the project engineer to get an overall appreciation of flow‐induced vibration concerns, or by the plant operator to understand tube failures. This overview pertains to critical regions of shell‐and‐tube heat exchangers, such as nuclear steam generators (SG), heat exchangers (HX), coolers, condensers and moisture‐separator‐reheaters (MSR).
2.1.1 Flow‐Induced Vibration Overview
The vibration behavior of process system components is governed by vibration excitation mechanisms and by damping mechanisms. Generally, in components such as heat exchangers there are several significant damping mechanisms: 1) friction damping between tube and tube support, 2) squeeze‐film damping at the support, 3) viscous damping between tube and shell‐side fluid, and 4) damping due to two‐phase flow.
Generally, the flow in heat exchanger tube bundles can be parallel (axial flow) or transverse (cross flow) to the tube. In nuclear steam generators, the flow is axial for a large portion of the tube bundle. Vibration excitation forces induced by axial flow are relatively small in heat exchangers. Thus, vibration excitation mechanisms in axial flow may generally be neglected. The vibration behavior is clearly governed by cross‐flow vibration excitation mechanisms.
Several vibration excitation mechanisms are normally considered in heat exchange components such as tube bundles in cross flow, namely: 1) fluidelastic instability, 2) periodic wake shedding, 3) turbulence excitation, and 4) acoustic resonance. Fluidelastic instability is by far the most important mechanism and must be avoided in all cases. Periodic‐wake‐shedding resonance may be of concern in liquid cross flow where the flow is relatively uniform. It is not normally a problem at the entrance region of steam generators because the flow is very non‐uniform and quite turbulent (Pettigrew et al, 1973). Turbulence may inhibit periodic wake shedding in tube arrays. Periodic wake shedding is generally not a problem in two‐phase flow except at very low void fractions (i.e., εg < 15%) or under unusual conditions, as discussed in Chapter 11. Turbulence excitation may be important in liquid cross flow. Periodic wake shedding resonance and turbulence excitation are not usually of concern in gas flow since the fluid density is generally low, thereby resulting in relatively small excitation forces. However, both mechanisms should be considered in some gas heat exchangers such as MSRs where relatively high fluid densities exist. Acoustic resonance must be avoided in heat exchangers with shell‐side gas flow. However, it is generally not a problem in liquid and two‐phase heat exchangers.
2.1.2 Scope of a Vibration Analysis
A heat exchanger vibration analysis consists of the following steps: 1) flow distribution calculations, 2) dynamic parameter evaluation (i.e., damping, effective tube mass, and dynamic stiffness), 3) formulation of vibration excitation mechanisms, 4) vibration response prediction, and 5) resulting damage assessment (i.e., comparison against allowables). The requirements applicable to each step are outlined in this overview. Each step is discussed in more detail in the following chapters of this handbook.
2.2 Flow Calculations
Flow‐induced vibration problems usually occur on a small number of vulnerable tubes in specific areas of a component (e.g., piping elements, entrance regions and tube‐free lanes in heat exchangers, and U‐tubes in nuclear steam generators). Thus, a flow analysis is required to obtain the local flow conditions throughout these heat exchange components. Flow considerations are discussed in detail in Chapter 3.
2.2.1 Flow Parameter Definition
The end results of a flow analysis are the shell‐side cross‐flow velocity, Up, and fluid density, ρ, distributions along critical tubes. For flow‐induced vibration analyses, flow velocity is defined in terms of the pitch velocity:
(2‐1)
where U∞ is the free stream velocity (i.e., the velocity that would prevail if the tubes were removed), P is the pitch between the tubes and D is the tube diameter. For finned tubes, the equivalent or effective diameter, Deff, is used. The pitch velocity is sometimes called the reference gap velocity. The pitch velocity is a convenient definition since it applies to all bundle configurations.
The situation is somewhat more complex in two‐phase flow. Another parameter, steam quality or void fraction, is required to define the flow conditions. Two‐phase mixtures are rarely homogeneous or uniform across a flow path. However, it is convenient and simple to use homogeneous two‐phase mixture properties as they are well defined. This is done consistently here for both specifying vibration guidelines and formulating vibration mechanisms. The homogeneous void fraction, εg, is defined in terms of the volume flow rates of gas,
(2‐2)
The homogeneous density, ρ, the free stream velocity, U∞, and the free stream mass flux,
(2‐3)
(2‐4)
(2‐5)
where ρg and ρℓ are the densities of the gas and liquid phase, respectively, and A is the free‐stream flow path area.
For both liquid and two‐phase cross flow, the pitch velocity, Up, and the pitch mass flux,
(2‐6)
2.2.2 Simple Flow Path Approach
For relatively simple components, where the flow paths are reasonably well defined, a flow path approach may be adequate to calculate flow velocities, as illustrated in Fig. 2-1. In the flow path analysis approach, characteristic flow paths (i.e., through the tube bundle, between the tube bundle and shell, etc.) between regions of common pressures are identified. Flow impedances (i.e., pressure drop coefficients) are estimated. The flows within each path are then calculated. The resulting flow velocity distributions are then used to estimate vibration excitation mechanisms and predict vibration response.
Fig. 2-1 Flow‐Path Approach.
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