Yuan Xing,Tao Zhi,Li Haiwang,Tian Yitu

National Key Laboratory of Science and Technology on Aero-Engine,Beihang University,Beijing 100083,China

Collaborative Innovation Center for Advanced Aero-Engine of China of Aerodynamics,Beihang University,Beijing 100083,China

Experimental investigation of surface roughness eff ects on flow behavior and heat transfer
characteristics for circular microchannels

Yuan Xing,Tao Zhi,Li Haiwang*,Tian Yitu

National Key Laboratory of Science and Technology on Aero-Engine,Beihang University,Beijing 100083,China

Collaborative Innovation Center for Advanced Aero-Engine of China of Aerodynamics,Beihang University,Beijing 100083,China

This paper experimentally investigates the effect of surface roughness on flow and heat transfer characteristics in circular microchannels.All test pieces include 44 identical,parallel circular microchannels with diameters of 0.4 mm and 10 mm in length.The surface roughness of the microchannels is Ra=0.86,0.92,1.02 μm,and the Reynolds number ranges from 150 to 2800.Results show that the surface roughness of the circular microchannels has remarkable effects on the performance offlow behavior and heat transfer.It is found that the Poiseuille and Nusselt numbers are higher when the relative surface roughness is larger.For flow behavior,the friction factor increases consistently with the increasing Reynolds number,and it is larger than the constant theoretical value for macrochannels.The Reynolds number for the transition from laminar to turbulent flow is about 1500,which is lower than the value for macrochannels.For the heat transfer property,Nusselt number also increases with increasing Reynolds number,and larger roughness contributes to higher Nusselt number.

1.Introduction

With continuing development of aircraft engines,turbine inlet temperatures become increasingly higher,often far exceeding the melting point of turbine blade materials.Efficient cooling techniques are among the most important methods to ensure safe operation of turbines.Many cooling techniques,e.g.film cooling and impingement cooling,have been applied to aero engines.Microchannels,which have superior heat transfer characteristics with higher surface to volume ratios,are attracting more and more attention for application in cooling techniques.After the landmark work of Tuckerman and Pease,1many researchers in the last decade have investigated theflow and heattransferbehaviorofmicrochannels(＜1 mm),which differ from those in the macro-scale.

Early in their investigation,Peng et al.2,3experimented with the behaviors offlowing fluid and heat transfer in rectangular microchannels with diameters ranging from 0.1 mm to 0.3 mm.Water was used as the working fluid.It was noted that the overall hydrodynamic performance of microchannels was different from conventional theories.Based on their experimental results,the friction factor in laminar and turbulence flow regimes was inversely proportional to Re1.98and to Re1.72,respectively.This is in stark contrast to what is expected from the conventional theories on laminar and turbulent regimes according to Filonenko.4What’s more,the authors found a transition occurred at Reynolds numbers 300–700,which was considered smaller than the transitional critical Reynolds number 2300.

Mala and Li5completed experiments in microtubes with diameters ranging from 50 μm to 254 μm.The results also indicated departure offlow characteristics from conventional theory of microtubes.In their experiment,the friction factor in laminar regime is higher than that predicted by conventional theory.The experimental results indicated the transition from laminar to turbulent flow mode at Reynolds numbers between 300 and 900.Yang and Lin6investigated the heat transfer and friction characteristics of water flow in microtubes.Experimental results reveal that there is no signi ficant size effect for water flow in tubes with diameters ranging from 123 μm to 962 μm.Zhao et al.7investigated the characteristics of nitrogen flow in microtubes with diameters of 2.05,5.03,and 10.10 μm.The results indicated that the flow characteristics had signi ficant discrepancies between the experimental data and predictions from the classical Poiseuille’s theory.Lelea et al.8found that the conventional theories were applicable in laminar flow regimes.Hasan et al.9employed numerical simulation and concluded that Reynolds number,thermal conductivity ratio and hydraulic diameter all affect the behavior of axial heat conduction.The authors explained that porous fin enhanced heat transfer performance along with the mechanism of water in microchannels reducing the pressure drop it affects.

As indicated above,most investigations show that thermal and hydrodynamic performance in microchannels is different from that of macrochannels.However,researchers have reached various conclusions about the cause of this divergence.Some investigators consider that the discrepancies might be caused by factors that are ignored in macrochannels.One of the most important of these,surface roughness,has attracted more and more attention.Tang et al.10investigated flow characteristics for nitrogen and helium in stainless steel microtubes,fused silica microtubes and fused silica square microchannels.The data in fused silica microtubes(Dhrange:50–201 μm,Dhis hydraulic diameter)are consistent with conventional predictions;however,the friction factors in stainless steel tubes(Dhrange:119–300 μm)are much higher than theoretical values.The authors believed that such significant deviations can be attributed to large surface relative roughness.Yang et al.11investigated the pressure drop and heat transfer performance of air flow in microtubes with inner diameters of 86,308,and 920 μm.The surface roughness of the microtubes is Ra=0.704,0.685,0.135 μm,respectively,and are all less than 1.5%of the diameter.The experimental friction factor shows a good agreement with the conventional theory.Lorenzini et al.12later conducted an investigation about compressible flow of nitrogen through circular microchannels from 26 μm to 508 μm with different surface roughness parameters.They found that,for both smooth and rough microtubes,the friction factor agrees well with conventional theory.It should be noted that when the Reynolds number was larger than 1300,the friction factor of smaller microchannels(＜100 μm)varies from the Poiseuille law.Liu et al.13studied the flow behaviors for air flow in rectangular microchannels with relative roughness of Ra=0.58,0.82,1.26.The experimental results indicated that a larger roughness tends toward larger Poiseuille numbers;thus,the effect of roughness cannot be ignored in experiments.Kharati-Koopaee and Zare14numerically studied the flow and heat transfer characteristics of air and water with aligned and offset roughness patterns in rectangular microchannels.The results indicated that the offset arrangement leads to lower pressure loss for both fluids and also a lower heat transfer rate for water than the aligned pattern.It should be noted that both roughness patterns contribute to better thermal performance.Zhang et al.15numerically investigated gas slip flow characteristics affected by rough surfaces.Theresultsrevealed thatgasflow behaviorin rough microchannels is affected by the statistical roughness height and rarefaction.Kandlikar et al.16investigated heat transfer behaviors for microtubes of different diameters,0.62 mm and 1.032 mm,and roughness ranging from Ra=1.0 μm to Ra=3.0 μm.This study finds that relative surface roughness bears no or little effect on the heat transfer characteristics for larger-diameter cases.However,the roughness effect is significant for the smaller diameters.Lin et al.17studied the effect of roughness on flowing fluid and heat transfer performance of air and CO2for microtubes with a 1 mm diameter.In the experiment,four different roughness features were generated.The results showed that the effect of roughness is different in laminar and turbulence flow regimes:in laminar flow,there was no difference of heat transfer between smooth and rough channels.However,in turbulent flow,rough channels have better thermal behavior.Koo and Kleinstreuer18numerically investigated the effect of surface roughness on heat transfer in micro-channels.They concluded that the Nusselt number increases with the increase in relative surface roughness in laminar flow.For turbulent flow,the Nusselt number becomes higher when the relative surface roughness of the tubes was larger.Guo et al.19built a model to investigate the influence of wall roughness on fluid flow and heat transfer in microchannels.The results showed that roughness plays a positive role in thermal performance as well as flow resistance.

Although the effects of roughness on flow and heat transfer behavior of microchannels have been studied by some,there is a lack of research on the behavior of roughness in undeveloped sections with air.What’s more,owing to the difficulties in measuring pressure,temperature and roughness,data about flow and heat transfer behavior in circular microchannels are lacking.Thus,considering the applications for turbine blades,heat transfer and flow behavior of air flow affected by surface roughness in circular microchannels are examined in this paper.

Experimental and theoretical investigation of the flow and heat transfer behavior in circular microchannels of 0.4 mm diameter and 10 mm length with various surface roughness follows.Based on experimental data,the corresponding empiric equations for Poiseuille and Nusselt numbers were developed.

2.Experiment description

2.1.Experimental facilities

The experimental facility is shown in Fig.1.Air was used as the working fluid.The air in the gas reservoir was compressed to 0.7 MPa by a gas compressor.Opening gas valve 0 results in air being released into the setup.Gas valve 1 and gas valve 2 were used to control air pressure in order to maintain the safety of the reservoir.A FCI-ST98 thermal flow meter installed after gas valve 2 was used to measure the mass flow rate of the air.Gas valve 3,which could be regulated steadily,was used to precisely control air flow.Air then flowed into a chamber to steady it before the test section and measure inlet pressure.Another chamber located downstream of the outlet measured outlet pressure.All pressures were monitored by the Rosemount transducers(0.15%accuracy).The temperatures were measured through type T thermocouples,which have an accuracy of±0.1 K.Both the Rosemount pressure sensor and the thermocouple readings were collected and transferred to a computer using a data acquisition card.

2.2.Experimental test section

Fig.2 shows a diagram of the test section,which is made of organic glass and includes three parts connected by bolts.The three fixture parts are named top,up and down.In the middle of the down fixture,a rectangular groove was fabricated with depth of 1 mm.The width and length of the groove are the same as the test piece,and the piece can be fixed into the rectangular groove.The up fixture has a rectangular channel on the same scale as the test piece to fix it together with the down fixture.

Three test pieces made of stainless steel were fabricated by drilling.The roughness was controlled in the fabrication procedure.The shape of a test piece is shown in Fig.3.Each piece includes 44 identical circular microchannels in parallel with diameters of 0.4 mm.The center distance between two adjacent circular microchannels is 0.9 mm.

The appearances of the channels are shown in Fig.4;all of them were measured by a confocal displacement device(Think Focus CL3-MG140).The surface roughness varies along the microchannels,and the profiles in the different channels of the same test piece are not the same.The surface roughness used in this paper is an average value.The detailed parameters of the test pieces are shown in Table 1.

Fig.1 Schematic diagram of experiment setup.

Fig.2 Expanded view offixture.

Fig.3 Test piece.

Fig.4 Appearance of different test pieces.

Table 1 Test piece parameters.

Fig.5 Structure of the copper block.

Fig.6 Heating device installation procedure.

The test piece was heated by a current heater that can provide a changing power output between 1.2 and 12 kW.The main component of the heater is a copper plate heated by two heating films.Two film heaters with the same resistances are connected in series.The structure of the copper plate is shown in Fig.5.Two blind holes(0.5 mm)were fabricated in the copper plate in order to measure its temperature.Two thermocouples were inserted into the two blind holes and placed on the top fixture.An assembly diagram of the heating device is shown in Fig.6.The copper plate and the film heaters were bonded by thermal silicone grease.The space between the copper plate and the organic glass plate is filled with asbestos,which reduces the ambient heat loss.The inlet and outlet temperatures of air were measured by one and five thermocouples independently.All thermocouples were calibrated before experimentation.

The heating devices were installed into the rectangular channel of the up fixture.The top fixture and up fixture were connected by bolts.

2.3.Experimental procedure

The test pieces were heated under constant heat flux.The temperature in test section was measured by T-type thermocouples.Three Rosemount pressure transducers were used to measure the pressure drop along the test section.The location of the pressure transducers and thermocouples is shown in Figs.1 and 2.The pressures of the two chambers were measured as the inlet pressure and outlet pressure.Differential pressure of the inlet and outlet was measured by the pressure holes located in the down fixture.

The mass flow rate was adjusted by needle valve according to the thermal flow meter and the pressure transducers.The data of temperature and pressure were collected as digital signals using ADAM-4018 chips and transferred to a computer.

3.Data reduction

For a better understanding of the flow behavior and heat transfer characteristics,the friction factor,Poiseuille number and Nusselt number are calculated.

The friction factor is defined as follows:

where Δp is the pressure drop along the test microchannels,ρ is the air density of the inlet,Dhis the hydraulic diameter of the channel,L is the length of microchannels and uaveis the average inlet velocity of air.Δp can be obtained by

where pinis inlet pressure,and poutis outlet pressure;they can be measured directly using pressure transducers.

uavecan be calculated from

where n is the number of the microchannels,Aciris the crosssectional area of the microchannels,and m is the total mass flow rate of the air.

The Poiseuille number is de fined as follows:

where qabsis the heat flux obtained by flow,Aheatis the heated area,which is the area of the two heat films,and Twis the wall temperature represented by the copper plate temperatures.Tfis the inlet temperature of air.Five thermocouples were used to measure the outlet temperature along the flow directions.

Therefore,the qabscan be obtained from

where cpis the specific heat capacity of the air,Tinis inlet temperature and Toutis the average outlet temperature;Tinand Toutcan be measured using thermocouples.

Averaged Nusselt number is defined as follows:

where λfis the coefficient of thermal conductivity offluid.The following expression of thermal performance is used in this paper:

4.Error analysis

An uncertainty analysis is performed on the Poiseuille number,Reynolds number,the averaged Nusselt number and thermal performance.For the Poiseuille number,error comes from Δp,m and ρ.For the Nusselt number,error is determined by λf,Tw,Tfand,according to the error transfer theory,20the uncertainty of Poiseuille number is calculated by

Through the above equations,maximum uncertainties of the Reynolds number,Poiseuille numbers,averaged Nusselt number and thermal performance are 5.46%,5.46%,5.97%and 4.45%,respectively.The uncertainties of the experimental apparatus are listed in Table 2.

5.Results and discussions

5.1.Flow characteristics

It can be observed in Fig.7 that the pressure drop of all microchannels increases with the increased mass flow rate.At low mass flow rates,the discrepancies between different channels are small for pressure drops with the various roughness parameters.This means that the influence of roughness is weak at low mass flow rates;however,discrepancies become larger and larger with the increase in mass flow rate.For a fixed mass flow rate,the channels with a larger roughness tend to have higher pressure drops.The above phenomenon obviously reveals that the surface roughness can signi ficantly affect pressure drop,and this in fluence becomes stronger as mass flow rate increases.Therefore,the effect of roughness cannot be ignored in microchannels.

Table 2 Uncertainties of the experimental apparatus and derived parameters.

Fig.7 Variation in pressure drop at different mass flow rates.

Fig.8 shows the friction factors of different test pieces with various relative roughness.Through comparison,it can be found that the entire friction factor goes down as the Reynolds number increases.The surveys of Schlichting21and White22showed that,for laminar flow in macrochannels,the effect of the relative surface roughness on the friction factor is negligible.This prediction is much different from the experimental results in microchannels.

The details of the conventional correlations used in this paper for estimating friction factors and heat transfer are given in Table 3.When Reynolds number is about 1500,the friction factor growth is little,meaning transition from laminar flow to turbulence occurs at this point.Compared with the theoretical critical Reynolds number of 2300,the experimental critical Reynolds number is lower.The transition phenomenon continues during Reynolds numbers ranging from 1400 to 1600.In a turbulent regime,the friction factor decreases continuously with the Reynolds number increasing until the friction factor tends to be constant.The results predicted by the conventional correlations in both laminar and turbulent flow regimes were used for comparison with experimental results.In a laminar regime,the friction factor is believed to be f=64/Re.In a turbulent flow regime,the friction factor follows the Blasius equation.23A comparison reveals that the flow resistance is larger than that in the macrochannels.This phenomenon can be explained by the effect of the entrance region and the roughness element on the internal surface.In the entrance region,the flow is affected by surface structure and movement with energy demission.For a fixed Reynolds number,the friction factor is larger when the relative roughness is higher due to the same reason.

Fig.8 Variation offriction factoratdifferentReynolds numbers.

Table 3 Conventional correlations applied in the present study.

The curves of experimental Poiseuille numbers are plotted in Fig.9.In laminar regimes,the Poiseuille number increases with the increase in Reynolds number.This is different from the conventional Poiseuille number that is regarded as a constant with value Po=64.Under the same flow conditions,the Poiseuille number is larger if the surface roughness is also large.

The effect of relative roughness on Poiseuille number and friction factor can also not be neglected.This means that roughness effects on flow behavior cannot be ignored in micro flow.This is because the roughness at the surface is an additional disturbance source;it can destroy the boundary layer and add a vortex to the main flow.The dissipation of the main flow follows,and pressure drop increases along the channel.However,for flow in macrochannels,the roughness is small enough comparing to the channel size;a vortex can affect the main flow only approaching walls.As such,the roughness effect can be ignored in macrochannels.

5.2.Heat transfer characteristics

This paper also investigates the heat transfer characteristic in circular microchannels.Fig.10 presents the curves of Nusselt numbers depending on Reynolds numbers;it is noted that for the same Reynolds number,Nusselt numbers for test pieces with different roughness parameters are different.In laminar and turbulence regimes,Nusselt number increases obviously with the increase in Reynolds number.In the transition regime,the rate of increase for Nusselt numbers becomes slower with increase in Reynolds number in some test pieces.A similar experimental phenomenon is also found in other literature,such as Peng and Peterson.25This anomaly is complex,may be caused by many factors,and is in need offurther investigation.In order to apply the microchannels to turbine blades,influence of the entrance region is included in experiments.Therefore,the heat transfer characteristic in this experiment is affected by transition from laminar flow to turbulence,surface roughness,entrance effect and pulsation of particles.

Fig.9 Comparison between experimental Poiseuille numbers and theoretical predictions.

Fig.10 Comparison between test piece Nusselt numbers.

Fig.11 shows a comparison of the Nusselt number with theoretical results.In the laminar regime with Reynolds numbers less than 2300,the Nusselt number is a constant at Nu=4.36.In transition and turbulence regimes,the Gnielinski24equation is employed.

Data obtained indicate the experimental Nusselt number is less than the conventional value.The divergence may be caused by the following factors:First,is the definition.For theoretical Nu,the wall temperature is the inner wall temperature.The inner wall temperature is more difficult to measure in actual application,and the wall temperature in this paper is the outer wall temperature of the copper,which is easier to measure.Second,when the diameter of circular microchannels is too small,it is difficult to ensure the microchannels are a theoretical circle.Third,considering the major application to turbine blades,the length of cooling channel is only 10 mm.Within this length range,the effect of the entrance friction factor on performance exists;therefore,the experimental Nusselt number may be affected by entrance effect.All the factors above may result in a difference in Nusselt number between theoretical and experimental results.

Fig.11 Comparison between experimental Nusselt numbers and theoretical predictions.

Fig.12 Comparison of thermal performance.

5.3.Thermal performance

The above analysis has shown the heat transfer characteristics of microchannels.However,it cannot express the comprehensive effects of roughness on flow behavior and heat transfer characteristics,so further investigation is necessary.The investigation of thermal performance has revealed that it is enhanced with the increase in Reynolds number,as shown in Fig.12.However,for the different microchannels with various roughness,the curves of experimental thermal performance are close to each other.This indicates that although rough surface structure in microchannels can enhance the heat transfer,flow resistance also increases.Therefore,the overall thermal performance does not change much.One of the reasons for this may be that,for the same mass flow rate,increase in roughness will decrease flow area,leading to increased flow velocity and subsequent reduced heat exchange efficiency.

6.Conclusion

The effects of relative roughness on flow behavior and heat transfer characteristics for circular microchannels are studied in this paper.Based on experimental results and theoretical analysis,the following conclusions can be reached:

Flow behaviors in circular microchannels are different from those in macrochannels:the critical Reynolds number is about 1500 for a channel with 0.4 mm diameter.The roughness effect cannot be ignored in microchannels:the friction factor increases markedly with the increasing surface roughness.

Heat transfer is also different from classical theories for macrochannels;in laminar flow regimes,Nusselt number increases with the increase in Reynolds number,but is considered a constant in macrochannels.

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Yuan Xing is a Ph.D.candidate in the School of Energy and Power Engineering at Beihang University.He received his B.S.degree from Beihang University in 2008.His research interests include aeropropulsion,cooling technique and conceptual air vehicles.

26 May 2016;revised 1 August 2016;accepted 5 August 2016

Available online 21 October 2016

Circular;

Flow behavior;

Heat transfer;

Microchannels;

Roughness

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*Corresponding author.Tel.:+86 10 82314379.

E-mail address:19820912@sina.com(H.Li).

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This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).