Method for creep-fatigue strength of plate-fin heat exchanger

A design method for creep-fatigue strength of a plate-fin heat exchanger belongs to the technical field of the heat exchangers.

With the development of technology, the energy consumption is increasing, so energy saving and emission reduction as well as the improvement of the energy utilization ratio have become focuses of public attention. The heat-transfer equipment, as a core member of the high temperature system, not only requires efficient heat transfer performance, but also requires a compact structure. However, the most commonly used type of heat-transfer equipment at present is the shell and tube heat exchanger which has a large footprint and low heat transfer efficiency and it can be difficult to meet the requirements of the aerospace, high-temperature gas-cooled reactor, gas turbine and other fields using the shell and tube heat exchanger.

The plate-fin heat exchanger features a compact structure and high heat transfer efficiency. It is highly promising to study the plate-fin heat exchanger. However, the service environment of the plate-fin heat exchanger is getting worse and the high temperature and high pressure environment calls for increasingly strict design requirements for the plate-fin heat exchangers. The fracture mode is time-dependent for the service at high temperature and alternating load and the current design codes for pressure vessels are limited to the shell and tube heat exchangers and based on the elastic-plastic fracture mechanics (EPFM) theory, have neither considered the characteristics of the creep and fatigue fractures nor involved the brazing process, service environment and other factors and cannot be directly adopted for the design of the plate-fin heat exchangers.

The technical problem to be solved by the disclosed design method relates to overcoming the shortcomings of the prior art by providing a design method for creep-fatigue strength of a plate-fin heat exchanger, which makes it possible to conduct the high-temperature strength design for the plate-fin heat exchanger in consideration of the brazing process, service environment, failure positions and other factors.

The technical solution adopted solves this technical problem by relating to a design method for creep-fatigue strength of a plate-fin heat exchanger. The method includes the following steps:

Step 1: Preliminarily design the structure of the plate-fin heat exchanger according to its design temperature and design pressure requirements and define the operating temperature, number of operating cycles and service life of the plate-fin heat exchanger; Step 2: Make a primary stress analysis for the plate-fin structure with the finite element software to identify the stress concentration parts and determine the allowable stress S t ; Step 3: Judge whether the stress level of the stress concentration parts satisfies the following conditions:

P m ≤S t ;P L +P b ≤K t *S t ;

Where, P m means the primary membrane stress, P L means the local membrane stress, P b means the primary bending stress, S t means the time-dependent allowable stress and K t assumes a value between 1.05 and 1.16; If these conditions are satisfied, then perform Step 4; if the primary stress is assessed unsatisfactory, change the structure and plate thickness of the plate-fin heat exchanger core and go back to Step 2;

Step 4: Carry out the creep rupture experiment and fatigue experiment on the plate-fin structure and on the aged base material in the service environment, calculate the stress magnification factor K σ and the strain magnification factor K s and correct the fatigue design curve and creep rupture design curve for the base material according to the experimental results;

Δε=Δε ph +K s Δε* th ,

Where, Δε ph means the strain range that is derived from the stress range Δσ ph obtained from the primary stress analysis; Δε* th means the ratio of the difference between the maximum value and the minimum value of the macroscopic stress σ* th obtained from the thermal fatigue analysis to the elastic modulus of the plate-fin heat exchanger core in the height direction;

The allowable stress S t as described in Step 2 and Step 3 includes the allowable stress S t1 of the fin area and the allowable stress S t2 of the seal area.

The step of acquiring the equivalent mechanical parameters and equivalent thermophysical parameters of the plate-fin structure as described in Step 5 comprises the substeps of:

a. Dividing the plate-fin heat exchanger core into several plate-fin cells of the same shape; b. Considering the plate-fin cells equivalent to uniform solid plates; c. Acquiring the equivalent mechanical parameters and equivalent thermophysical parameters of a plate-fin cell, thus obtaining the equivalent mechanical parameters and equivalent thermophysical parameters of the whole plate-fin heat exchanger core.

The said equivalent mechanical parameters include the anisotropic equivalent elastic modulus, equivalent shear modulus and Poisson's ratio; the said equivalent thermophysical parameters include the equivalent thermal conductivity, equivalent coefficient of thermal expansion, equivalent density and equivalent specific heat.

The said anisotropic equivalent elastic modulus is calculated as follows:

A coordinate system is established by taking the midpoint of the bottom of the front of the plate-fin heat exchanger as its origin, taking the direction parallel to the axis of the flow path ( 3 ) in a horizontal plane as its x-axis, taking the direction perpendicular to the axis of the flow path ( 3 ) as its y-axis and taking the vertical direction as its z-axis,

The Poisson's ratio is calculated as follows:

The said equivalent shear modulus is calculated as follows:

A coordinate system is established by taking the midpoint of the bottom of the front of the plate-fin heat exchanger as its origin, taking the direction parallel to the axis of the flow path ( 3 ) in a horizontal plane as its x-axis, taking the direction perpendicular to the axis of the flow path ( 3 ) as its y-axis and taking the vertical direction as its z-axis,

The said equivalent thermal conductivity is calculated as follows:

A coordinate system is established by taking the midpoint of the bottom of the front of the plate-fin heat exchanger as its origin, taking the direction parallel to the axis of the flow path ( 3 ) in a horizontal plane as its x-axis, taking the direction perpendicular to the axis of the flow path ( 3 ) as its y-axis and taking the vertical direction as its z-axis,

The said equivalent coefficient of thermal expansion is calculated as follows:

A coordinate system is established by taking the midpoint of the bottom of the front of the plate-fin heat exchanger as its origin, taking the direction parallel to the axis of the flow path ( 3 ) in a horizontal plane as its x-axis, taking the direction perpendicular to the axis of the flow path ( 3 ) as its y-axis and taking the vertical direction as its z-axis,

The equivalent density and equivalent specific heat are calculated as follows:

Compared with the prior arts, the present invention has the following beneficial effects:

1. The design method for creep-fatigue strength of a plate-fin heat exchanger comprehensively considers the influences of the brazing process, service environment, failure positions and other factors of the plate-fin heat exchanger, conducts equivalent homogenization for the plate-fin heat exchanger core, calculates the equivalent mechanical parameters and equivalent thermophysical parameters of the plate-fin heat exchanger, solves the problem that the plate-fin heat exchanger cannot be designed for high temperature strength directly with the finite element software owing to its complex periodic structure, provides a theoretical basis for the high-temperature strength design for the plate-fin heat exchanger, thus making an effective life prediction for the plate-fin heat exchangers servicing at high temperature and alternating load and providing an effective method for the design of the plate-fin heat exchanger servicing at high temperature. 2. Equivalent homogenization divides the plate-fin structure into the same plate-fin cells and considers the plate-fin cells equivalent to uniform solid plates so as to calculate the equivalent mechanical parameters and equivalent thermophysical parameters of the plate-fin structure, thereby solving the problem that it is difficult to perform the finite element simulation for the plate-fin heat exchanger owing to the periodic complex structure of the plate-fin heat exchanger so that the thermal fatigue analysis for the plate-fin heat exchanger is performed subsequently with the finite element analysis software. 3. The equivalent mechanical parameters and equivalent thermophysical parameters of the plate-fin heat exchanger core are given as an analytic expression, solving the problem that the parameters have to be acquired only through the complex computer simulation or experiment before, facilitating the calculation of the effective parameters and greatly improving the design efficiency of the plate-fin heat exchangers.

FIG. 1 illustrates a main view for the plate-fin heat exchanger core.

FIG. 2 illustrates a main view for the plate-fin cells.

FIG. 3 illustrates a broken-line graph for the creep-fatigue life evaluation.

The preferred embodiments of this disclosure are illustrated in FIGS. 1 to 3 .

The design method for creep-fatigue strength of a plate-fin heat exchanger includes the following steps:

Step 1: Preliminarily design the structure of the plate-fin heat exchanger according to its design temperature and design pressure requirements and define the operating temperature, number of operating cycles and service life of the plate-fin heat exchanger.

The number of operating cycles is the product of the design service life and the number of annual shutdown; the service life is the design life. As shown in FIGS. 1 to 2 , the plate-fin heat exchanger core includes plates 1 and fins 2 , with the fins 2 provided between every two adjacent plates 1 , and is formed through superposing and brazing several plates 1 and fins 2 in a staggered fashion, thus forming several flow paths 3 between every two adjacent plates 1 and the cross section of the flow paths 3 is an isosceles trapezoid.

Step 2: Make a primary stress analysis for the plate-fin structure with the finite element software to identify the stress concentration parts and determine the allowable stress S t .

The influence of the brazing seam on the structural stress is not taken into account during the analysis, and the brazing bonding rate is assumed to be 100%. Then, the method involves considering the thermal aging of the material in the process of brazing, service environment (such as the influence of the helium atmosphere on the material strength in the high temperature gas-cooled reactor) and seal structure, and carrying out the experimental analysis to determine the allowable stress. The allowable stress S t is the time-dependent allowable stress and the allowable stress S t includes the allowable stress S t1 in the fin area and the allowable stress S t2 in the seal area. For acquiring the allowable stress S t1 in the fin area, uniaxial tensile and creep rupture experiments are carried out on the aged base material in the service environment (such as helium atmosphere) for the brazing high temperature and service environment. For acquiring the allowable stress S t2 in the seal area, it is necessary to carry out the tensile strength experiment on the filler metal. Finally, according to the ASME design criteria and correction results, the method involves determining the allowable stress S t1 in the fin area and the allowable stress S t2 in the seal area. The allowable stress of the fin area takes the minimum value of the following four factors: {circle around (1)} Yield stress at design temperature*(1/1.1)*p, {circle around (2)} 67% of minimal stress resulting in the creep rupture*q, {circle around (3)} 80% of minimal stress resulting in the start of the creep at the third stage*q, and {circle around (4)} Minimal stress up to 1% of the total strain (elasticity, plasticity and creep). The strain in the seal structure is limited, the allowable strain takes one third of the fracture elongation of the filler metal and the allowable stress of the seal area takes the minimum of the following three factors: {circle around (2)} Base material yield stress at the design temperature*(1/1.1)*p, {circle around (3)} Allowable strain*base material elastic modulus, and {circle around (4)} 67% of minimal stress generated by creep rupture*q. Where, p means the ratio of the yield stress of the aged base material to that of the un-aged base material; and q means the ratio of the creep rupture strength of the aged base material to that of the unaged base material.

Step 3: Judge whether the stress level of the stress concentration parts satisfies the following conditions:

P m ≤S t ;P L +P b ≤K t *S t .

Where, P m means the primary membrane stress, P L means the local membrane stress, P b means the primary bending stress, S t means the time-dependent allowable stress and K t takes a value between 1.05 and 1.16. If these conditions are satisfied, perform Step 4. If the primary stress is assessed unsatisfactory, change the structure and plate thickness of the plate-fin heat exchanger core and go back to Step 2. The conditions for satisfying the above-mentioned judgment conditions are as follows: the plate-fin structure fails when the stress of the stress concentration parts in the fin area reaches the allowable stress of the fin area; the seal structure fails when stress of the stress concentration parts in the seal structure reaches the allowable stress of the seal area. Failure of any of the plate-fin structure and seal structure will result in the failure of the plate-fin heat exchanger core, which needs to be redesigned to reduce the structural stress level. The stress is assessed with the allowable stress S t1 of the fin area and the allowable stress S t2 of the seal area, respectively. If the stress of the fin area satisfies the allowable stress S t1 and the allowable stress of the seal area satisfies the allowable stress S t2 , the stress is assessed satisfactory. If the stress of the fin area does not satisfy the allowable stress S t1 or the stress of the seal area does not satisfy the allowable stress S t2 , the stress is assessed unsatisfactory.

Step 4: Carry out the creep rupture experiment and fatigue experiment on the plate-fin structure and on the aged base material in the service environment, calculate the stress magnification factor K σ and the strain magnification factor K s and correct the fatigue design curve and creep rupture design curve for the base material according to the experimental results.

Step 5: Acquire the equivalent mechanical parameters and equivalent thermophysical parameters of the plate-fin structure so as to make a finite element analysis for thermal fatigue for the plate-fin heat exchanger.

The plates 1 and fins 2 of the plate-fin heat exchanger core are formed through brazing, compact in structure and different from the conventional homogeneous material. The plate-fin type heat exchanger core features a periodic porous structure and the periodicity and complexity of the core structure of the heat exchanger makes it difficult to directly make the finite element analysis which must be made with the equivalent homogenization method. In order to make the finite element analysis for the plate-fin heat exchanger core, the homogenization method has been introduced. The homogenization method means that the composite has a regular or approximate regular structure, this fairly regular heterogeneous material can be assumed to have a periodic structure, and it should be emphasized that these non-homogeneous materials are very small compared to the size of the composite. In view of this, such types of materials are sometimes referred to as the composites with periodic microstructures. However, it is quite difficult to analyze these boundary values containing a large number of heterogeneous materials even using modern high-speed computers. To overcome this difficulty, it is necessary to find a method to replace the composite with an equivalent material model and this process is called homogenization. The essence of homogenization is to replace the composite of periodic structure with the equivalent material and acquiring the performance parameters of the equivalent material is the key step of homogenization. The step of acquiring the equivalent mechanical parameters and equivalent thermophysical parameters of the plate-fin heat exchanger core include the following substeps: Step a. Divide the plate-fin heat exchanger core into several plate-fin cells of the same shape.

In the present embodiment, the structure shown in FIG. 2 is a plate-fin cell so that the plate-fin type heat exchanger core can be regarded as a combination of a plurality of plate-fin cells.

Since the structure of the plate-fin cells is not uniform, the plate-fin cells are regarded as a homogeneous material, that is, the plate-fin cells are considered equivalent to uniform solid plates so as to replace the nonuniform plate-fin structure with equivalent solid plates.

Step c. Acquire the equivalent mechanical parameters and equivalent thermophysical parameters of a plate-fin cell so as to obtain the equivalent mechanical parameters and equivalent thermophysical parameters of the whole plate-fin heat exchanger core. The equivalent mechanical parameters and equivalent thermophysical parameters here may also be acquired through the finite element analysis software or experiments.

The equivalent mechanical parameters include the anisotropic equivalent elastic modulus, equivalent shear modulus and Poisson's ratio. The equivalent thermophysical parameters include the equivalent thermal conductivity, equivalent coefficient of thermal expansion, equivalent density and equivalent specific heat. A coordinate system is established by taking the midpoint of the bottom of the front of the plate-fin heat exchanger as its origin, taking the direction parallel to the axis of the flow path 3 in a horizontal plane as its x-axis, taking the direction perpendicular to the axis of the flow path 3 as its y-axis and taking the vertical direction as its z-axis so as to calculate the equivalent mechanical parameters and equivalent thermophysical parameters of the plate-fin heat exchanger core. The equivalent elastic modulus of the plate-fin heat exchanger core is calculated as follows: The equivalent elastic modulus in the direction of the z-axis is calculated with the balance between the force applied on the plates 1 and the force applied on the vertical portion of the fins 2 ,

a y =a 0 ,

a x =a 0 ,

Δε=Δε ph +K t Δε* th .

Step 6. Calculate the fatigue damage D f and creep damage D c of the plate-fin heat exchanger,

Step 7. If D f +D c is less than 1, then perform step 8; if D f +D c is greater than or equal to 1, then perform Step 1.

According to the ASME creep-fatigue damage assessment criteria, as shown in FIG. 3 , D f is taken as the X-axis and D c is taken as the y-axis and D c +D f =1 is the envelop generated by the cracks based on the calculated total creep damage D c and total fatigue damage D f . If D f +D c is less than 1, namely, (D f , D c ) is below the envelope, then it means that the plate-fin heat exchanger will not fail within its entire design life at design temperature and pressure and satisfies the design requirements and it is necessary to perform Step 8. If D f +D c is greater than or equal to 1, it means that the plate-fin heat exchanger does not meet the design requirements. In this case, it is necessary to improve the structure, replace the material, reduce the service pressure and temperature under the allowable conditions and repeat Step 1 until (D f , D c ) is below the envelope so that the high temperature strength design for the plate-fin heat exchanger is completed.

The descriptions above are merely preferred embodiments of the present invention and shall not be regarded as any other form of restrictions on the present invention and the technical contents disclosed above may be modified or developed by any technician skilled in the art to the equivalent embodiments with equivalent change. However, any and all simple modifications, equivalent changes and developments that are made to the above-mentioned embodiments based on the technical essence of the present invention without being separated from the contents of the technical solutions of the present invention are still covered by the protection scope of the technical solution of the present invention.