1、中文 3155 字 Velocity distribution and vibration excitation in tube bundle heat exchangers AbstractDesign 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 exchan
2、gers, a non-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 di
3、stribution 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 desig
4、n applications. 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 o
5、f heat exchangers 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. INTRODUCTION For a safe design of real heat exchangers, to avoid damages caused by fluid-elastic instability, the
6、 effective velocity 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
7、. By parameter 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 th
8、e stability ratio 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 he
9、at exchangers with 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 GEOMETRY The flow distribution in different inlet sect
10、ions of tube bundle 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 i
11、n the following sections 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 nei
12、ghbouring tubes are 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 averag
13、e equivalent velocities 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 velocities and the critical velocity for the 30_ tube array, the second K_.60_/
14、value is determined 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
15、by analysing the experimental 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.
16、 Figure 2 shows as an 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_s 1.T
17、he correction 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
18、 first row and 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 th
19、e tubes in the 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 fi
20、lled out with 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
21、 second actual 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:
22、28. Two nearly 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. I
23、n the further 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
24、compared with 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 predicted critical volume flow rates are too high. In method B it is assumed that the flow toward the bundle and the second row occu
25、rs only in the 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 combination 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 AREAS The model does not describe the true velocity distribution, but the equivalent
