Numerical simulations of heat transfer of hot wire anemometer

NUMERICAL SIMULATIONS OF HEAT TRANSFER OF HOT-WIRE ANEMOMETER LI WENZHONG (M.Eng. NUAA) A THESIS SUBMITTED FOR THE DEGREE OF PHILOSOPHY OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2003 ACKNOWLEDGEMENTS I would like to express my deepest appreciation and gratitude to my supervisors, Associate Professor Khoo Boon Cheong and Dr. Xu Diao for their invaluable guidance, advice and support throughout the entire courses of my research study. I also wish to acknowledge Prof. P. Freymuth from University of Colorado, Boulder for the discussions we had, the interest he has shown in this work and the advice he has given. I would also wish to acknowledge the staff in the Supercomputing Visualization Unit of National University of Singapore for their excellent service and great help. My entire family deserves a special gratitude for their unlimited support, encouragement and love throughout my stay in NUS. Specially thanks to my wife Ma Nan for her understanding and assistance. Last, but not the least, I would also like to my acknowledgement to the National University of Singapore for its Research Scholarship. Li Wenzhong ii CONTENTS ACKNOWLEDGEMENTS ii CONTENTS .iii SUMMARY . vi NOMENCLATURE viii LIST OF FIGURES . xi LIST OF TABLES . xiv CHAPTER INTRODUCTION 1.1 Introduction to hot-wire anemometry . 1.2 Electronic principles of constant temperature hot wire 1.3 Advantage of hot-wire anemometry . 1.4 The thermal response of a hot wire in a fluctuating flow . 1.5 Hot-wire correction under influence of wall proximity 1.6 Motivation and objective of the study 1.7 Structure of thesis . 10 CHAPTER NUMERICAL METHOD AND SOLUTION PROCEDURE . 13 2.1 Introduction . 13 2.2 Basic equations and non-dimensional parameters 13 2.3 Boundary conditions . 19 2.4 Discretization 20 2.5 Second-order upwind scheme . 23 2.6 Linearized form of the discrete equation 24 2.7 Under-relaxation . 25 2.8 Discretization of the momentum equation 25 2.9 Discretization of the continuity equation 26 2.10 Temporal discretization 27 iii 2.11 Pressure-velocity coupling 29 2.12 Solution method 32 2.13 Convergence criteria . 33 CHAPTER MOMENTUM AND HEAT TRANSFER FROM CYLINDER IN FREESTREAM STEADY LAMINAR FLOW 37 3.1 Introduction . 37 3.2 Governing equations and boundary conditions . 40 3.3 Numerical calculations 42 3.4 Numerical results and discussions 43 3.5 Conclusions . 57 CHAPTER THE THERMAL RESPONSE OF A HOT WIRE IN NEAR WALL REGION MEASUREMENTS 70 4.1 Introduction . 70 4.2 Literature survey on hot-wire heat transfer near a wall 71 4.3 Governing equations and boundary conditions . 76 4.4 Numerical calculations 77 4.5 Grid distribution, domain size independent check and numerical accuracy. 77 4.6 Plausible causes for the discrepancy between the near-wall hot-wire correction curves of Chew et al. and Lange et al. for adiabatic wall correction . 78 4.7 Main parameters affecting the near-wall hot-wire correction factor: . 84 4.8 Comparison with the experiment based on Y+ and h0 . 86 4.9 Near-wall hot-wire correction curves based on Re and h0 92 4.10 Simulation results based on Y+ and U+ . 94 4.11 On the critical Yc+ and h0 96 4.12 On the velocity correction factor, Cui, based on temperature loading of 1.1 …………………………………………………………………………… .99 iv 4.13 Conclusions . 101 CHAPTER THE THERMAL RESPONSE OF A HOT WIRE IN A FLUCTUATING FREESTREAM FLOW . 142 5.1 Introduction . 142 5.2 Governing equations and boundary conditions . 145 5.3 Numerical calculations 146 5.4 Heat transfer characteristics of the hot wire in free stream fluctuating flow …………………………………………………………………………….147 5.5 Conclusions . 155 CHAPTER SUMMARY OF CONCLUSIONS . 170 v SUMMARY A thorough numerical investigation of the laminar flow and heat transfer around a single circular cylinder was performed. In the first part of this dissertation, a summary of results of numerical investigations of the two-dimensional flow around a heated circular cylinder located in a laminar crossflow is presented. Numerical investigations were carried out for the low Reynolds number range normally encountered in near-wall hot-wire measurements, and for temperature loading of 1.8, which is typical for hot wire measurement. The computations yield information on Nu with Reynolds number. The temperature dependence of the fluid properties (air) was taken into account and this resulted in a temperature dependence of the Nu-Re results. The results obtained are important, as they form the reference against which the subsequent computations with wall effects are compared in order to obtain the near-wall corrections. Based on the results about domain size, natural convection, viscous dissipation and temperature influence on the fluid properties in the first part of this dissertation, in the second part of the dissertation, a numerical study was carried out to obtain the nearwall measurement correction curve for the hot wire having been calibrated under freestream condition at the two extreme cases of isothermal and adiabatic wall conditions. Unlike previous studies particularly in experiments where the correction curve is primarily based on only the distance (h) between the wall and the wire expressed in wall units (Y+ hUτ υ ), it is found that a second dimensionless parameter h0 ( h D ) accounting for the effect of the hot-wire diameter (D) is necessary to fully describe the vi overall near-wall correction curve. Calculations also reveal the reason for the apparent discrepancy between the near-wall hot-wire correction curves of Chew et al. (1995) and Lange et al. (1999b) next to a thermally non-conducting wall. In the third part of the dissertation, a numerical study was carried out to obtain the thermal response of a hot wire in a fluctuating freestream flow. The ranges of the parameters considered in this study are 0.025≤ Re≤ 200, 0≤ Sc≤ 0.32 (Sc is nondimensional frequency) and A≤ 0.6 (A is dimensionless amplitude of the imposed streamwise velocity pulsation). The results showed that for any fluctuating flow, a hot wire having been calibrated under imposed mean free stream condition could be used to measure it. The very rapid thermal response of the hot wire has enable the faithful measurement of fluctuating velocity in the typical range of frequency and amplitude encountered in a turbulent flow. vii NOMENCLATURE A Cd Dimensionless amplitude of the imposed axial velocity pulsation Drag coefficient = Fd ρU ∞2 D Cp Specific heat of fluid at a constant pressure Cu Correction factor = Cua Correction factor for adiabatic wall case Cui Correction factor for isothermal wall case D Diameter of hot wire du+ Correction factor = + Reynolds number = d U0 U meas U meas − U Uτ Uτ D υ U0 c P (TW − T∞ ) Ec Eckert number = f Pulsating frequency of the incoming flow g Gravitational acceleration Gr Grashof number = h The distance from the center of the hot wire to the wall H’ Heat flux through the closed circulation which surrounds the cylindrical hot wire h0 The non-dimensional distance from the center of the hot wire to the wall = ( ) gβ T −T D3 w ∞ υ ∞ h D viii k Thermal conductivity of fluid L Hot wire length Nu Nusselt number = Nu0 Nusselt number at free stream Num Measured Nusselt number Nuf Nusselt number based on film temperature Pe Peclet number = RePr Pr Prandtl number = Re Reynolds number = Ref Reynolds number based on film fluid property qD H' dA = A ∫ k ∞ (Tw − T∞ ) πk ∞ (Tw − T∞ ) µ ∞ Cp ∞ k∞ U∞ D υ Strouhal number which is used as a non-dimensional quantity to describe the vortex S shedding frequency S = D τU f fD = f Reν ∞ Sc Non-dimensional frequency S c = t Time T Temperature U0 The true upstream incoming flow velocity at the location of hot wire center Umeas Measured velocity value Uτ Friction velocity Y+ Non-dimensional wall distance = Yc+ Critical Y+, beyond which wall influence can be neglected hU τ υ = h0 Uτ D υ ix Volume coefficient of expansion Kinematic viscosity (µ/ ) ω Frequency of the pulsation τ Temperature loading = τs Period of the vortex shedding i,j Denotes Cartesian coordinate directions ∞ At the inlet of computational domain Tw T∞ x CHAPTER • SUMMARY OF CONCLUSIONS It is important to note that the critical Y+ for negligible wall influence on nearwall measurement is also highly dependent on h0 for both the adiabatic wall and isothermal wall cases. Future works associated with the results in this chapter are the further investigation of the physics behind the critical Yc+, and how the temperature loading affects the critical Yc+. In Chapter 5, the comparison of hot-wire heat transfer characteristics in a uniformed free stream flow and a fluctuating free stream flow was conducted to determine the hot-wire response. The ranges of the parameters considered in this study are 0.025≤ Re≤ 200, 0≤ Sc≤ 0.32 and A≤0.6. The following are findings drawn from the study of Chapter 5: • For any fluctuating flow, a hot wire having been calibrated under imposed mean free stream condition can be used for measurement of mean quantities. The deviation of the mean Nusselt number ratio ( N u N u ) from 1.0 is limited to less than ±5%. In the lower Re range of Re≤ 1.0, the said ratio deviates from 1.0 is kept below ±1%. • The very rapid thermal response of the hot wire has enabled the faithful measurement of fluctuating velocity in the range of frequency (4~10000Hz) and amplitude (A≤ 0.4) with essentially very little or limited phase lag between the imposed and measured velocities. And this fast response is highly enough to measure the fluctuating velocity encountered in a typical turbulent flow. 172 CHAPTER SUMMARY OF CONCLUSIONS Future works associated with the results in this chapter are investigating the different conductivity of the wall and h0 on the frequency response of the near-wall hot wire, and exploring the physics behind the frequency response due to the wall effect. Details of the various conclusions as summarized above are found at the end of the respective chapters. 173 REFERENCES REFERENCES Alfonsi, G. and Giorgini, A. 1991 Nonlinear perturbation of the vortex shedding from a circular cylinder. J. 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Fluid Mech. 406, 337-346 Fey, U., Koenig, M., Eckelmann, H. 1998 A new Strouhal–Reynolds-number relationship for the circular cylinder in the range 47< Re[...]... investigate (numerically) the thermal response of a hot wire subjected to an imposed fluctuating flow Because the response of the electrical system in the anemometer is invariably much better than the physical thermal response, the findings of the thermal response of the hot wire will reveal the overall response and sensitivities of the hot- wire system 1.5 Hot- wire correction under influence of wall proximity... heat transfer characteristics of the hot wire with its calibration curve obtained under free stream condition, since more or even less heat is released from the hot wire due to the influence of wall effects Further, the presence of the hot- wire prongs may alter the flow field thereby resulting in larger convective heat loss The subject of increased aerodynamic interference effects in near-wall hot- wire. .. response of the electrical system in the anemometer is invariably much better than the physical thermal response, the results of the thermal response of the hot wire should reveal the overall response and sensitivities of the hot- wire system 1.6.3 Objective of this study The purpose of this project is to conduct an accurate simulation and provide a deeper physical insight of a near-wall hot- wire operation... while flush sensors (hot films) are usually used to measure the wall shear stress Hot- wire sensors are made from a short lengths of resistance circular wire Hot- film sensors consist of a thin layer of conducting material 1 CHAPTER 1 INTRODUCTION deposited on a non-conducting substrate Hot- film sensors may also be cylindrical or other forms, such as those that are flush-mounted Hot- wire anemometers have... for hot- wire correction in near-wall configuration 5 CHAPTER 1 INTRODUCTION The hot wire, when operating under wall-remote conditions, is incumbent on the heat transfer characteristics of hot wire as exposed in the measured flow to be the same as that during the calibration Such assumption, however, is no longer valid when the same hot wire is used in near-wall measurements The wall may change the heat. .. correction is independent of the wall conductivity”, but Bhatia et al (1982) showed otherwise Overall, it may be mentioned that these experimental works do not elicit a consistent behavior of the hot wire near the wall 1.5.3 Numerical investigations on hot- wire near-wall correction In view of the inherent experimental difficulties of the near-wall measurement, it is obvious that a numerical experiment to... nonconducting wall of adiabatic thermal boundary condition Chew et al showed that for the non-conducting wall, as the hot wire is positioned increasingly close to the wall, the heat loss from the wire remains higher than the corresponding case without the presence of the wall; they attributed this phenomena to the distortion of velocity field by the wall and consequent alteration of the heat transfer characteristics... cause a corresponding change of the convective heat loss to the surrounding fluid from an electrically heated sensing probe The variation of heat loss from the thermal element can be interpreted as a measure of the fluid velocity changes There are two fundamentally different types of thermal anemometry, cylindrical sensors and flush sensors Cylindrical sensors (hot wires and hot films) are normally employed... some of the important parameters like wall conductivity, wire diameters, distance from the wall, temperature loading on the near-wall measurements Also from imposed known fluctuating flow, one can obtain the heat transfer response of a hot wire in a free-stream fluctuating flow The results of this study can be valuable to researchers who perform near-wall turbulence measurement using the hot wire 1.7... the recent work of Chew et al (1998) Chew et al (1998) also systematically investigated the other effects of wire diameters and over -heat ratio imposed Therefore, some corrections on the measured velocity are needed for the near-wall measurement for the hot wire having calibrated under free stream flow condition 1.5.2 Experimental investigations on hot- wire near-wall correction A number of experimental . NUMERICAL SIMULATIONS OF HEAT TRANSFER OF HOT- WIRE ANEMOMETER LI WENZHONG (M.Eng. NUAA) A THESIS SUBMITTED FOR THE DEGREE OF PHILOSOPHY OF ENGINEERING DEPARTMENT OF MECHANICAL. Introduction to hot- wire anemometry 1 1.2 Electronic principles of constant temperature hot wire 2 1.3 Advantage of hot- wire anemometry 2 1.4 The thermal response of a hot wire in a fluctuating. thorough numerical investigation of the laminar flow and heat transfer around a single circular cylinder was performed. In the first part of this dissertation, a summary of results of numerical