and tube‐support materials should be chosen to minimize fretting‐wear damage. Similar materials such as Inconel1 ‐600 (I600) tubes and I600 supports must be avoided. Incoloy‐800 (I800), Inconel‐690 (I690) and I600 tubes with 410, 304L, 316L, 321 stainless steel or carbon steel supports are considered acceptable material combinations. A fretting‐wear coefficient, KFW, of 20 x 10‐15 m2/N may be used as a first approximation for these tube and support material combinations (Guérout and Fisher, 1999). Other material combinations may be used. However, it would be desirable to obtain reliable fretting‐wear coefficients before choosing the material combination. Fretting‐wear coefficients are discussed in detail in Chapter 13.
The tube supports, whether they be flat bars, lattice bars, broached holes, scalloped bars or circular holes must be deburred to make sure there are no sharp edges between tube and support.
2.6.3 Wear Depth Calculations
To be conservative, it may be assumed that fretting‐wear is taking place continuously for a total time, T, corresponding to the life of the component and equal to half the life of the station, Ts. Thus, T = 0.5Ts and the total fretting‐wear volume, V, is then calculated from Eq. (2-53):
The resulting tube wall wear depth, dw, can be calculated from the wear volume. This calculation requires the relationship between dw and V. For example, for a tube within a circular hole or a scalloped bar, it may be assumed that the wear is taking place uniformly over the thickness, L, and half the circumference, D, of the support. Thus:
Alternately, for lattice bars and for flat bars, it may be assumed that wear is taking place only on the tubes. Thus, the bars and the wear scars remain flat. For lattice bars in the straight‐leg section, wear occurs on both sides of the tube and M = 4 in Eq. (2-54b); for flat bars in the U‐bend, we assume that wear occurs on one side of the tube and M = 8 in Eq. (2-54b). This geometry leads to
where
Thus, the tube wall fretting‐wear depth, dw, may be estimated using Eqs. (2-53) and either (2-54a), or (2-54b) and (2-54c).
2.7 Acceptance Criteria
The flow‐induced vibration analysis should demonstrate that the heat exchanger is acceptable by satisfying the design acceptance criteria outlined below.
2.7.1 Fluidelastic Instability
The maximum flow velocity in a heat exchanger should be below the critical flow velocity for fluidelastic instability, Upc, based on a fluidelastic instability constant, K = 3.0, for liquid and two‐phase flows. Thus,
(2‐55)
2.7.2 Random Turbulence Excitation
The vibration response to random turbulence excitation should be sufficiently low to prevent excessive tube wall reduction due to fretting wear. The tube wall fretting‐wear depth, dw, calculated as per Section 2.6.3 for the entire life of the component should be less than a specified percentage of the nominal design tube wall thickness (e.g., 40%).
2.7.3 Periodic Wake Shedding
Resonance due to coincidence of tube frequency and periodic‐wake‐shedding frequency should be avoided. If the latter is not possible, the maximum (zero‐peak) tube vibration amplitude, Ymax, at resonance should be less than two percent of the tube diameter, thus:
(2‐56)
Below 0.02D, the vibration amplitude is generally not sufficient to spatially correlate the formation of vortex shedding with the motion of the tube, thereby resulting in a much‐reduced uncorrelated vibration response.
2.7.4 Tube‐to‐Support Clearance
The tube‐to‐support clearance must be small enough to provide an effective support. Thus, pinned support conditions may be assumed provided the tube‐to‐support diametral clearance for drilled holes, broached holes, scallop bars, egg crates and lattice bars is less than or equal to 0.4 mm.
For flat‐bar‐type U‐bend supports, the vibration analysis should satisfy Section 2.7.2 for the out‐of‐plane direction while assuming that one (any one) support may not be effective in the U‐bend region. In the in‐plane direction, the diametral clearance between tube and flat bar support should be sufficiently small to provide effective support (e.g., <0.1 mm).
2.7.5 Acoustic Resonance
The analysis should show that acoustic resonance conditions are avoided in the heat exchanger tube bundle. This should be based on at least two generally recognized criteria (e.g., Blevins and Bressler, 1987 and Ziada et al, 1989). The heat exchanger relevant parameter, whether it be shedding frequency, fs, acoustic frequency, fan, geometry, P/D, L/D or resonance parameter, Gs, or Gi, should be at least 25% away from the resonance criteria or boundary, thus:
(2‐57)
2.7.6 Two‐Phase Flow Regimes
Flow
