Heat exchanger pressure drop calculation formula

Pressure drop in the context of heat transfer, especially within systems like heat exchangers, refers to the reduction in fluid pressure as the fluid moves through the system. This phenomenon is a critical consideration in the design and operation of heat transfer equipment. The pressure drop occurs due to frictional forces between the fluid molecules and the internal surfaces of the system, as well as due to any changes in fluid velocity, direction, or both, caused by the system’s geometry (like bends, valves, and other obstructions).

In heat exchangers, for example, a fluid’s pressure drop can impact its boiling or condensation points, which are essential for the heat transfer process. High pressure drops require more pump or fan power to move the fluid through the system, increasing operational costs and potentially affecting the overall efficiency of the heat transfer process.

The pressure drop is influenced by several factors:

1. Fluid Properties: The viscosity, density, and flow rate of the fluid directly affect the pressure drop. Higher viscosity and density can lead to higher frictional forces, increasing the pressure drop.
2. System Geometry: The length, diameter, surface roughness, and configuration of the pipes or channels through which the fluid flows affect the pressure drop. Longer and narrower pipes with rougher surfaces increase the friction, leading to a higher pressure drop.
3. Flow Regime: The nature of the fluid flow (laminar or turbulent) influences the pressure drop. Turbulent flow typically results in a higher pressure drop due to increased fluid friction and mixing.
4. Heat Transfer Equipment Design: The design of heat exchangers, including the type (shell and tube, plate, etc.), the arrangement of flow paths, and the presence of baffles or fins, can significantly affect the pressure drop.

Understanding and managing the pressure drop is crucial for optimizing the performance and efficiency of heat transfer systems. Designers often aim to balance the heat transfer efficiency with the pressure drop to ensure that the system meets the required thermal performance without incurring excessive energy costs.

Calculating the pressure drop in a heat exchanger involves understanding the complex interactions between the fluid properties, the geometry of the heat exchanger, and the flow conditions. Here’s a simplified overview of how you might approach this calculation, focusing on a single-phase flow in a conventional shell-and-tube heat exchanger for illustration.

Basic Formula

The basic formula for calculating the pressure drop ($\Delta P$) in a pipe or a similar structure is given by the Darcy-Weisbach equation:

 

Where:

• $\Delta P$ is the pressure drop (Pa, psi),
• $f$ is the friction factor (dimensionless),
• $L$ is the length of the pipe or the equivalent length in the heat exchanger (m, ft),
• $D$ is the hydraulic diameter of the pipe or channel (m, ft),
• $\rho$ is the fluid density (kg/m³, lb/ft³),
• $v$ is the fluid velocity (m/s, ft/s).

Steps for Calculation

1. Determine Fluid Properties: Obtain the density ($\rho$) and dynamic viscosity ($\mu$) of the fluid at the working temperature.
2. Establish Flow Conditions: Calculate the fluid velocity ($v$) using the volumetric flow rate ($Q$) and the cross-sectional area ($A$) of the pipe or channel (considering the hydraulic diameter if not a circular pipe). The velocity can be found from $v=Q/A$.
3. Hydraulic Diameter: For non-circular channels, like those in many heat exchangers, calculate the hydraulic diameter where $P$ is the wetted perimeter of the channel.
4. Calculate Reynolds Number: Use the Reynolds number ($Re$) to characterize the flow regime, using   ​​.
5. Determine Friction Factor ($f$): The friction factor depends on whether the flow is laminar ($Re<2000$) or turbulent ($Re>4000$). For laminar flow, $f=64/Re$. For turbulent flow, the Colebrook or another empirical correlation is often used, which can involve iterative calculation or lookup charts.
6. Pressure Drop Calculation: Apply the Darcy-Weisbach equation with the determined values to calculate the pressure drop across the heat exchanger.

Considerations

• This method assumes a single-phase flow (all liquid or all gas), without phase changes like boiling or condensation.
• For complex geometries, corrections may be needed, and manufacturer data or computational fluid dynamics (CFD) simulations can provide more accurate results.
• For heat exchangers with multiple passes or complex flow paths, the overall pressure drop is the sum of the pressure drops across each section, including any losses from fittings, expansions, or contractions.

This calculation gives a basic estimate. For detailed design and optimization, engineers often rely on software tools and empirical data specific to the type of heat exchanger and application.

Let’s go through a simplified example of calculating the pressure drop in a shell-and-tube heat exchanger for water flowing through the tube side. This example will illustrate the basic principles and steps involved in the calculation.

Given Data:

• Water flow rate ($Q$): 0.1 m³/s
• Inner diameter of each tube ($D$): 25 mm (0.025 m)
• Number of tubes ($N$): 100
• Length of each tube ($L$): 5 m
• Water temperature: 25°C
  • Density of water at 25°C ($\rho$): 997 kg/m³
  • Dynamic viscosity of water at 25°C ($\mu$): 0.89 mPa·s (0.89×10−3−3 Pa·s)

Steps:

Let’s proceed with these calculations:

Based on the calculations:

• The total cross-sectional area of the tubes is approximately 0.0491 m².
• The velocity of water in the tubes is about 2.04 m/s.
• The Reynolds number is 57,053, indicating turbulent flow.
• The friction factor, using the Blasius equation, is approximately 0.0205.
• The calculated pressure drop across the heat exchanger tubes is about 8,471 Pa (or roughly 8.47 kPa).

This example simplifies many aspects of heat exchanger design and operation but illustrates the basic steps to calculate the pressure drop for water flowing through the tube side of a shell-and-tube heat exchanger. In real-world applications, additional factors such as the effect of tube layout, the presence of tube inserts, and the condition of the tube surfaces would also need to be considered. ​​

Reducing the pressure drop in a heat exchanger can improve energy efficiency and potentially lower operating costs. Here are several strategies to consider for lowering the pressure drop:

1. Optimize Flow Distribution

• Ensure uniform flow distribution across the heat exchanger to prevent localized high-velocity areas that can increase pressure drop. This can be achieved through careful design of inlet and outlet manifolds.

2. Increase Tube Diameter

• Using tubes with a larger diameter decreases the fluid velocity for a given flow rate, which reduces the pressure drop due to friction. However, this might also affect the heat transfer performance and the overall size of the heat exchanger.

3. Reduce Flow Velocity

• Reducing the flow rate will lower the velocity of the fluid and, consequently, the pressure drop. This approach should be balanced with the heat transfer requirements, as lower flow rates can reduce heat transfer efficiency.

4. Use Smoother Tubes

• The surface roughness of the tubes affects the friction factor. Using tubes with smoother internal surfaces can reduce the friction factor and thus the pressure drop.

5. Optimize Tube Length

• Shorter tubes result in a lower pressure drop because the frictional losses are proportional to the length of the path the fluid travels. However, shorter tubes may require more passes or a larger heat exchanger footprint to achieve the desired heat transfer.

6. Minimize Bends and Fittings

• Each bend, fitting, valve, and other obstructions add to the pressure drop. Minimize these elements or choose designs that offer lower resistance to flow.

7. Use Baffles Sparingly

• In shell-and-tube heat exchangers, baffles improve heat transfer by forcing fluid to flow across the tubes, increasing turbulence. However, they also contribute to pressure drop. Adjusting the baffle spacing, cut, and orientation can optimize the balance between heat transfer and pressure drop.

8. Consider Different Heat Exchanger Types

• Some types of heat exchangers inherently have lower pressure drops than others. For example, plate heat exchangers often have lower pressure drops compared to shell-and-tube designs for the same heat duty. Evaluating different heat exchanger types can be beneficial.

9. Routine Maintenance

• Fouling increases pressure drop by adding resistance and potentially narrowing the flow path. Regular cleaning and maintenance to remove fouling can maintain a lower pressure drop.

10. Computational Fluid Dynamics (CFD) Analysis

• Using CFD simulations can help in understanding the flow dynamics within the heat exchanger and identifying regions of high pressure drop that can be redesigned or optimized.

When considering these strategies, it’s essential to maintain a balance between reducing the pressure drop and achieving the required heat transfer rate. Changes aimed at reducing the pressure drop can sometimes adversely affect heat transfer performance, so each modification should be carefully evaluated for its overall impact on heat exchanger performance.

The pressure drop in a plate heat exchanger can vary widely depending on several factors, including the design of the heat exchanger, the type and properties of the fluids being processed, the flow rate, and the specific operating conditions. Here are some key factors that influence the pressure drop in plate heat exchangers:

1. Flow Configuration: Plate heat exchangers can be configured for countercurrent, cocurrent, or cross-flow, each affecting the pressure drop differently. Countercurrent flow typically offers better thermal performance, but the optimal flow configuration for minimizing pressure drop depends on the specific application.
2. Plate Design: The corrugation pattern, plate thickness, and spacing between plates significantly impact the pressure drop. More aggressive corrugation patterns increase turbulence (enhancing heat transfer) but also increase the pressure drop.
3. Viscosity of Fluids: High-viscosity fluids tend to have higher pressure drops due to increased frictional resistance.
4. Flow Rate: Higher flow rates increase the pressure drop because the fluid’s velocity through the narrow channels between plates is higher, leading to greater frictional losses.
5. Temperature: Fluid properties, including viscosity and density, are temperature-dependent. Higher temperatures can decrease the viscosity of liquids, potentially reducing the pressure drop.
6. Fouling: The buildup of deposits on plate surfaces can narrow the flow channels and increase roughness, leading to a higher pressure drop.

Typical Values

As a rough guideline, the pressure drop in a plate heat exchanger might typically range from a few kPa to several hundred kPa. For example, in HVAC applications where water is a common fluid, the pressure drop might be designed to stay below 100 kPa to keep pump requirements and operating costs reasonable. In more demanding industrial applications, pressure drops can be higher, especially if the fluids are more viscous or the heat transfer requirements are more intensive.

Estimation

To estimate the pressure drop in a specific plate heat exchanger, manufacturers often provide performance charts or calculation tools that take into account the specific design and operating conditions of their products. These tools use empirical data and correlations based on the heat exchanger’s geometry, plate design, and typical operating conditions to estimate the pressure drop for given flow rates and fluid properties.

For accurate design and analysis, consulting with the heat exchanger manufacturer or using specialized software is recommended, as these resources can provide the most precise estimates based on comprehensive data and modeling of the specific heat exchanger design.