CN113343495B - Thermal performance model correction method for tube-shell type lubricating oil-fired radiator - Google Patents
Thermal performance model correction method for tube-shell type lubricating oil-fired radiator Download PDFInfo
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Abstract
The present application provides aThe method for correcting the thermal performance model of the shell-and-tube type fuel-oil radiator comprises the following steps: obtaining a test result of a shell-and-tube type lubricating oil-burning radiator, and determining a Nu based on the test result t Reynolds number Re t And the prandtl number Pr t (ii) a According to Nussel number Nu (Nu) t Reynolds number Re t And the prandtl number Pr t Performing multiple nonlinear regression to obtain Nu t Reynolds number Re t And the prandtl number Pr t The tube side of (1) is a dimensionless relational expression; the dimensionless relational expression is brought into a primary tube side fuel oil convection heat exchange surface heat transfer coefficient formula to replace primary tube side fuel oil convection heat exchange Nu t And calculating a formula, thereby realizing the correction of the initial theoretical calculation model. The thermal performance model correction method for the tube-shell type lubricating oil-fired radiator corrects the initial thermal performance calculation model based on the test data, and has the advantages of convenient operability, simple model correction process and accurate corrected thermal performance calculation.
Description
Technical Field
The application belongs to the technical field of heat performance calculation of radiators, and particularly relates to a thermal performance model correction method for a tube-shell type lubricating oil-fired radiator.
Background
A shell-and-tube aircraft engine fires-the structure that the oil radiator is used for providing cooling for the lubricating oil system or is used for providing the demand of heating for fuel oil, because of its simple and reliable, can provide very big heat transfer area for fuel oil and lubricating oil under the condition of small enough overall dimension and weight, guarantee the work safety of the high-pressure fluid in the radiator simultaneously, on the other hand, the fuel oil temperature that flows through the radiator rises, has improved the atomization effect of fuel oil in the combustion chamber, has improved engine efficiency to a certain extent. Therefore, the shell-and-tube radiator which can bear high pressure, has a compact structure and a large heat exchange area becomes the preferred construction form of the fuel-oil radiator of the aviation turbine and turbofan engine at present.
The preliminary estimation of the heat exchange characteristic of the lubricating oil burning radiator is a key link of thermal analysis and circulation volume design of a lubricating oil system, and the heat exchange performance determines the heat load tolerance capacity of the lubricating oil system in a wire-covering range. Therefore, it is particularly important for the design of the lubricating oil system to grasp the heat exchange characteristics of the shell-and-tube type lubricating oil burning radiator.
At present, methods such as certain theoretical analysis conclusions and test correlation of a conventional shell-and-tube radiator are generally adopted for calculating the thermal performance of the aviation fuel-lubricating oil radiator.
However, in the analysis method using the conventional shell-and-tube radiator, because the structure of the fuel-lubricant radiator of the aircraft engine becomes more compact, the heat exchange working medium, the reynolds number and the operation condition are different from those of the general typical shell-and-tube radiator, referring to the core structure of the shell-and-tube fuel-lubricant radiator shown in fig. 1, the lubricant flows in from the lubricant inlet 11 and flows out from the lubricant outlet 12, the fuel flows in from the fuel inlet 13 and flows out from the fuel outlet 13, and heat exchange is completed inside the heat exchanger, but when the fuel-lubricant radiator is very thin (the outer diameter is only about 2-3 mm) and the number is as many as several hundreds, and meanwhile, when pits are distributed on the surface, some theoretical analysis conclusions and test correlation methods of the typical shell-and-tube radiator are no longer applicable to the more compact aircraft fuel-lubricant radiator. The method not only influences the accuracy of the performance prediction of the aviation lubricating oil system, but also influences the correctness of the thermal analysis of the engine system.
In addition, a radiator tester needs to be built in the test correlation method, the thermal performance characteristics of the radiator are obtained through the test method, but the test method is often high in cost and long in time, and if the structure of the lubricating oil radiator is improved, a test needs to be carried out again, so that the problems of cost increase and the like are caused.
Disclosure of Invention
It is an object of the present application to provide a method for model-correcting the thermal performance of a shell-and-tube type fuel-oil radiator to solve or mitigate at least one of the problems of the background art.
Firstly, the application provides a method for correcting a thermal performance model of a shell-and-tube type fuel oil radiator, which comprises the following steps:
obtaining a test result of a shell-and-tube type lubricating oil-burning radiator, and determining a Nu based on the test result t Reynolds number Re t And the prandtl number Pr t ；
According to Nussel number Nu (Nu) t Reynolds number Re t And the prandtl number Pr t Performing multiple nonlinear regression to obtain Nu t Reynolds number Re t And the prandtl number Pr t The tube side of (1) is a dimensionless relational expression;
the dimensionless relational expression is brought into a primary tube side fuel oil convection heat exchange surface heat transfer coefficient formula to replace primary tube side fuel oil convection heat exchange Nu t And calculating a formula, thereby realizing the correction of the initial theoretical calculation model.
<xnotran> , Nu </xnotran> t Reynolds number Re t And the prandtl number Pr t The process comprises the following steps:
obtaining thermal resistance of the fuel oil radiator in a test state by performing inverse calculation on test data by adopting an eta-NTU (normalized temperature coefficient of thermal transfer) calculation formula, wherein the thermal resistance comprises shell side fuel oil convective heat transfer thermal resistance, shell side fouling thermal resistance, heat transfer pipe wall heat conduction thermal resistance of a heat transfer pipe, pipe side fouling thermal resistance and pipe side fuel oil convective heat transfer thermal resistance;
calculating to obtain the heat transfer coefficient alpha of the convective heat transfer surface of the fuel oil at the tube side according to an initial theoretical calculation model and the convective heat transfer thermal resistance of the fuel oil at the tube side t Further, the Nussel number in the test state is obtained
In the formula, nu t Is the Nussel number, D ti Is the diameter of the baffle plate at the side of the radiator pipe, lambda t Is the coefficient of thermal conductivity;
calculating to obtain Reynolds numbers under corresponding test states according to the fuel flow and the fuel inlet temperature under different test states
Prandtl number->
In the formula (d) ti Is the diameter of the heat transfer pipe; g mt Is the mass flow rate; mu.s t Is viscosity; v is a cell t Is the kinematic viscosity coefficient; rho t Is the density; c. C pt Is the specific heat at constant pressure; lambda [ alpha ] t Is the thermal conductivity.
In the above embodiment, the constant specific heat under pressure c pt ＝1737.5+9.63t t ，t t The qualitative temperature is indicated.
In the above embodiment, the density ρ t ＝814.2-0.735t t ，t t The qualitative temperature is indicated.
In the above embodiment, the kinematic viscosity coefficient v t Satisfies the following conditions: lnln (upsilon) t +0.8)＝20.811-3.697lnT t ，T t Qualitative temperature: t is t ＝t t +273.15，t t The qualitative temperature is indicated.
In the above embodiment, the thermal conductivity λ t ＝0.1192-0.0002t t ，t t The qualitative temperature is given.
In the above embodiment, the mass flow rate
q mt Is the fuel mass flow; a. The tc Is the tube side flow area.
In the above embodiment, the fuel mass flow rate q mt ＝q vt ρ t ，q vt Is the volume flow.
In the above embodiment, the tube-side dimensionless relation is:
in addition, the application also provides a shell-and-tube type oil-burning radiator, which is obtained according to any thermal performance model correction method.
The thermal performance model correction method for the tube-shell type lubricating oil-fired radiator corrects the initial thermal performance calculation model based on the test data, and has the advantages of convenient operability, simple model correction process and accurate corrected thermal performance calculation.
Drawings
In order to more clearly illustrate the technical solutions provided by the present application, the following briefly introduces the accompanying drawings. It is to be expressly understood that the drawings described below are only illustrative of some embodiments of the invention.
FIG. 1 is a schematic diagram of a typical shell-and-tube type oil-fired radiator core structure.
Fig. 2 is a schematic view of a tube side core plane structure in the present application.
Fig. 3 is a schematic view of a turbulator pit heat transfer tube of the present application.
Fig. 4 is a schematic flow chart of a model correction method according to the present application.
FIG. 5a is a comparison curve of the heat exchange amount of the initial theoretical model, the calculation result of the corrected model and the test value under the working condition 1 of the lubricating oil inlet temperature and the fuel oil inlet pressure.
FIG. 5b is a comparison curve of the heat exchange amount of the initial theoretical model, the calculation result of the corrected model and the test value under the working condition 2 of the lubricating oil inlet temperature and the fuel oil inlet pressure.
FIG. 6 is a diagram illustrating a calculated error distribution of the modified model.
Detailed Description
In order to make the implementation objects, technical solutions and advantages of the present application clearer, the technical solutions in the embodiments of the present application will be described in more detail below with reference to the drawings in the embodiments of the present application.
In order to realize the structural characteristics of compact structure, large heat exchange area density, turbulent flow pit heat transfer pipe type and the requirement of accurate calculation of variable working condition performance of an aero-engine shell-and-tube type fuel-oil radiator, the application provides a method for correcting a conventional fuel-oil radiator thermal performance model calculation method by combining variable working condition test results, so that the variable working condition performance of the fuel-oil radiator can be accurately reflected by the corrected theoretical model calculation result.
By combining the tube-shell type fuel-oil radiator shown in fig. 1 and the structural core structure and geometric schematic diagram of the tube-shell type fuel-oil radiator shown in fig. 2 and 3, the heat transfer tube thereof is provided with a flow disturbing pit. The structural parameters have no influence on correction and can be deleted
The typical flow steps of the thermal performance checking calculation of the shell-and-tube type heat-dissipating lubricating oil heater sequentially comprise the following parameters:
1) Determining heat transfer surface characteristics;
2) Determining a fluid physical property parameter;
3) Reynolds number;
4) Determining j and f according to the basic characteristics of the heat transfer surface, and calculating to obtain the heat transfer coefficient of the convection surface;
5) The overall heat transfer coefficient;
6) NTU and radiator efficiency η;
7) Outlet temperature and heat dissipation.
For the working condition of the aero-engine shell-and-tube fuel-and-oil radiator with a more compact structure, the theoretical performance of the aero-engine shell-and-tube fuel-and-oil radiator is predicted by adopting the preliminary heat transfer calculation model, meanwhile, the heat dissipation performance of the shell-and-tube fuel-and-oil radiator under the corresponding working condition is measured through tests, and the theoretical curve comparison of the heat dissipation capacity per temperature difference between the two is shown in fig. 5a and fig. 5 b.
It can be seen from fig. 5a and 5b that a certain difference exists between the calculation curve of the initial heat transfer calculation model and the test curve, and the calculation error caused by the difference can be increased by 30% along with the fuel flow. Therefore, the calculation method of the initial heat transfer calculation model is not suitable for calculating the heat radiation performance of the shell-and-tube type fuel-oil radiator of the aircraft engine with a more compact structure.
In order to overcome the above problems, the present application provides a method for correcting an initial model for performance calculation of a main radiator, so as to obtain a more accurate calculation result.
Because the influence of the temperature change of the lubricating oil inlet on the heat dissipation capacity of the radiator per unit temperature difference is very small and is far smaller than the influence caused by the flow change of the lubricating oil inlet, the data under the test state is suitable for researching the heat exchange performance of the fuel side. Therefore, the proposed theoretical model correction method starts with the heat exchange performance correction of the fuel measurement, realizes the correction of the theoretical calculation model through a series of heat dissipation performance analysis, and ensures good accuracy.
As shown in fig. 4, the method for correcting the thermal performance model of the shell-and-tube fuel-oil radiator mainly includes the following steps:
s1, obtaining a test result of a shell-and-tube type fuel-oil radiator, and determining a Nu based on the test result t Reynolds number Re t And the prandtl number Pr t ；
<xnotran> S2, Nu </xnotran> t Reynolds number Re t And the prandtl number Pr t Performing multiple nonlinear regression to obtain Nu t Reynolds number Re t And the prandtl number Pr t The tube side of (1) is a dimensionless relational expression;
and S3, substituting the tube side dimensionless relational expression into an original tube side fuel oil convective heat exchange formula to replace an original Nut calculation formula for calculating the convective heat exchange of the tube side fuel oil, so that the correction of the initial theoretical calculation model is realized.
The method comprises the following specific steps:
1. and (3) inversely calculating test data by adopting a calculation formula of a thermal efficiency-heat transfer unit number method (eta-NTU) to obtain the total thermal resistance of the radiator in a test state, wherein the thermal resistance comprises shell side lubricating oil convective heat transfer thermal resistance, shell side fouling thermal resistance, heat transfer pipe wall heat transfer thermal resistance, pipe side fouling thermal resistance and pipe side fuel convective heat transfer thermal resistance. Wherein the shell side fouling thermal resistance, the heat transfer pipe wall heat conduction thermal resistance and the pipe side fouling thermal resistance are basically fixed; because the flow of the shell side lubricating oil is kept unchanged in various test states, and the influence of the change of the temperature of the lubricating oil inlet on the heat dissipation performance of the radiator is small, the convective heat transfer thermal resistance of the shell side lubricating oil can be considered to be basically kept unchanged, and the value can be calculated by an initial model;
calculating the heat transfer coefficient alpha of the convective heat transfer surface of the fuel oil at the tube side by using an initial model and the convective heat transfer thermal resistance of the fuel oil at the tube side t Further, the Knudsen number can be obtained
Nu t Is the Nussel number, D ti Is the diameter of the baffle plate at the side of the radiator pipe, lambda t Is the coefficient of thermal conductivity;
corresponding Reynolds number Re is obtained by calculating the fuel flow and the fuel inlet temperature under different test states t And the prandtl number Pr t ：
Specific heat at constant pressure c pt ＝1737.5+9.63t t The unit J/(kg. K), t t The qualitative temperature is adopted;
density p t ＝814.2-0.735t t Unit of g/cm 3 ；
Kinematic viscosity coefficient upsilon t Satisfies the following conditions: lnln (upsilon) t +0.8)＝20.811-3.697lnT t Unit mm 2 /s，T t Qualitative temperature (K): t is t ＝t t +273.15，t t Qualitative temperature (. Degree. C.).
Coefficient of thermal conductivity lambda t ＝0.1192-0.0002t t Unit W/(m.k)
Then the available prandtl number
Reynolds number
q mt ＝q vt ρ t Wherein q is mt Is the fuel mass flow rate, A tc Is the tube side flow area, g mt For mass flow rate, d ti Is the diameter of the heat transfer tube t Is viscosity.
2. For the number Nu of processed Nu t Reynolds number Re t And prandtl number Pr t Performing multiple nonlinear regression on the data to obtain a dimensionless experimental correlation formula of the heat exchange of the fuel oil at the tube side:
3. putting the above formula into the heat transfer coefficient of the convection heat exchange surface
In the prior art, the Nu replaces the Nu of the conventional calculation tube side fuel convective heat transfer t And in the calculation formula, correcting the initial theoretical calculation model.
The heat dissipation capacity curve of the radiator in unit temperature difference under different working conditions obtained by correcting the model is shown in fig. 5a and 5 b. In order to illustrate the accuracy of the correction model, calculation errors of the correction model corresponding to the working condition 1 of the inlet temperature of the lubricating oil and the inlet pressure of the fuel oil and each state point of the test are shown in fig. 6.
As can be seen from the comparison curves of fig. 5a and 5b, the error of the heat dissipation capacity per unit temperature difference of the shell-and-tube fuel-oil radiator calculated by the correction model is basically within 10% compared with the test value, and the comparison error of 90% of data points is within 5%, as shown in fig. 6, it is demonstrated that the model correction method of the present application has high accuracy, and can be popularized and applied to the calculation model correction of various aero-engine shell-and-tube radiators.
The above description is only for the specific embodiments of the present application, but the scope of the present application is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present application should be covered within the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.
Claims (2)
1. A thermal performance model correction method for a tube-shell type fuel-oil radiator is characterized by comprising the following steps:
obtaining a test result of a shell-and-tube type lubricating oil-burning radiator, and determining a Nu based on the test result t Reynolds number Re t And the prandtl number Pr t The process comprises the following steps:
obtaining thermal resistance of the fuel oil radiator in a test state by performing inverse calculation on test data by adopting an eta-NTU (normalized temperature coefficient of thermal transfer) calculation formula, wherein the thermal resistance comprises shell side fuel oil convective heat transfer thermal resistance, shell side fouling thermal resistance, heat transfer pipe wall heat conduction thermal resistance of a heat transfer pipe, pipe side fouling thermal resistance and pipe side fuel oil convective heat transfer thermal resistance;
according to the initial theoretical calculation model determined by the test result and the heat resistance of the convective heat transfer of the fuel oil at the tube side, the heat transfer coefficient alpha of the convective heat transfer surface of the fuel oil at the tube side is obtained by calculation t Further, the Nussel number in the test state is obtained
In the formula, nu t Is the Nussel number, D ti Is the diameter of the baffle plate at the side of the radiator pipe, lambda t Is the coefficient of thermal conductivity; lambda [ alpha ] t ＝0.1192-0.0002t t ；
Calculating to obtain Reynolds numbers under corresponding test states according to the fuel flow and the fuel inlet temperature under different test states
Prandtl number
，
In the formula (d) ti Is the diameter of the heat transfer tube; g mt In order to be able to measure the mass flow rate,
q mt is the fuel mass flow rate, q mt ＝q vt ρ t ，q vt Is the volume flow rate, A tc Is the tube side flow area; mu.s t As a viscosity, lnln (upsilon) is satisfied t +0.8)＝20.811-3.697lnT t ，T t Is the qualitative temperature under the thermodynamic temperature scale: t is t ＝t t +273.15，t t Is a qualitative temperature under the temperature scale of centigrade; upsilon is t Is the kinematic viscosity coefficient; rho t Is density, p t ＝814.2-0.735t t ；c pt Specific heat at constant pressure, c pt ＝1737.5+9.63t t ；λ t Is the coefficient of thermal conductivity;
according to Nussel number Nu (Nu) t Reynolds number Re t And the prandtl number Pr t Performing multiple nonlinear regression to obtain gateIn that Nussel number Nu (Nu) t Reynolds number Re t And prandtl number Pr t The tube side dimensionless relation of (a) is:
the dimensionless relational expression is brought into a primary tube side fuel oil convection heat exchange surface heat transfer coefficient formula to replace a primary tube side fuel oil convection heat exchange Nu t And calculating a formula, thereby realizing the correction of the initial theoretical calculation model.
2. A shell-and-tube type oil-fired radiator obtained according to the thermal performance model correction method of claim 1.
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