Compressed instability equivalent length of seamless heat exchange tubes

Heat exchange tubes are pivotal in various industrial processes, facilitating the transfer of heat during operations such as heating, cooling, and drying. These tubes are subject to fluctuating stresses due to changes in temperature and pressure, necessitating careful assessment and design to ensure their reliability and efficiency.

One critical aspect of mechanical design for heat exchange tubes is their susceptibility to compression-induced instability. This instability can arise when the fluid pressure inside the tube surpasses a certain limit, leading to vibrations that impair the tube's performance. The concept of instability equivalent length (Le) is introduced to quantify this phenomenon, serving as a vital metric in the tube's design and evaluation.

Redefinition of Instability Equivalent Length:

The instability equivalent length (Le) is a measure that equates the heat transfer impact of a fluid when it experiences localized instability to the length of a heat exchanger operating under uniform flow conditions. In simpler terms, it represents the portion of the heat exchanger that is affected by fluid instability as if the entire flow were uniformly distributed.

Revised Calculation Method for Instability Equivalent Length Under Pressure:

1. General Approach:𝐿𝑒=0.06𝐷(𝑅𝑒𝐷)0.8Le=0.06D(ReD)0.8Here,𝐷Ddenotes the internal diameter of the flow channel, and𝑅𝑒𝐷ReDis the Reynolds number within that channel. This formula is applicable for heat exchangers handling Newtonian fluids under steady-state conditions.

2. Specialized Approach:For scenarios where heat transfer might be affected by stratification, the following formula can be employed:𝐿𝑒=𝐹𝑟0.09×𝐿Le=0.09Fr×LWhere𝐹𝑟Fris the Froude number, and𝐿Lis the actual tube length. This method is suitable for calculating the instability equivalent length in heat exchangers with non-Newtonian fluids.

The calculation of the instability equivalent length under pressure typically involves two main steps: determining the fluid pressure from fluid dynamics equations and applying the instability reduction formula for heat exchanger tubes.

Specific Formula for Pressure Instability Equivalent Length:𝐿𝑐𝑟=0.03𝐷[(𝜌𝜈𝑓𝜌𝑠𝜇)14]ℎLcr=0.03D[(ρsμρνf)41]hIn this formula,𝐿𝑐𝑟Lcris the pressure instability equivalent length,𝐷Dis the pipe's internal diameter,𝜌ρis the fluid density,𝜈𝑓νfis the fluid's kinematic viscosity,𝜌𝑠ρsis the density of the tube wall material,𝜇μis the material's stiffness, andℎhis the tube length.

When performing actual calculations, it's essential to ascertain the values of the relevant parameters, some of which can be derived from experiments or literature, while others must be determined based on specific operating conditions and design requirements.

Practical Case Analysis:Consider a stainless steel heat exchange tube with a 50mm diameter and a 5mm thickness, transferring heat with hydrogen gas under pressures ranging from 15MPa to 25MPa. Given hydrogen's properties—density of 0.082kg/m³ and kinematic viscosity of 0.0000193m²/s—the tube wall material's density is 7800kg/m³, with a stiffness of 2.1E11Pa, and the tube length is 10m.

Using the formula, the pressure instability equivalent length of the heat exchange tube is calculated as:𝐿𝑐𝑟=0.03×50[(0.082×0.00001937800×2.1𝐸11)14]×10≈1.03𝑚Lcr=0.03×50[(7800×2.1E110.082×0.0000193)41]×10≈1.03m

For the design of the heat exchange tube, ensuring that the pressure instability equivalent length does not exceed 1.03m is crucial for maintaining stable operation.

Factors Influencing Instability Equivalent Length:

The Reynolds number of the fluid in the pipeline.

The straightness of the tube.

The friction resistance coefficient within the tube.

The degree of vortex generation in the tube.

The impact of longitudinal flow within the tube.

The influence of bends and reducers on the flow state.

During the design and operational phases, it is imperative to analyze the actual conditions and make necessary adjustments and controls based on the specific circumstances.