Hydraulic resistance of a shell-and-tube heat exchanger: calculation 

Hydraulic resistance of a shell-and-tube heat exchanger: calculation and practical nuances

Calculation of the hydraulic resistance of a shell-and-tube heat exchanger determines not only the choice of pumping equipment, but also the total cost of owning the installation over 10–15 years of operation. An error in determining the pressure drop even by 10–15 kPa can lead to cavitation, vibration of the tube bundle or excessive energy consumption of up to 30%. In our engineering practice, we have repeatedly encountered situations where theoretical calculations using standard formulas diverged from real data on the bench due to ignoring local resistances in the distribution chambers. This article contains a step-by-step algorithm for calculating pressure loss in pipe and annulus space, based on real projects, and not just textbooks.

Physical essence of the process and impact on operation

Hydraulic resistance is the sum of the energy losses of the coolant flow as it moves through the channels of the apparatus. These losses consist of friction against the walls of pipes and partitions, as well as local resistance in places where the direction or cross-section of the flow changes. For the design engineer, the key parameter is balance: reducing the flow rate reduces the hydraulic resistance, but at the same time reduces the heat transfer coefficient, requiring an increase in the heat exchange surface and the dimensions of the apparatus.

In actual operation, exceeding the design resistance leads to the fact that the circulation pump operates outside its optimal efficiency zone. We have recorded cases where pumps at facilities in Siberia failed after 6 months precisely because of excessive resistance from the interpipe space caused by incorrect spacing of segment partitions. Therefore, the calculation must take into account not only clean pipes, but also the fouling factor, which can increase the resistance by 1.5–2 times by the end of the overhaul period.

When selecting equipment, it is important to understand the difference between design and actual resistance. Manufacturers often indicate minimum values for a “clean” state, which misleads customers. The actual calculation must include an adjustment for the roughness of the pipes after several years of operation and the presence of deposits. If your process is pressure sensitive, request your supplier to provide hydraulic calculations for both circuits using a safety factor of 1.1–1.2.

Methodology for calculating the resistance of the pipe space

The pipe space usually has more predictable hydraulics because the flow moves through straight channels. However, even here there are hidden factors that influence the final result. The calculation begins with determining the speed of the coolant, which for liquids is usually in the range of 0.5–2.5 m/s, and for gases - 5–30 m/s. Exceeding these values leads to erosion of the pipe material, especially at the points where the flow enters the pipes.

Step 1: Determine Reynolds number and flow regime

The first step is to calculate the Reynolds criterion (Re), which characterizes the fluid flow regime. The formula looks like Re = (w * din) / ν, where w is the flow velocity, din is the internal diameter of the pipe, ν is the kinematic viscosity. For water at 20°C, the viscosity is about 1.004·10⁻⁶ m²/s, but when heated to 80°C it drops by almost half, which radically changes the flow regime and the coefficient of hydraulic friction. In our calculations, we always take the viscosity for the average flow temperature, and not for the inlet temperature, in order to avoid system error.

If Re< 2300, the flow is laminar, and the resistance is proportional to the speed to the first power. When Re >10,000 the flow is turbulent, and the resistance increases in proportion to the square of the speed. Transition zone (2300< Re< 10000) is the most dangerous for calculations, since the formulas give the greatest error. In industrial practice, we strive to design devices with developed turbulent flow (Re >10000), since this provides better heat transfer, despite the increase in hydraulic losses.

Step 2: Calculation of friction losses along the length of pipes

The main part of losses in the pipe space is due to friction against the walls. The Darcy-Weisbach formula is used: ΔPtr = λ * (L / din) * (ρ * w² / 2). Here λ is the coefficient of hydraulic friction, depending on the roughness of the pipes and the Reynolds number. For new steel pipes, the absolute roughness is assumed to be 0.2 mm, but for pipes after 5 years of operation this parameter can reach 1.0 mm or more due to corrosion and scale.

A critical mistake that we have seen in other people's projects is the use of the coefficient of friction for smooth pipes (as for copper or plastic) when calculating steel heat exchangers. This underestimates the calculated resistance by 20–30%. For an accurate calculation, use the Moody diagram or Altschul formula for the roughness transition zone. Remember that the length L in the formula is the total length of all moves. If the heat exchanger is multi-pass (for example, 4 passes), the length must be multiplied by the number of passes, also taking into account losses in the reversing chambers.

Step 3: Taking into account local resistances in chambers

Losses in distribution chambers and when turning the flow are often underestimated, although they can account for up to 40% of the total resistance of the pipe space. When the flow from the collector enters the pipes, a sharp narrowing occurs, and when it exits, it expands. The local resistance coefficients (ζ) for the entrance to the pipe are approximately 0.5, and for the exit - 1.0. In multi-pass devices, rotation losses are added in the lids, which depend on the design of the partitions.

We recommend using manufacturers' empirical data for specific camera types as theoretical values may vary. For example, in devices with a floating head, the design of the reversing chamber differs from devices with fixed grids, which affects the hydraulics. If you do not have accurate data from the manufacturer, allow an additional 15–20% margin for local resistances in excess of the calculated values ​​according to the formulas.

Difficulties in calculating the interpipe space

The annulus is a much more complex hydraulic system due to the presence of segmental baffles that change the direction of flow. The flow here moves in a zigzag manner, constantly flowing around the pipes, which creates vortex formation and additional losses. It is in this circuit that most often problems with vibration and noise arise if the calculation is incorrect.

Influence of the type and pitch of partitions

Segmental partitions are the main element that forms the resistance of the interpipe space. The distance between the baffles (pitch) directly affects the flow rate and the number of cross-washes. Reducing the pitch increases speed and turbulence, improving heat transfer, but increases hydraulic resistance exponentially. The optimal pitch is usually 0.2–0.5 of the casing diameter, but depends on the permissible pressure drop.

In our practice, there was a case when the customer demanded to reduce the spacing of the partitions to increase efficiency, without coordinating this with the pumping department. As a result, the pressure in the interpipe space increased from 0.05 MPa to 0.18 MPa, which exceeded the rated capabilities of the installed pumps. It was necessary to replace pumping equipment post-factum, which increased the project budget by 15%. Always check the hydraulic design of the heat exchanger with the pump characteristics before approving the drawings.

Leaks and bypass flows

Actual flow in the annulus is never ideal. Part of the coolant leaks through the gaps between the pipes and holes in the partitions, as well as through the gap between the edge of the partition and the casing wall. These leaks do not contribute to effective heat exchange, but do affect the overall hydraulic picture. Standard calculation methods (for example, the Bell-Delaware method) introduce special correction factors for leaks.

Ignoring these coefficients results in the actual speed of the main flow being higher than the calculated one, since less liquid passes through the core than expected in the total flow rate. This may cause localized overheating or erosion. When ordering a heat exchanger, check with the manufacturer which calculation method was used and whether corrections for structural clearances were taken into account according to GOST or TEMA.

Comparative analysis of calculation methods

It is important for engineers to choose the right calculation tool, since different methods provide different accuracy and complexity. Below is a comparison of the main approaches used in modern industry.

The Bell-Delaware method remains the gold standard for most industrial applications. It quite accurately takes into account the geometry of a real device, including gaps, and does not require supercomputer power. Simplified formulas are only valid at the conceptual design stage, when the exact beam design is unknown. CFD modeling is justified only for unique projects with extreme parameters, where the cost of an error exceeds the cost of the modeling itself.

Practical examples and error analysis

Theory is important, but real numbers provide a better understanding of the scale of the problems. Let's look at two typical cases from our production practice that illustrate the importance of detailed calculations.

Case 1: Chemical plant, pumping viscous media

The task was to select a heat exchanger for cooling an organic solvent with high viscosity. The initial calculation, performed by the contractor without taking into account the temperature dependence of viscosity, showed a resistance of 0.03 MPa. However, during startup in the fall, when the temperature of the raw material dropped, the viscosity increased 3 times. The actual resistance reached 0.12 MPa, the pump was unable to push through the medium, and production stopped.

Solution:We recalculated taking into account the worst-case scenario for temperature and viscosity. The decision was made to increase the casing diameter and reduce the number of strokes in order to reduce the flow rate. The hydraulic resistance in operating mode stabilized at 0.06 MPa, which ensured reliable operation of the pumps even in winter. This case teaches us: always check the properties of the fluid over the entire operating temperature range, not just at the nominal point.

Case 2: Housing and communal services heating system, cavitation

At the heat supply facility, constant noise and vibration were observed in the area of the heat exchange unit. Diagnostics showed that the calculated resistance was underestimated and the pump was operating with a large excess pressure. This led to throttling of the flow by valves and the occurrence of cavitation in the heat exchanger itself due to local pressure drops in narrow sections of the partitions.

Solution:Instead of replacing the pump (which would be expensive), we suggested changing the configuration of the partitions in the annulus during the next repair, increasing the pitch. This reduced the resistance and brought the pump to the operating range of the characteristic curve. The noise disappeared, the equipment life increased. Conclusion: sometimes it is easier to change the hydraulics of the device than to change the pumping equipment.

Standards and regulatory framework

When performing calculations, it is necessary to rely on authoritative sources and standards to ensure the legal and technical validity of the project. In international practice, the main document is the TEMA (Tubular Exchanger Manufacturers Association) standard, which regulates calculation methods and tolerances.

For work in the CIS and Russian markets, the key document isGOST R 53683-2009“Heat exchangers. Calculation and design." This standard is harmonized with international standards and contains proven methods for determining heat transfer coefficients and hydraulic resistance. It is also useful to refer to the recommendationsHTFS (Heat Transfer and Fluid Flow Service), whose algorithms underlie most modern engineering programs.

Compliance with these standards ensures that your calculation will be accepted by experts and regulatory authorities. Deviation from the standards is possible only with special justification and agreement with the customer, but this always carries additional risks.

The role of production quality and materials in hydraulics

Even the most accurate theoretical calculation may be useless if the physical design of the device deviates from the design parameters. The quality of assembly, the accuracy of manufacturing of tube sheets and the condition of the inner surface of the pipes directly affect the actual hydraulic resistance. This is where the manufacturer's experience and specialization play a decisive role.

CompanyWuxi Kaisheng Electric Power and Petrochemical Equipment Co., Ltd.specializes in the development and production of high-quality heat exchange equipment for the energy and petrochemical industries. Our manufacturing approach takes into account the critical importance of hydraulic performance: we manufacture tube bundles from a variety of materials - from 316 stainless steel and C46400 marine brass to copper-nickel alloys and titanium, providing tightly controlled surface roughness. This minimizes unexpected pressure losses due to processing quality.

Our products, including titanium shell-and-tube heat exchangers, ASME high-pressure units and air coolers, are certified to international PED and ASME standards. We understand that in industries such as seawater desalination or oil refining, the slightest deviation in flow geometry can have serious consequences. Therefore, each of our products undergoes strict control, ensuring compliance with the calculated hydraulic models. The use of our components, such as 321 steel tube sheets or N06625 alloys, ensures not only high corrosion resistance, but also stable hydraulic parameters throughout the life of the installation.

Frequently Asked Questions

How to quickly calculate resistance without complex software?

For a quick assessment, use the simplified formula ΔP ≈ k * w², where k is an empirical coefficient depending on the type of device. For shell-and-tube heat exchangers with water, k is usually in the range of 1500–3000 Pa s²/m² for the tube space. This method will give an error of up to 30%, but will allow you to quickly estimate the order of magnitude and select a “first approximation” pump. This method is not acceptable for the final project.

Does pipe material affect hydraulic resistance?

Yes, it does, but indirectly. The material determines the roughness of the inner surface. Steel pipes have a roughness of about 0.2 mm, copper pipes - 0.01–0.05 mm, glass or plastic - even less. The difference in the coefficient of friction between a new steel and copper pipe can reach 20% in a fully turbulent zone. However, after 2–3 years of operation, the roughness of the steel increases due to corrosion, negating the initial advantage of copper.

What to do if the calculated resistance is too high?

There are three solutions: 1) Increase the diameter of the apparatus (reduce the flow rate); 2) Reduce the number of strokes in the pipe space; 3) Increase the pitch of the partitions in the interpipe space. The cheapest option is to change the pitch of the partitions, but this reduces the efficiency of heat transfer. An increase in diameter leads to an increase in the price of the metal. Choose a compromise based on your priorities: energy efficiency of pumps or compact installation.

Conclusion and recommendations for choosing equipment

Correct calculation of the hydraulic resistance of a shell-and-tube heat exchanger is the foundation for the reliability of the entire thermal circuit. Do not blindly trust catalog data; ask manufacturers for detailed hydraulic calculations for your specific environmental parameters. Помните, что экономия на этапе проектирования часто оборачивается многократными затратами на электроэнергию и ремонт в процессе эксплуатации.

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