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1、Velocity distribution and vibration excitation in tube bundle heat exchangersAbstractDesign criteria for tube bundle heat exchangers, to avoid fluidelastic instability, are based on stability criteria for ideal bundles and uniform flow conditions along the tube length. In real heat exchangers, a non
2、-uniform flow distribution is caused by inlet nozzles, impingement plates, baffles and bypass gaps. The calculation of the equivalent velocities, according to the extended stability equation of Connors, requires the knowledge of the mode shape and the assumption of a realistic velocity distribution
3、in each flow section of the heat exchanger. It is the object of this investigation to derive simple correlations and recommendations,(1) for equivalent velocity distributions, based on partial constant velocities, and(2) for the calculation of the critical volume flow in practical design application
4、s. With computational fluid dynamic (CFD) programs it is possible to calculate the velocity distribution in real tube bundles, and to determine the most endangered tube and thereby the critical volume flow. The paper moreover presents results and design equations for the inlet section of heat exchan
5、gers with variations of a broad range of geometrical parameters, e.g., tube pitch, shell diameter, nozzle diameter, span width, distance between nozzle exit and tube bundle.INTRODUCTIONFor a safe design of real heat exchangers, to avoid damages caused by fluid-elastic instability, the effective velo
6、city distribution over the entire tube length should be known, particularly in the section with nozzle inlet and in the baffle windows. Up to now only rough assumptions. Computational fluid dynamic (CFD) programs enable the calculation of the flow field in tube bundle heat exchangers . By parameter
7、studies the influence of the geometry can be investigated. Correlating the calculated velocities with the mode shape function, and regarding the design criteria accepted for ideal bundles, the vibration excitation can be simulated for each tube in the complex geometry, described by the stability rat
8、io K_, as defined in equation.By variation of the inlet geometry, it becomes possible to derive simple correlations for equivalent velocity distributions and corresponding flow areas in tube bundle heat exchangers. The three-dimensional steady-state flow field on the shell side of heat exchangers wi
9、th rigid tubes is calculated using the commercial CFD program STARCD.The program solves the well know 3D NavierStokes equations for incompressible turbulent flow by using the standard k- model.INVESTIGATION OF THE INLET SECTION GEOMETRYThe flow distribution in different inlet sections of tube bundle
10、 heat exchangers has been investigated. The tubes first are supported in two fixed bearings, so the support length is equal to the tube length L. The investigation of a one-pass section is justified, since the velocity distribution in the inlet section is independent of the flow in the following sec
11、tions of a multi-span heat exchanger; designing real heat exchangers. Calculating the steady-state flow field, a constant volume flow rate VP was fixed, in order to determine the axial velocity distribution in the tube gaps. The velocities in the six gaps of each tube with the neighbouring tubes are
12、 analysed. The fluid at the shell-side is air at normal conditions. By applying the extended Connors equation, the equivalent velocities for each gap are achieved. The root mean square values of the equivalent velocities of the opposite gaps are determined. With these three average equivalent veloci
13、ties it is possible to define the approach flow direction and two stability ratios: the first K_.30_/ value is defined for the normal approach flow direction, using the maximum of the three equivalent velocitiesand the critical velocity for the 30_ tube array, the second K_.60_/ value is determined
14、with the two average equivalent velocities in transversal flow direction and a critical value ucr:, which is estimated as a linear relation of the critical velocities ucr:.30_/ and ucr:.60_/, depending on the angle of the flow direction. The basis of this procedure was confirmed by analysing the exp
15、erimental Figure 2. Stability ratio for the tubes in the first three rows approached by flow in a bundle with a reduced distance b_ D 0:73 and a volume flow rate VP D 1:93 m3.In figure 1 the endangered tubes for both K_ values in the second tube row approached by flow are shown. Figure 2 shows as an
16、 example the K_ values for all Velocity distribution and vibration excitation in tube bundle heat exchangers tubes in the first three tube rows approached by flow at a reduced distance b_ D 0:73, that means, without the tube row No. 1. The volume flow rate was VP D 1:93 m3_s1.The correctio
17、n factors cn used in this case are listed in table II.Experimental data by Jahr 5 show that in homogeneous flow and in ideal bundles, the second row becomes first critical, the first rowonly at about 50%higher throughput, depending on _ . The reason is the lower upstream velocity of the first row an
18、d thereby a lower force on the tube, even though the gap velocities are the same in the first and the second tube row. The highest K_ values were taken in the second row. This value determines the value of the critical volume flow rate.The maximum values of the stability ratios K_ of the tubes in th
19、e first and the second actual tube row are plotted in figure 3 as a function of the reduced distance b_ for the described bundles. The highest value of K_ D 0:8 appears for normal triangular flow direction (K_.30_/) on the tube number 1 of tube row No. 2, when the shell is completely filled out with
20、 tubes. This tube layout should be avoided. The highest K_ values are achieved for the normal triangular flow direction in the second tube row approached by flow. Only at b_ D 0:73, the calculated K_ value in the first actual tube row is a little bit higher than the maximum value in the second actua
21、l tube row, and the K_.60_) values get up to the value of K_max; that is due to the peak transversal velocity at the nozzle exit. Moreover, in figure 3 it is shown that the transversal flow direction is not critical. This is true for all investigated bundles with a pitch ratio of _ D 1:28. Two nearl
22、y linear functions for the stability ratio between 0 _ b_ _ 2:5 and for b_ 2:5 can be determined. The value of about b_ D 2:5 seems to be a good choice, but b_ should not be lower than 1.The results for the K_.60_/ values of the other investigated pitch ratios will be presented in 11. In the further
23、 sections of the paper all results are presented for the calculated stability ratios of the normal triangular flow direction K_.30_/. In figure 4 the critical volume flow rates, calculated by the described method with STAR-CD, are plotted over the reduced distance b_. These results are compared with
24、 two different simple design methods. In method A a uniform flow in the cross-sectional area is supposed. That is not admissible in this case, because the predictedcritical volume flow rates are too high. In method B it is assumed that the flow toward the bundle and the second row occurs only in the
25、 nozzle-projection area.The design by method B achieves values being too low by a factor of 23. Surely, these considerable differences for one-through-flow will become lower in real heat exchangers, depending on the number of flow sections. It is the object of this investigation to find a combinatio
26、n of the two methods A and B, getting a safe prediction of the “measured” critical volume flow rates.MODEL FOR THE VELOCITY DISTRIBUTION AND THE FLOW AREASThe model does not describe the true velocity distribution, but the equivalent velocities, i.e. the excitation force on themost endangered tube w
27、ill be approximated. In figure 5, the basic data of the model for determining the distribution of the equivalent velocities and the corresponding flow areas in the second tube row are shown. L is the support length of the tubes and s is length of the chord in the second tube row. The model has been
28、developed and tested for a central position of the inlet nozzle and for a symmetrical mode shape function. It assumes that the most endangered tube is located in the center of the nozzle. Three flow sections with partial constant velocities have been distinguished in the model:maximum flow under the
29、 inlet nozzle with the cross-sectional area Fq1 and the equivalent velocity u1. All other velocities are referred to this highest value, i.e. the velocity ratio lower positive flow with the cross-sectional area Fq2 and the velocity ratio possible negative recirculation flow with the cross-sectional
30、area Fq3 and 3 D u3=u1. The flow rate in the partial section III is about 210% of the total flow rate, but the equivalent velocity is negligible, since the mode shape function _ is nearly zero. The reduction of the flow area by Fq3 is more important. So, the equivalent velocity u3 was assu
31、med to be zero. The first condition is the assumption, that the true velocities u.z/ and the model values ur should produce the same excitation force in each partial section r. For example, the equivalent velocity u1 in figure 5 is calculated by taking into account the velocity distribution ucr:.z/
32、and the mode shape function _.z/ only in the partial section I along the length L1: If the reduced nozzle diameter dS=L is high, then no recirculation occurs and L2 D L. The length L2 can be determined by the “measured” flow distribution. In figure 6 the velocity distribution in the tube gaps, refer
33、ed to the velocity in the nozzle vS, for one geometry is illustrated. The marked line shows the velocity distribution for the most endangered tube in the tube gap No. 1. At the intersection of this line with the neutral point line, the length L2 can be found. The profiles of the velocities in the tu
34、be gaps Nos. 2 and 3 are very similar; the values are negligibly lower. The tube gap No. 4, placed outside the nozzle-projection area shows significant lower velocity values, which reduce further for the tube gaps Nos. 5 and 6. Figure 6 contains also the values of the length L1=L and the equivalent
35、velocities u1=vS and u2=vS, calculated by the model equations. The results for the reduced flow length L2=L of all investigated tube bundles are illustrated in figure 7. To avoid recirculation, the nozzle diameters have to exceed values dS _ .0:33 to 0:5/L, depending on the pitch ratio . The followi
36、ng functions for the reduced length L2 could be obtained: In order to determine the jet expansion factors X, the reduced volume flows are plotted over all variants of X. Figure 8 shows an example. The searched solutions are found for such values of the jet expansion factor, where the volume flow rat
37、e, calculated by the model, is equal to the critical volume flow rate, calculated by STAR-CD. There are two solutions, but the solutions at the lower X values are not always plausible . For this reason the higher X values were taken. In figure 8 it can be observed that near the minima the influence
38、of the jet expansion factor is not significant, except the noncommendable case b_ D 0:375. The curves are clear graduated, so, increasing the reduced distance b_, the jet expansion factor also increases. The analysis showed that the distance a was not suitable correlating the values of X.
39、The distance b is the appropriate parameter considering the influence of the nozzle diameter and to define, whether the first row overlaps the nozzle flow area, which should be ensured choosing b_ _ 1:0. In figure 9 all values of the jet expansion factor X for DM D 600 and 700 mm are plotted over th
40、e reduced distance b_. For a safe design the following function can be define (20) For values b_ 0:4, i.e. those shells, which are completely filled with tubes, there is X D 1:0. By this function and by the derived equations, the cross-sectional areas Fq1 and Fq2 can be calculated. In figure 10 the
41、velocity ratio 2 D u2=u1 is plotted over the reduced difference length .L_2 L1/=L; L_2 being calculated by equation (15), also when L_2 should be Figure 9. Jet expansion factor X depending on the reduced distance b_. Figure 10. Velocity ratio 2 depending on the reduced difference length.
42、greater than L. The values of 2 show larger deviations and in some cases a dependence on b_. In reality, the plotted values 2 are the values calculated for the most endangered tube, therefore they are the maximum values in the cross-sectional area Fq2. Considering the radial velocity distribution sh
43、own in figure 6, average values for u2 are needed. Therefore, it makes sense to take the lower fitting line. Thereby values between at a reduced difference length of 0.5 are achieved. The velocity ratio 2 can be described by a linear function: Applying the model calculation, critical volume flow rat
44、es are achieved on the safe side between 80 and 100% of the simulated values, that corresponds to a deviation of _10% from an average value. In figure 11 the volume flow rate, calculated by the derived model equations, for shell diameters DM D 600 mm and DM D 700 mm are shown. The results for the sh
45、ell diameters DM D 400 mm and 1200 mm are not shown here, but join together with the presented results. The calculated absolute values of u1 and VPcr: have been validated againstmeasurements in single-span tubes heat exchangers. As for the velocity distribution, only the relative values for are nece
46、ssary to be known. For this purpose, a validation against CFD results is adequate.CONCLUSIONThe presented method produces equivalent velocity distributions and corresponding cross-sectional areas in real heat exchanger bundles and enables the designer to predict the vibration excitation by fluid-ela
47、stic instability more accurate than before. The derived equations are valid for the inlet section in the second row of normal .30_/ and in the third row of rotated .60_/ triangular arrays of both single- and multispan tubes heat exchangers, considering the influence of the different energy ratios in
48、 the partial sections 1. Up to now only cases with a central position of the inlet nozzle has been evaluated; so, the investigation is not yet concluded. The following problems have to be clarified: _ influence of the transversal flow direction in a normal triangular array (30_) at higher pitch rati
49、os 11, _ no symmetrical mode shape function and no central position of the inlet nozzle, _ model accommodations for other tube arrangements, _ development of a model, describing the partial flow rates in the baffle windows of real heat exchangers 管壳式换热器速度场及其振动情况分析为了使流体流动稳定，管壳式换热器的设计要基于稳定条件下在理想管道长度下的匀速流动。在实际生产的换热器中，流体流动不均匀会造成进口喷嘴，撞击管板及支路产生位移偏差等情况。根据Connors稳定性方程的延伸，得出等效的速度计算方法，需要了解到换热器找截流面的速度分布和振动情况。本次研究的目标是调查推导出其相关性及为这种计算方法提出意见和建议。 基于局部的恒速度，对应着相同的速度分布。 计算临界体积流量在实际设计中的应用，利用流体流动力学软件都可以计算实际管路中速度场的分布情况，从而确定流动的临界条件，进而出临界的体积流量。其对换热器的设计过程中进口段得分析及研究结果应用广泛，包括如下的几何参数，
