Introduction

A large number of production facilities in many industries use processes in which heat is transferred between different fluids. The basic principle of heat transfer is extremely simple, two fluids at different temperatures are placed in contact with a conductive barrier (the tube wall) and heat is transferred from the hotter fluid to the colder fluid until they reach the same temperature level. In industrial processes this is carried out in heat exchangers of various types and styles usually purpose built for the process and site conditions of the application.

The driving force for heat transfer is the difference in temperature levels between the hot and cold fluids, the greater the difference the higher the rate at which the heat will flow between them. With complex processing sequences the designer must optimise the temperature levels at each stage to maximise the total rate of heat flow.

A second factor controlling the transfer of heat is the area of the conductive barrier provided for heat flow. The greater the area then the larger will be the amount of heat that will flow in a given time with a given temperature difference within the heat exchanger. The designer has to minimise this area to provide cost effective solutions to his client and with skill the amount of area can be minimised and configured to reduce the containment volume and overall cost.

The third and perhaps the most important factor controlling the transfer of heat is the rate at which the heat flows into or out from each of the fluids. A high resistance to heat flow in either fluid will produce a slow overall rate of transfer. The level of resistance to heat flow results from many different factors including the inherent thermal characteristics of the fluids but can be influenced by the designer in a very positive way by the generation of turbulence within the fluids to prevent the creation of a thermally resistant static ‘boundary layer’ of fluid in contact with the heat transfer surface.

The fourth factor, also under the control of the designer, is the flow of heat through the conductive barrier between the fluids. The material chosen has to be compatible with the fluids of the process, it must not corrode or contaminate a food product, it must have an appropriate level of mechanical strength to withstand working temperatures and pressures and it must have a low resistance to heat flow so that it does not become the overriding factor in the heat transfer process.

The mathematical equations which describe the process of heat transfer are fairly simple:

Heat Transfer equation

Where:

  • Q is the amount of heat transferred, W
  • A is the area for heat transfer, m²
  • DT is an effective temperature difference, ºK
  • U is the overall heat transfer coefficient, W/m².°K

The value ofU is slightly more complex to calculate:

Overall Heat Transfer Coefficient equation

Where:

  • h1 andh2 are the partial heat transfer coefficients, W/m².°K.
  • Rw is the thermal resistance of the wall, m².°K/W.
  • Rf1 andRf2 are the fouling factors, m².°K/W.

While the values forRf are usually specified by the client, the values ofh andRw can be influenced directly by the designer by the choice of tube size and thickness and the materials of construction. The values of the partial heat transfer coefficientsh depend greatly on the nature of the fluids but also, crucially, on the geometry of the heat transfer surfaces they are in contact with. Importantly the final values are heavily influenced by what happens at the level of the boundary layers, the fluid actually in contact with the heat transfer surface.

Heat Transfer Processes

A lot of the academic research taking place into heat transfer processes concentrates on ways of predicting with accuracy the precise values of the boundary layer resistance and on ways of affecting the values without paying too high a penalty in terms of increased pressure losses.

Many techniques to reduce the tube side boundary layer resistance have been tried including various styles of tube ‘inserts’ which take the form of complex wire shapes or flat twisted strips fitted inside the tubes and various styles of tube deformation. Most have the disadvantage of increasing the resistance to fluid flow, the pressure loss, at a rate which increases more rapidly than the decrease in boundary layer resistance.

One technique which does not have this disadvantage however is that of deforming the tube with either a continuous spiral indentation or an intermittent spot indentation. Research has shown that by choosing the depth, angle and width of the indentation carefully, the rate of decrease in boundary layer resistance can exceed the rate of increase in pressure loss. This form of enhancement is illustrated in the following pictures.

Corrugated tube detail
Solidworks Hard Corrugation Sample

The continuous disturbance of the boundary layer of the tube side fluid increases the amount of turbulence within the fluid as described mathematically by the ‘Nusselt number’ and, providing the tube side fluid has the higher resistance to heat flow, will increase the overall rate at which heat is transferred.

This turbulent behaviour is illustrated in the following simulation video: Flow with particles animation inside a corrugated tube .

Corrugated tubes

What are they

When the overall heat transfer rate for a given heat exchanger is limited by the tube side partial heat transfer coefficient (ainside) the overall surface area of the heat exchanger can usually be reduced if this coefficient is improved in some way. Many methods of artificially enhancing this coefficient have been tried, some successful other less so.

  • Wire or strip inserts are sometimes used pushed into each tube to stir the boundary layer liquid away from the tube wall into the bulk of the fluid. This type has the disadvantage of a substantial increase in pressure loss per unit length and any particles or product pieces entrained in the fluid render them useless.
  • Internal ribs or fins along the length of the tube which are designed to increase the internal surface area per unit length of tube. Even moderate viscosity fluids can bridge the gap between the fins to give a layer of cold static fluid which negates any benefits that may be present.
  • Deformed and twisted tubes where the tube is flattened to reduce the effective hydraulic diameter and increase the coefficient accordingly. Once again any particles or product pieces entrained in the fluid render them inadvisable as blockage can easily occur.
  • The shallow spiral deformation (commonly called corrugation) which causes the boundary layer to be disrupted without too large a reduction in flow area. Providing the working diameters are chosen carefully this does not prevent the free passage of particles and pieces and does not allow even the most viscous fluids to bridge adjacent corrugations.

Why they were developed

An increasing requirement for food products to be pasteurised for long term storage and general hygiene led to the realisation that the heat transfer characteristics of a large proportion of food products were poor. In addition to this they commonly contain pieces of fruit, vegetable or meat which must maintain their integrity during processing to keep the quality of the product at an acceptable level. Without enhancement the heat exchangers required for processing even modest quantities of some food products can be unrealistically large and expensive.

Because of these inherent operational requirements, methods of reducing size and cost for this type of heat exchanger led to the development of tubes which can be used with fluids containing large size particles but still increase the rate of heat transfer by disrupting the boundary layer to give values of heat transfer coefficient higher than would normally result from the flow conditions being used.

Experimentation with different styles and types of tube deformation led to a general form consisting of a shallow spiral deformation down the length of the tube which has been optimised by further experimentation. Whilst being deep enough to disrupt the boundary layer they are not deep enough to constitute a barrier for any solids content which could cause blockage.

Standard corrugations tend to differ only in the angle which the spiral indentation takes down the tube, some having a steeper angle to the longitudinal centreline of the tube.

Experimentation with high viscosity food products has led to further development as an intermittent indentation which has proved more effective at values of Reynolds number between 40 and 200 and is now used when high viscosity causes these low Re values. A picture of so called 'dimple' corrugation is shown below.

Solidworks Dimple Corrugation Sample

Advantages of corrugation

  • They can generate tube side heat transfer coefficients up to 2½ times greater than the equivalent smooth tube with less than 2½ times increase in pressure loss.
  • They do not obstruct the flow area of the tube to a significant extent so they can be used in safety for fluids with high solids or fibre content without fear of blockage.
  • Increasing the tube side heat transfer coefficient brings the temperature of the tube wall closer to the temperature of the bulk fluid on the tube side this minimising any tendency to cause fouling due to ‘burn-on’, freezing or chemical changes.
  • With higher coefficients the heat exchanger size can be reduced and therefore minimises product hold up volumes and residence time within the heat exchanger as well as reducing the overall material content of the heat exchanger. When exotic materials are used this can have a significant effect on the overall cost of the unit and installation.
  • The effectiveness of in-situ cleaning processes, Cleaning in Place, is increased because of the increased turbulence generated by the corrugated tube at standard circulation velocities.
  • The higher turbulence created in lower viscosity fluids minimises any tendency for deposition fouling even at low flow velocities.
  • If fouling does occur on the tube side the deposits will normally be easier to remove as the corrugation leads to an uneven film thickness which experience has shown is less adherent than an equivalent deposit on a smooth tube.

The major advantages can be summarised as follows:

  • Reduction in heat exchanger size
  • Reduction in product hold up volume
  • Reduction in processing time
  • Reduction in fouling potential
  • Tube wall temperature closer to tube side fluid
  • Increased cleaning potential
  • More efficient processing of viscous fluids

Industries in which applications which would benefit in a positive way from any of the advantages listed could become users of the corrugated tube heat exchangers to provide size and weight savings and more effective processes.