Numerical and experimental study to examine methods to increase the convectional heat transfer of recuperator tubes

The use of structured tubes in tube bundle recuperators is intended to improve the energy efficiency of gas-fired industrial furnace systems with central air preheating. Currently, smooth tubes as well as smooth tubes with internal twisted tape are commonly utilised. The increased surface area of structured tubes leads to an increased heat transfer between the off-gas and the combustion air. However, structuring leads to an increased pressure loss. The aim is to find an optimal operating range in which the pressure losses are still acceptable and the greatest increase of heat transfer compared to the reference will be achieved. Smooth tubes and also smooth tubes with twisted tapes are considered as reference systems in comparison to two concave structured tubes. CFD simulations were used to investigate the influence of the operating parameters of combustion air velocity and off-gas velocity on heat transfer according to industrial scale. The simulations have shown that the heat flow increases with the honeycomb depth and strongly depends on the operating conditions. Experimental measurements in a test bench were carried out to validate the model and confirm the positive influence of structuring on heat transfer.


Introduction
One way to make industrial furnaces more energy efficient is to install an upstream recuperator.The principle of heat recovery in a recuperator is based on two separate flows, whereby the heat is transferred from the medium with higher temperature to the one with lower temperature.Regardless of industrial furnaces in the metal, ceramics, or chemical industry, the combustion air can be preheated [1][2][3].One way to make air preheating more efficient is to increase the heat transfer area between the two fluid flows and to increase the degree of flow turbulence.In many cases, the supplied combustion air is led through the tubes which are surrounded by the off-gas from outside.To increase the heat transfer, turbulence generators, twisted tapes, can be installed in smooth tubes.Another possibility is to apply structures to conventional smooth tubes which enlarge the surface area and intensify the turbulence.
Several different techniques have been used in the past to structure tubes for heat exchangers.One way to improve the surface roughness is to punch dimples in a metal sheet, which is then formed into a tube shape by rolling.Maithani and Kumar [4] examined such a dimpled surface with regard to the development of the correlation of Nusselt number and friction factor.Nusselt number and friction factor increase with a growing ratio of dimple depth to pressure diameter up to the value 1, after where they decrease.Aroonrat and Wongwises [5] confirms this with their own investigations on dimpled pipes.The heat transfer coefficient and the friction pressure loss rise with increasing dimple depth.
Studies have also been conducted on the influence of different twisted tape geometries.In their experimental study, Bas and Ozceyhan [6] investigated the influence of the twist ratio and the clearance ratio on the heat transfer and flow friction.They found that the twist ratio has a greater influence on the above-mentioned variables.Zheng et al. [7] have carried out a numerical study of heat transfer which investigates the performance and flow characteristics of structured tapes.Heat transfer is greatly improved owing to the disturbance to flow structures by the tape dimples.
This study addresses the investigation of concave structured tubes and compares the performance of the structured tubes to the two common cases of smooth tubes with and without twisted tape under identical operating conditions of recuperators.The inward structuring was deliberately chosen in order to realise a simple manufacturing with a forming tool and to create a maximum heat transfer area.

Materials and Methods
The investigations are carried out on two structured tubes and two reference geometries.Smooth tubes with and without internal twisted tape are used as reference geometries as they are commonly installed in recuperators.The tubes to be examined have an outer diameter of dtube = 42.The purpose of this investigation is to represent the heat exchange in a recuperator between the supplied combustion air and the off-gas.Since the experimental investigations cannot implement with a real off-gas composition, atmospheric air is used instead for both the experiments and the numerical model for comparability.

Numerical modelling
A simplified model of a tube bundle recuperator, figure 2, was used for the numerical investigations.It consists of a 3 x 3 tube bundle within a flow channel.The width of the channel corresponds to the tube length of l2 = 500 mm.This means that the tubes are only half as long as in the experimental investigations.The reduced tube length is necessary due to computing time savings.The spacing between the tubes is 1.7 times the tube diameter dt.The model describes two different fluid flows that are separated from each other.The off-gas enters the channel (blue rectangle) at a temperature Toff-gas = 500 °C.The inlet velocity of the off-gas is varied between voff-gas = 1 m/s to voff-gas = 5 m/s.The red rectangle represents a pressure outlet of the off-gas domain.The combustion air is supplied at a temperature of Tair = 20 °C via the tube inlets (blue circles).This is followed by a 100 mm long intake section.Here, a uniform flow profile can be established before the actual test tube is flowed through.The combustion air velocity is varied in the range vair = 1 m/s to vair = 20 m/s.The air flows out of the tube via a pressure outlet.All pressure outlets have the boundary condition of a gauge pressure pgauge = 0 Pa.The walls of the investigated tubes are modelled using shell conduction with one layer which have a virtual thickness of xlayer = 2.5 mm.All other walls are assumed to be adiabatic.For the numerical investigations, the realizable k-ε model of Ansys Fluent 2022 R1 was used.

Experimental setup
For the investigation of the heat transfer between an off-gas and the combustion air, a flow channel is adapted with an exchangeable channel segment to examine one separate tube, see figure 3. The air flowing through the channel can be heated up to maximum of Toff-gas = 500 °C by electrical heating elements inside the channel and is circulated via a cross-flow fan.More information about the hole test bench can be found in Strämke [8].The existing measurement technology, consisting of thermocouples and pressure sensors in the channel, is used to ensure a homogeneous temperature throughout the flow of off-gas onto the test tube.At the beginning of the inlet section of a single tube, a side channel compressor generates an air flow into the tube.Within the inlet section, the volume flow V ̇air, the flow velocity vair, the inlet pressure pair,in and the inlet temperature Tair,in into the structured tube are measured.In the test tube section, the tube wall temperature Ttube is measured by a welded-on thermocouple first.The built-in IR permeable windows at the top of the channel allow a non-contact temperature measurement of the tube surface with an IR camera at two more positions.This offers the advantage that the flow around the test tube is not affected and the total tube wall temperature can be observed.In the subsequent outlet section, the outlet temperature Tair,out and the outlet pressure pout are measured.

Calculation heat transfer coefficient
The local heat transfer coefficient at the inner tube wall is calculated via an energy balance.Based on the first law of thermodynamics, the change in the stored energy in a control volume, here the change of combustion air temperature, is set equal to the convectively exchanged heat flux.This assumption is admissible because the tube is considered to be thermally thin.The evaluation of whether a component is to be classified as thermally thin or thick is made via the Biot number, equation (1) [9].If Bi << 0.1, then the component is considered to be thermally thin.In this case, thermally thin means that the wall temperature measured outside of the tube and the wall temperature on the inside may be assumed to be the same at the same time.The temperature gradients in the component are neglected.
Due to the fact that the heat transfer coefficient is unknown, it must be replaced by the known heat flow according to the general equation of convective heat transfer, equation (2).Substituting equation (2) into equation (1) yields equation (3).
The minimum temperature difference ∆T between the combustion air and the off gas is ∆T = 80 °C.The maximum heat flux density q̇ for the heat transfer between the off gas and the combustion air via the tube wall is given as q̇ = 13.040W/m 2 .These experimentally determined values are deliberately set low for the present calculation in case of the temperature difference and high for the heat flow density in order to represent all experimental states.According to [10], the thermal conductivity λ of stainless steel is 16 to 20 W/(m•K) in a temperature range between 100 and 400 °C.The lowest thermal conductivity is assumed for the calculation.This results in a Biot number of Bi = 0.013, which is significantly smaller than 0.1 and the tube can be assumed to be thermally thin.The heat flow from the channel flow to the combustion air is calculated according to the simplified steady-flow thermal energy equation 4 [9].
By rearranging the equation for calculating the convective heat transfer of flow-through tubes and the heat flow calculated by equation ( 4), the heat transfer coefficient on the inside of the tube can be determined [11].

Numerical study
The numerical investigations show that the increase of the heat flux, the heat transfer coefficient and the pressure loss strongly depend on the operating parameters.Figure 4 shows the increase in heat flux of the smooth tube with tape and the concave structured tubes compared to the smooth tube.The smooth tube with tape shows an increase of approx.20 % compared to the smooth tube overall operating points.In case of the concave structured tubes it is noticeable that the increase is dependent on the operating parameters.At an off-gas velocity of voff-gas < 1 m/s, the advantage of structuring is only minimal.Here the increase is around 20 %.While at combustion air velocities vair < 5 m/s the greatest increases are achieved compared to a smooth tube.With increasing structure depth, the increase in heat flux grows.Accordingly, the maximum increase is 45 % for the concave 3 mm structured tube and 80 % for the concave 6 mm structured tube.Figure 5 illustrates the increase of the heat transfer coefficient of the investigated tubes in the full operating range.The heat transfer coefficient is increased by an average of 30 % with the use of a tape compared to a smooth tube in the full operating range.For the concave structured tubes, the increase in heat transfer coefficient is non-uniform over the operating range.Here, a particularly large increase is seen when the combustion air velocity is vair < 5m/s.In this range, a doubling of the heat transfer coefficient is achieved with a concave 6 mm structuring.Beyond that, the increase is approx.65 %.The deeper structuring in the concave 6 mm structured tube leads to a very significant increase in pressure loss compared to a smooth tube, which is 500 % on average.An exception is the range of vair = 5 to vair = 10 m/s, where the increase in pressure loss is between 380 % and 430 %.

Experimental validation
With the test set-up presented in chapter 2.2, the tubes were examined with regard to the heat transfer and the pressure losses.Table 1 compares the results of the numerical simulations and the experimental measurements for one operating point.The operating conditions refer to an off-gas velocity voff-gas = 5 m/s and a combustion air velocity vair = 10 m/s.It should be noted that the simulations were carried out at an off-gas temperature Toff-gas,num = 500 °C and the experimental trails at Toff-gas,exp = 400 °C.The 500 °C off-gas temperature of the simulation corresponds to industrial specifications.However, it was not possible to maintain a uniform flow at this temperature in time during the experiment, which is why a lower off-gas temperature had to be selected in order to be able to guarantee identical conditions for all tests.The smooth tube with the twisted tape experimentally shows an increase in heat flux and heat transfer coefficient compared to the smooth tube.The deviation from the numerical solution is 26 % for the heat flux and 83 % for the heat transfer coefficient.When determining the difference in pressure loss between the smooth tube and the tube with tape, it is shown that the pressure loss is 85 % lower in real terms than calculated numerically.This is less due to the numerical model than to the different installation of the tape.In the model, the tape was inserted into the centre of the tube in a floating position.In reality, the tape is welded at one point inside the tube.This means that the tape is placed at any angle in the tube and the area of flow between the tape and tube wall changes along the tube length.This was not numerically feasible, as different zones would have overlapped.
The advantages of the structured tubes compared to the smooth tubes turn out to be greater than the numerical results when studied experimentally.The increase in heat flux is experimentally measured to be 55 % better in the case of the concave 3 mm structured tube and 78 % for the concave 6 mm structured tube.This corresponds to an increase of about 35 % compared to the numerical results.The increase in the heat transfer coefficient is measured to be higher, by 106 % for the concave 3 mm structured tube and 150 % for the concave 6 mm structured tube, relative to the numerical solutions.Also, the increase in pressure loss is significantly higher when measured.There, the numerical model underestimates the pressure loss by 345 %.
A correction of the parameters due to the temperature difference of 100 °C and tube length difference of 500 mm in the numerical and experimental results was omitted, since the increases are always related to the smooth tube with the corresponding tube length and off-gas temperature.This allows the performance of the individual tubes to be compared with each other.

Discussion
The heat transfer is affected positively by a structuring or the use of a tape compared to a smooth tube.This is due to the increased turbulence in the fluid flow inside the tube.Within the structural patterns, backflows or recirculation are observed.The intensity of the backflows rises with increasing structural depth.Concave structures reduce the mean flow-through area of the tubes, creating an increase in the mean flow velocity inside the tube and also contributing to an increase in heat transfer.However, this also leads to an increase of pressure loss through the tube.The twisted tape increases turbulence through swirls, but no recirculation occurs here.
From the results it can be observed that the heat flux and the heat transfer coefficient do not rise equally, although the quantities are closely related.This behaviour is an indication that the increased heat transfer is not solely due to the increased tube surface.The heat flux is dependent on the tube surface, whereas the heat transfer coefficient is independent of it.The heat transfer coefficient is significantly influenced by the adjacent flow.If the degree of turbulence at the surface increases, the heat transfer coefficient rises.Thus, the heat transfer coefficient increases more than the heat flux with increasing structure depth.
The positive influence of structured tubes on the heat transfer and the increased pressure loss could be confirmed experimentally.It has been shown that the numerical model underestimates both the heat transfer and the pressure loss.Since this tendency can be seen repeatedly, it must be assumed that the turbulence of the airflow in the tube is underestimated by the simulation.The numerical investigations were all carried out with the identical model, corresponding to the same mesh properties, in order to compare the tubes with each other.Probably a general mesh for the different tube geometries is not sufficient to be able to obtain quantitative statements.Here, a specific mesh adjustment should be made in the structures depending on the structure depth.Nevertheless, the numerical results are lower, but reveal the same characteristics as observed experimentally.
Both the numerical and experimental investigations show that the tape with twisted tube results in a lower thermal advantage than the concave structured tubes.As the highest heat transfer is achieved with the concave 6 mm structured tube.Aroonrat and Wongwises [5] findings can be confirmed, with respect to the increased heat transfer at grater structure depth.
Based on the results, estimates can be made in which operating conditions smooth tubes should be substituted with structured tubes to improve the energy efficiency of gas-fired industrial furnace systems.Since the increase in heat transfer and pressure loss of smooth tubes with tape is independent of the operating conditions, they can be used flexibly in recuperators with a wide range of operating modes.For specialised applications, especially at low combustion air velocities, the concave structured tubes have advantages.Depending on the acceptable pressure losses, both concave xd,1 = 3 mm and concave xd,2 = 6 mm structured tubes offer a better heat exchange.
4 mm and a length of ltube = 1000 mm.The tube wall thickness is xtube = 2.5 mm.The reference tubes are made of available stainless steel X5CrNi18-10 (1.4301), which are seamlessly welded.The twisted tape has a diameter of dtape = 30 mm and a length of ltape = 1000 mm.The pitch of the tape is ptape = 125 mm.The structured tubes, figure 1, have been additively manufactured from X5CrNiMo17-12-2 (1.4401) stainless steel.They have the same dimensions as the smooth tubes plus the structuring which corresponds to a concave honeycomb structure.The width of the honeycomb is xw = 6 mm.The honeycomb depth xd differs for the two structured tubes, one amounts xd,1 = 3 mm and the other one xd,2 = 6 mm.

Figure 1 .
Figure 1.Sketch of the structured test tubes

Figure 2 .
Figure 2. Geometry of the model; black/grey: wall, blue: velocity inlet, red: pressure outlet

Figure 3 .
Figure 3. Cross-section of the channel segment with structured tube and measurement technology

5 )
wall ⋅ ( (T wall -T air,in )-(T wall -T air,out ) ln T wall -T air,in T wall -T air,out ) = ṁa ir ⋅ c p,air ⋅(T air,out -T air,in ) A wall ⋅ ( (T wall -T air,in )-(T wall -T air,out ) ln T wall -T air,in T wall -T air,out ) (40th UIT International Heat Transfer Conference (UIT 2023) Journal of Physics: Conference Series 2685 (2024) 012010

Figure 4 .
Figure 4. Increase of the heat flux ∆Q ̇ across the full operating range

Figure 5 .
Figure 5. Increase of the heat transfer coefficient ∆α across the full operating rangeThe changes in pressure loss of the investigated structured tubes compared to the smooth tube are shown Figure6.The application of a structure or the use of a tape leads to an increase in pressure