic boundary conditions.
Thus, when the strut is sufficiently long, the temperature distribution of the strut in the x-direction can be reduced to:
when the crystal is mounted near the top of the strut, i.e. x≡l, the above formula can be rewritten as:
namely:
from the above equation, increasing the value of mL can improve the accuracy of the crystal measurement. Thus for a cylindrical strut, there are:
therefore, when the length L of the support rod is increased, the convection heat transfer coefficient h is improved, the outer diameter R of the support rod is reduced, and the support rod made of the material with the small heat transfer coefficient k is beneficial to improving the measurement accuracy.
3. Three-dimensional steady-state heat transfer numerical simulation and temperature correction equation verification of crystal measurement high-temperature gas temperature strut
The effectiveness of the first section hot gas temperature correction method was tested using the example setup in literature (ref. English J.DeVoe, A.Thomas, R.DeVoe and e. Ginzburst, gas Temperature Measurment in Engine Conditions Using Uniform Crystal Temperature Sensors (UCTS), proceedings of ASME Turbo Expo 2018GT 2018-76890). Because of the geometry of the examples, 1/4 of the geometric model is taken here as the calculation model.
In FIG. 4, the rectangular parallelepiped metal foil is made of nickel-based alloy, and has dimensions of 4mm×4mm×2mm, and the temperature measurement crystal has dimensions of 0.1mm×0.19mm×0.2mm. To test the temperature measuring strut length, the effect of the crystal mounting position on the gas temperature measurement and correction was selected to be 3mm in strut length (including 1mm length extending into the foil). Meanwhile, in FIG. 3, the outer diameter of the support rod is 1.2mm, the inner diameter is 0.8mm, the bottom of the crystal is 0.75mm from the top of the support rod, and the height of the nickel-based alloy is 2mm. The thermal conductivity k of each material used for numerical simulation is shown in table 1.
Table 1 thermal conductivity coefficients of numerical modeling materials
| Material | Coefficient of thermal conductivity k (W/mK) |
| Nickel-based alloy | 26 |
| Cement binder | 0.6 |
| Temperature measuring crystal | 20 |
| Ceramic material | 30 |
The temperature of a gas strut, a crystal and gas in a turbine channel under different flow conditions is simulated by using commercial Fluent2020 computational fluid dynamics software, and a theoretical model is combined with simulation data to correct and analyze errors of a high-temperature gas temperature field. The temperature of the hot gas flowing above the top of the metal sheet is 1660 ℃, and the convection heat exchange coefficient is 4838W/m 2 The temperature is lower than the temperature; the temperature of the cold air flowing downwards at the bottom is 696.1 ℃, and the convection heat exchange coefficient is 7183.4W/m 2 The temperature is lower than the temperature; the temperature of the other boundary conditions is an adiabatic boundary condition.
The three-dimensional computational grid employs a locally refined hybrid grid, as shown in fig. 5. The default size of the entire computational space grid is 0.1mm, and the refined grid size of the other parts is 0.03mm.
The temperature distribution cloud after the numerical calculation reached steady state is shown in fig. 6 using commercial computational fluid dynamics software. The numerical simulation temperature of the temperature measuring crystal is T c =1595 ℃, relative error is:
the calculated results are 5% comparable to the relative error results in literature (J.DeVoe, A.Thomas, R.DeVoe and E. Ginzburst, gas Temperature Measurment in Engine Conditions Using Uniform Crystal Temperature Sensors (UCTS), proceedings of ASME Turbo Expo 2018GT 2018-76890).
The length L=2mm of the temperature measuring support rod, and the numerical temperature T of the bottom of the support rod s The temperature of the corrected temperature measurement crystal is T, which can be calculated according to equation (1) and equation (2) =1492 ℃ and other known parameters to obtain C=0.306 ∞ The corrected measurement relative error drops to about 1%, error drops, and the correction method is verified. The crystal temperature measurement correction and error evaluation method for measuring the air flow temperature in the hot end component channels of the turbine blade and the like has certain advantages and advancement.
Referring to fig. 7, the invention firstly establishes a heat transfer model of a support rod for measuring the temperature of high-temperature fuel gas by the crystal, and then obtains key parameters of the temperature error of the high-temperature fuel gas by the crystal, such as increasing the length L of the support rod, the convective heat transfer coefficient h, the outer diameter R of the support rod, the thermal conduction coefficient k of the support rod material and the like; the temperature of a gas strut, a crystal and gas in a turbine channel under different flow conditions is simulated by using the existing commercial computational fluid dynamics software, and a high-temperature gas temperature correction and error evaluation method is constructed by combining the results obtained by a theoretical model with simulation data. The invention provides a crystal temperature measurement correction and error evaluation method for measuring the temperature of air flow in a hot end component channel of a turbine blade and the like, which is a reliable theoretical support design method compared with the support design problem when the temperature measurement crystal measures high-temperature fuel gas at the present stage. And a high-temperature gas temperature correction and error evaluation method is constructed, so that the measurement error of a crystal temperature measurement result is reduced. The measuring error generated when the temperature measuring crystal measures high-temperature fuel gas is effectively reduced. The method has important significance for improving the prediction accuracy evaluation level of the temperature in the field of aeroengine temperature field test.
The above-described embodiments are merely preferred embodiments of the present invention and should not be construed as limiting the scope of the present invention. All equivalent changes and modifications within the scope of the present invention are intended to be covered by the present invention.
Claims (4)
1. The temperature measuring crystal measuring high-temperature gas temperature correction and error evaluation method is characterized by comprising the following steps of:
1) Establishing a heat transfer model of a crystal measurement high-temperature fuel gas temperature supporting rod: respectively considering a convection heat transfer model and a heat transfer model of convection heat transfer, heat radiation heat transfer and heat transfer, and obtaining a corresponding correction equation based on theoretical deduction of the two models; meanwhile, the convective heat transfer coefficient is estimated, and an empirical formula for estimating the convective heat transfer coefficient is obtained;
2) Providing a crystal measurement high-temperature gas temperature error analysis method to obtain the influencing factors of the crystal measurement high-temperature gas temperature error: theoretical deduction is carried out on an error analysis method, the difference between the temperature of a temperature measuring crystal arranged in the support rod and the temperature of incoming flow is greatly influenced by the temperature of the bottom of the support rod, and when the crystal is closer to the top, the crystal is closer to the temperature of incoming flow, and the measurement error is smaller; the influence factors of the temperature errors of the high-temperature fuel gas measured by the crystal are increased, the length L of the support rod is increased under the condition that other parameters are consistent, the convective heat transfer coefficient h is improved, the outer diameter R of the support rod is reduced, and the support rod is made of a material with a small heat transfer coefficient k, so that the measurement accuracy is improved;
3) And (3) correcting the calculation result obtained by the numerical simulation method, and verifying the accuracy of the correction equation obtained in the step 1).
2. The temperature measurement crystal measurement high-temperature gas temperature correction and error evaluation method is characterized in that in the step 1), the correction equation is as follows:
wherein, dash and sinh represent hyperbolic functions, L is a supporting rodLength x of (x) c The temperature measuring crystal is positioned at the supporting rod; taking outWherein h is a convection heat transfer coefficient, k is a uniform heat transfer coefficient of the thermosetting adhesive and the ceramic tube support rod, A is the area of the cross section of the support rod, P is the perimeter of the cross section of the cylindrical support rod, and C is a correction parameter; t (T) ∞ For incoming flow temperature, T s T is the temperature of the bottom of the supporting rod c The temperature at the measuring point of the temperature measuring crystal is measured.
3. A temperature measurement crystal measurement high-temperature gas temperature correction and error evaluation method is characterized in that in the step 1), the specific steps of estimating the convection heat transfer coefficient and obtaining an empirical formula for estimating the convection heat transfer coefficient are as follows:
for fluid flow around a cylinder, the dimensionless Nusselt number is defined as:
wherein D is the diameter of the temperature measuring support rod, lambda is the heat conduction coefficient of incoming gas, h is the convective heat transfer coefficient, nusselt number Nu is the function of incoming gas Reynolds number Re and Plantain number Pr, and the function definitions of incoming gas Reynolds number Re and Plantain number Pr are respectively:
in the above, ρ, U ∞ Mu and c p Density, speed, dynamic viscosity coefficient and constant pressure specific heat capacity of incoming gas; the empirical formula given by the experiment for solving Nu is as follows:
wherein, alpha is the included angle between the incoming flow and each point on the cylinder, and for the standing point alpha=0; the empirical formula for estimating the convective heat transfer coefficient is as follows:
where h is a convective heat transfer coefficient, re is an incoming gas Reynolds number, pr is a Plantt number of the incoming gas, lambda is a heat transfer coefficient of the incoming gas, and D is a diameter of the temperature measuring support rod.
4. The method for correcting and evaluating the temperature of the high-temperature fuel gas by using the temperature-measuring crystal is characterized in that in the step 2), the method for analyzing the temperature error of the high-temperature fuel gas by using the crystal is provided, and specifically comprises the following steps:
the temperature distribution along the x direction on the support rod mainly depends on the temperature of the bottom of the support rod, namely, the temperature of a temperature measuring crystal installed in the support rod and the temperature of incoming flow are greatly influenced by the temperature of the bottom of the support rod, and under the condition that other parameters are consistent, the closer the installation is to the bottom of the support rod, the larger the difference between the temperature of the crystal and the temperature of incoming flow is; as the temperature of the cross section of the support rod is affected by the bottom part to be smaller along the x direction of the support rod, the heat conducted forwards is gradually reduced and gradually goes to 0, namely the adiabatic boundary condition is gradually met;
wherein, theta is the included angle between the incoming flow and each point on the cylinder,a derivative of excess temperature at the top of the strut;
when the strut is long enough, the temperature distribution of the strut along the x-direction can be reduced to:
wherein θ s Indicating excessive temperature at the bottom of the support rod;
when the crystal is mounted near the top of the strut, i.e. x≡l, the above formula is rewritten as:
wherein θ c The excess temperature of the temperature measuring crystal;
namely:
from the above equation, increasing the value of mL can improve the accuracy of the crystal measurement; thus for a cylindrical strut, there are:
therefore, when the length L of the support rod is increased, the heat convection coefficient h is improved, the outer diameter R of the support rod is reduced, and the support rod made of the material with the small heat conduction coefficient k is favorable for improving the measurement accuracy.
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