THES‘B This is to certify that the thesis entitled DEVELOPMENT OF A TEMPERATURE MEASUREMENT SYSTEM WITH APPLICATION TO A JET IN A CROSS FLOW EXPERIMENT presented by Candace Elaine Wark has been accepted towards fulfillment of the requirements for M. S . Jegree in Mechanical Engineering ortunily Institution 0-7639 MS U is an Affirmative Action/Equal Opp DEVELOPMENT’OF A TEMEEEATURE MEASUREMENT SYSTEM ‘IIEH.APPLICATFQN TO A IET'IN A CROSS FLOW EXPERIMENT By Candace Blaine Wart AlTEESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Depart-ant of Mechanical Engineering 1984 ABSTRACT DEVELOPMENT OF A TEMPERATURE MEASUREMENT SYSTEM WITH APPLICATION TO A JET IN A.CROSS FLOW EXPERIMENT By Candace Elaine Mark A temperature measurement system. which allows the simultaneous sampling each (.64 msec) of up to 80 separate thermocouples. has been developed. Electronic and thermal noise give an effective resolution of nominally 1.44'C. The time constant values 1. for each of the 64 thermocouples. were determined experimentally at seven mps. A "universal" form of the velocity dependence: A-A(u) for 2i u $12 mps. was analytically inferred and experimentally verified for four thermo- couples. Software routines were used to correct the measured temperatures for the effect of L for each thermocouple. The tempera- ture measurement system has been used in an experimental pregram to determine the effects of cross stream disturbance levels on the dynam- ics of a jet in a cross flow for two momentum flux ratios (1-ij3/p.U:-16.64) and for three overheat values (Ti-T;-22.2.41.7.66.2'C). The results indicate that a dynamic effect of the overheat exists for even these small temperature values. Various measures of the thermal field. for the disturbed case. suggest that it remains relatively compact while being buffeted by the ambient turbulence field. ACKNOWLEDGEMENTS I would like to express my appreciation to my parents for their support during my educational career. I would like to recognize the support of NASA Lewis Research Center. grant monitor Dr. 1.0. Holdeman. The careful work by M. Omar Ahmed in preparing the figures is greatly appreciated. I would like to thank Mr. Peter J. Disimile for the encouragement and sup- port he has provided. I wish to express my 'gratitude for the support and guidunce provided by my thesis advisor. Professor John F. Foss. 11° TABLE OF CONTENTS LIST OF TABLES ................................................. LIST OF FIGURES ................................................ LIST OF SYMBOLS ................................................ FORWARD ........................................................ PART I -- TEMPERATURE MEASUREMENT SYSTEM CHAPTER 1 INTRODUCTION ......................................... .l.l Temperature Measurements ......................... 1.2 The role of the Time Constant in a Temperature Measurement System ................. 1.2.1 The First Order Response Equation ....... 1.2.2 The Role of A in the Data Acquisition Process ................... 2 TEMPERATURE MEASUREMENT SYSTEM ....................... 2.1 The Physical System .............................. 2.1.1 Thermocouples and Support Array ......... 2.1.2 Reference Junctions and Assembly ........ 2.1.3 Electronic Processing Units ............. 2.1.4 Data Acquisition System ................. 2.2 System Performance Evaluation .................... 2.2.1 Evaluation of the Processing Boards ..... 2.2.2 Thermocoup1e Time Constant Evaluation ... 2.2.3 Reynolds Number Dependence of Time Constants ........................ 3 DATA ACQUISITION PROCEDURE ........................... 3.1 Offset Determination ................ - ............ 3.2 Sampling Rate Considerations .................... 3.3 Time Constant Correction and Data Storage ....... Page v vi ix xiii \lmm 10 10 10 11 11 12 13 13 14 16 18 18 19 19 TABLE OF CONTENTS (Continued) Page PART II -- JET IN A CROSS FLOW EXPERIMENT CHAPTER 1 INTRODUCTION ........................................... 22 2 EXPERIMENTAL EQUIPMENT AND PROCEDURE ................... 25 2.1 Experimental Equipment ............................ 25 2.1.1 Facility for the Cross Flow ................ 25 2.1.2 Jet Delivery System and Exit Conditions .... 26 2.1.3 Jet Heating Considerations ................. 27 2.2 Experimental Procedure ............................ 27 2.2.1 Velocity and Jet Temperature Determination ............................ 27 2.2.3 The Temperature Measurement System ......... 29 3 DISCUSSION OF EXPERIMENTAL RESULTS ..................... 31 3.1 Introduction to Discussion of Results ............. 31 3.2 Thermal Energy Considerations ..................... 33 3.3 Jet Temperature Considerations .................... 35 3.4 Comparison of Present Results with Kamotani and Greber ............................. 41 3.5 Comparison of Undisturbed with Disturbed Cross Flow Conditions ........................... 41 4 CONCLUSIONS ............................................ 46 FIGURES .......................................................... 48 REFERENCES ....................................................... 117 iv LIST OF TABLES TABLE Page II.1 Influence of X on measured temperature values ......... 32 II.2 Cross stream disturbance effect on centroid of temperature field ................................ 43 FIGURE a: \10\ 01 $hUJhJ-4 12 13 14 15 16 17 18 20 21 22 23 24 LIST OF FIGURES The Temperature Sensing Probe ........................ Thermocouple Array Assembly .......................... l of 18 Thermocouple Modular Elements ................ Schematic Representation of the Present Flow Facility ........................................... Schematic Representation of One of Four E1ectronic Processing Boards ....................... Detail of a Sample and Hold Circuit .................. Experimental Configuration for the Time Constant Evaluation ......................................... Schematic Representation of a Thermocouple's Response to the Impulsive Removal of a Thermal Input ...................................... Plot of Time Constant (A) as a Function of Velocity (u) ....................................... Reynolds Number Dependence of A ...................... Schematic Representation of Jet Trajectory, Showing Lab Coordinates (x, y, z) and Jet Coordinates (e, n, c) .............................. Schematic Representation of the FSFL Wind Tunnel .... Normalized Velocity Distribution of Shear Layer at Jet Exit Location ............................... Turbulence Intensity Normalized on Free Stream Velocity ........................................... Turbulence Intensity Normalized on Local Mean Velocity ........................................... Energy Spectrum Results at Jet Exit Location for Disturbed Cross Flow Case .......................... Energy Spectrum Results at Jet Exit Location for Undisturbed Cross Flow Case ........................ Schematic of Jet Supply and Exit Conditions .......... Placement of Thermocoup1e Array in Flow Facility ..... Cross Stream Boundary Layer for Undisturbed Cross Flaw Case .......................................... Cross Stream Boundary Layer for Disturbed Cross Flow Case .......................................... Undisturbed Cross Flow (u.c.f.) Mean Temperature Isotherms: J = 16, Tj t - T0° = 22.2°C ............. u.c.f. Mean Temperature Isotherms: J = 16, Tjet ' Tm : 41.7OC ooooooooooooooooooooooooooooooooo u.c.f. Mean Temperature Isotherms: J = 16, Tjet " Tm 3 61.1°C ................................. vi Page 48 49 SO 51 52 53 54 55 57 60 61 62 63 64 65 66 67 68 69 7O 71 LIST OF FIGURES (Continued) FIGURE Page 25 u.c.f. Mean Temperature Isotherms: J = 64, Tj t - Ta = 22.6°C .................................. 72 26 f. Mean Temperature Isotherms: J = 64, Tjet - To = 41.7°C .................................. 73 27 u.c. f. Mean Temperature Isotherms: J = 64, Tet-Tm=61.1°c .................................. 74 28 Dis urbed Cross Flow (d. c. f. ) Mean Temperature Isotherms: J = 15,Tjet - Ta = 22. 2° C ............. 75 29 d.c.f. Mean Temperature Isotherms: J = 16, Tjet - Tm = 41.7°C .................................. 76 30 d.c.f. Mean Temperature Isotherms: J = 16, Tjet - Ta = 61.1°C .................................. 77 31 d. c. f. Mean Temperature Isotherms: J = 64, T Jet - Ta: 22. 2°C .................................. 78 32 d. c. Jf. Mean Temperature Isotherms: J = 64, Tjet - Ta = 41. 7°C ..................... . ............. 79 33 d.c.f. Mean Temperature Isotherms: J = 64, Tjet - To = 61.1°C .................................. 80 34a Overheat Influence on 5 Component Centroid (calculated using isotherm contours) ................ 81 34b Overheat Influence on 5 Component Centroid (calculated using discrete temperatures) ............ 82 35 Temperature Histogram for u. c. f.: J= 16, Thermocoup1e at s/d = 4.79, t/d = 4.73 .............. 83 36 Temperature Histogram for u.c.f.: J = 16, Thermocoup1e at s/d = 2.64, t/d = 4.63 .............. 84 37 Temperature Histogram for u.c.f.: J = 64, Thermocoup1e at s/d = 4.79, t/d = 4.73 .............. 85 38 Temperature Histogram for u.c.f.: J = 64, Thermocoup1e at s/d= .5, t/d = 4.55 ................ 86 39 Temperature Histogram fo or d. c. f.: J= 16, Thermocoup1e at s/d= 5. 64, t/d = 3. 64 .............. 87 40 Temperature Histogram for d. c. f.: J = 16, Thermocouple at s/d= 2.78, t/d= 3.00 .............. 88 41 Temperature Histogram for d.c f J = 64, Thermocoup1e at s/d= 3.87, t/d= 3.31 .............. 89 42 Temperature Histogram for d. c. f.: J = 64, ' Thermocouple at s/d= 1. 75, t/d= 5.33 .............. 90 43a Location of Temperature Centerline (R=4) from Kamotani and Greber (1971) ..................... 91 43b Location of Temperature Centerline (R=8) from Kamotani and Greber (1971) ..................... 92 44 Undisturbed Cross Flow (u.c.f.) Contours of a Temperature Standard Deviation: J = 16, Tjet - Ta = 22.2°C ................ . ................. 93 45 u.c.f. Contours of Constant Temperature Standard Deviation: J= 16, T Jet - Ta: 41. 7°C .............. 94 46 u. c. f. Contours of Constant Temperature Standard Deviation: J = 16, Tjet - Tm: 6L 1°C .............. 95 vii LIST OF FIGURES (Continued) FIGURE 47 48 49 so 51 52 53 54 55 56 57 58 59 6O 61 62 63 64 65 66 67 Page u.c.f. Contours of Constant Temperature Standard Deviation: J = 64, T'et - To = 22.2°C .............. 96 u.c.f. Contours of Cons ant Temperature Standard Deviation: J = 64, T Jet - Ta = 41. 7°C .............. 97 u. c. f. Contours of Constant Temperature Standard Deviation: J = 64, T Jet - To = 61.1°C .............. 98 Disturbed Cross Flow (d. c. f. ) Contours of Constant Temperature Standard Deviation: J=16, Tjet - Ta = 22.2°C .................................. 99 d.c.f. Contours of Constant Temperature Standard Deviation: J = 16, T et - T, = 41.7°C .............. 100 d.c.f. Contours of Consgant Temperature Standard Deviation: J = 16, Tjet - Ta = 61.1°C .............. 101 d.c.f. ContourJ of Constant Temperature Standard Deviation: =64, T = 22. 2°C .............. 102 d. c. f. ContourJ of Constgni Temperature Standard Deviation: J= 64, Tjet - T. = 41. 7°C .............. 103 d.c.f. ContourJ of Constant Temperature Standard Deviation: 64, T et - Te 8 61.1°C .............. 104 Variation of s JComponen’l of Centroid with Time J = 16, T et - Ta = 6L 1°C .......................... 105 Variation 0% t Component of Centroid with Time J = 16, T et - Ta = 61.1°C .......................... 106 Variation 0% 5 Component of Centroid with Time J = 64, T et — Ta = 61.1°C .......................... 107 Variation 0% t Component of Centroid with Time J a 64, Tjet - Tm = 61.1°C .......................... 108 Undisturbed Cross Flow (u. c. f. ) Instantaneous Temperature Isotherms, J = 16, Tjet - T =61.1°C, Time = .2 sec ....................................... 109 u.c.f. Instantaneous Temperature Isotherms J = 16, T Jet - Ta = 61.1°C, Time= .65 sec .......... llO d.c.f. Instantaneous Temperature Isotherms J = 16, Tje t - T = 61.1°C, Time= .2 sec ........... 111 d.c.f. Instantaneous Temperature Isotherms J = 16, Tjet - To = 61.1°C, Time = .65 sec .......... 112 u.c.f. Instantaneous Temperature Isotherms J = 64, T Jet - Ta = 6L 1°C, Time= .3 sec ........... 113 u.c.f. Instantaneous Temperature Isotherms J= 64, Tje t - Ta = 61.1°C, Time= .58 sec .......... 114 Disturbed Cross Flow (d. c. f. ) Instantaneous Temperature Isotherms, J= 64, Tjet - T 61.1°C, Time= .3 sec ............................... 115 d.c.f. Instantaneous Temperature Isotherms J = 64, Tjet - Tm = 61.1°C, Time = .58 sec .......... 116 viii if I“ an “1" 1"!" LIST OF SMfiS area of isotherm I surface area of thermocouple bead cross sectional area of thermocouple wire discharge coefficient specific heat at constant pressure specific heat (see equation 1.1) diameter of jet orifice (10mm) disturbed cross flow dimmeter of thermocouple wire (from Petit et al. (1982)) input voltage output voltage offset voltage voltage associated with temperature at thermocouple voltage associated with temperature at reference junction energy at frequenoy f acceleration due to gravity gain convective heat transfer coefficient momentum flux ratio (pjvglp.D:) conductivity thermal conductivity of gas (Petit et al. (1982)) thermal conductivity of wire (Petit at al. (1982)) distance between thermocouple prongs (see Figure 20) (see Figure 20) ix Nu Ri mass flux Nusselt number pressure heat flux heat transfer rate velocity ratio Vj/uo Reynolds number Richardson number (Ri 'dS(T3‘TL)IUg'Tr) vertical coordinate of thermocouple array s component centroid of isotherm I s coordinate of thermocouple i horizontal coordinate of thermocouple array t component centroid of isotherm I t coordinate of thermocouple i corrected temperature value initial temperature jet temperature (Tjet) temperature at time k maximum temperature in c-n plane of jet measured temperature laboratory ambient temperature 1000‘ (Tc-T.) I (Ti-T.) internal energy velocity undisturbed cross flow cross stream average velocity free stream velocity at step in FSFL wind tunnel average jet velocity N N N ‘4 H D work rate streamwise coordinate (see Figure 4) transverse coordinate (see Figure 4) streamwise lab coordinate (see Figure 11) transverse lab coordinate (see Figure 11) lab coordinate (see Figure 11) density time constant kinematic viscosity jet coordinate (parallel to I) (see Figure 11) jet coordinate (tangent to jet trajectory) (see Figure 11) jet coordinate (perpendicular to t and u) (see Figure 11) non-dimensional temperature (Kamotani and Greber (1911)) mean value FORIARD The following manuscript is presented in two parts. Part I is the discussion of a temperature measurement system which was used in the experimental program discussed in Part II. The two discussions are presented separately since the temperature measurement system is not solely intended for the present experimental program: i.e.. it is a system that will be quite useful in.many other experimental pro- grams. Those details which are specific to the present experimental program will be found in Part II.- PART I TEMPERATURE EASUREWT SYSTEM CHAPTER 1 INTRODUCTION 1.1 Tbmperature Moasurements Accurate temperature measurements have become increasingly impor- tant in many areas of combustion, heat transfer. and fluid mechanics research. The relevance of such measurements to combustion and heat transfer research is quite obvious whereas, in fluid mechanics research, one often desires to obtain information regarding a fluid flow problem by using heat as a passive contaminant to thermally mark the region of interest in the flow. Several methods for measuring temperature exist. Bimetallic and liquid-in-glass thermometers utilise the familiar process of thermal expansion. Optical techniques include Raman Scattering and Rayleigh Scattering: both. of which require sophisticated equipment (Peterson 1979). Another method uses thermistors which are in the class of sen- sors whose resistance changes with temperature. A thermoelectric sensor. (thermocouple) is composed of two dissimilar materials which form a closed ciruit. If the two junctions sense different tempera- tures. an electromotive force (emf) will be established. This effect. which was discovered in 1821 by T.J. Seebeck. is the basis for ther- moelectric temperature measurement. In 1834. J.C.A. Peltier discovered that when current flows across the junction of two metals heat is either released or absorbed at that junction. This can. therefore. cause a junction to be at a temperature different from.that of its surroundings. In 1851 I. Thomson found that an additional emf is produced when there is a temperature gradient along a homogeneous wire. The total emf generated in a thermocouple is due to both the Peltier emf which is proportional to the difference in junction.tem- peratures and the Thomson.emf which is proportional to the difference between the squares of the junction temperatures. These proportional- ity constants depend on.the two dissimilar materials used. and can in principal be found from a calibration of the thermocouple with a known temperature. In actual practice however. the total voltage is of interest and therefore the emf's generated by the Peltier and Thomson effects are not determined separately. It should be noted that irre- versible Joule heating effects (1’!) are present and will raise the temperature of the circuit above the local surroundings. however if the current in the circuit is that due to the thermoelectric effect only. Joule heating can be neglected (Doebelin 1966). Errors involved in using thermocouples may result from radiation. conduction. or time constant effects. These effects cause the meas- ured temperature of the probe to be different from that of the surrounding medium. The radiation error is a result of the difference in temperature caused by radiation from.the wire or prongs to the sur- rounding walls. Conduction of heat. between the thermocouple wires and the prongs. will introduce error into the temperature measurement This error being known as the conduction correction. The response time of the thermocouple can also result in temperature measurement errors and. of the above three effects. has received the most atten- tion in the available literature. Radiation from the probe is proportional to the fourth power of the temperature. and thus will have a correction which increases shar- ply with temperature. As pointed out by Bradley and Matthews (1968). the magnitude of the correction decreases as wire diameter decreases. Moffat (1958) performed a series of tests to determine the effect that various levels of radiation loss had on the response time of a 16 gage round-wire loop junction thermocouple. For gas temperatures up to 1600°F it was found that radiation had a small effect on the response of the probe. The distance (1) from.the temperature sensing junction to the support prongs is a critical factor if conduction effects are to be negligible. Petit et al.(1982) use the ratio 1110 - (21/4,)((k'/k')Nu)1/2 to determine the relative importance of conduc- tion effects: specifically. if 1110 > 10 then conduction effects are assumed to be negligible. Bradley and Metthews (1968) use the ratio l/d' to characterise conduction effects. The authors do not give a value for this ratio but cite some specific examples. The response time of a thermocouple. also known as its time con- stant (A). is a function of both the heat transfer coefficient (h) . and the surface area of the thermocouple bead (A‘). The heat transfer coefficient is in turn a function of velocity and temperature. The most widely used methods for the determination of the time constant are the internal heating techniques. Such techniques as proposed by Shepard and Iarshawsky (1952) and Kunugi and Jinno (1959) have been employed by Petit et al. (1982). Lockwood and Moneib (1979) and Bal- lantyne and Moss (1977). These techniques determine the time constant based on the transient behavior of the thermocouple when the wire is run with a periodic current or after the removal of a DC current. Petit et al.(1982) made comparisons between the internal heating technique of Shepard and Iarshawsky (1952) and an external heating technique described in Petit et al. (1979). A.3.5um dia. Pt-Rh 10% wire is subjected to a sinusoidal or square current and is located just upstream. in a known flow field, from. the given 'thermocouple. Their results showed significant differences in the measured time con- stants between the internal and external heating techniques. which the authors attributed to both Joule and Peltier effects. Compensation for the time response of the thermocouple probe can be performed using either analog or digital techniques. The basis for which electrical circuits compensate in part for the time response of the probe was formulated by Shepard and Iarshawsky (1952). The electrical circuit requires a prescribed time constant for use in a differentiating circuit. Ballantyne and Moss (1977) studied the sig- nal distortion resulting from the use of an average time constant value in the electrical circuit. The authors found that where there were large local variations in the time constant values. significant distortion of the compensated temperature statistics resulted. In regions of moderate heat transfer fluctuations however. the analog technique would seem to work well if one could obtain a correct aver- age value for the time constant. Lockwood and Moneib (1979). in measuring temperature fluctuations in a heated round free jet. obtained good results using this method. Digital compensation requires fast sampling rates and a moderate amount of processing time. The main advantage of using digital compensation is that an average value for the time constant need not be used. instead variations of A. if known. could be implemented into the processing software. Of the two junctions in a thermoelectric circuit. one is commonly referred to as a reference junction. The reference junction must be kept at a known temperature if one is to determine the temperature at the desired location. An ice bath is very common and its temperature is reproducible to about .001'c (Doebelin 1966). Another method is to allow the reference junction to sense ambient temperature: the net emf thus generated would then correspond to a temperature difference with respect to the ambient. When using a single thermocouple. one can obtain statistical quantities of temperature at discrete locations in space or a tempera- ture time series at a given point in space. An array of several thermocouples will provide for the above mentioned quantities and. if all thermocouples are sampled simultaneously. will also provide for instantaneous isothermal maps of the given flow field. The present temperature measurement system is a multi-point. fast response. simul- taneously sampled array of 66 thermocouples. which can be used to both evaluate the temporal evolution of the instantaneous temperature field and obtain temperature statistics at discrete values in the flow field. 1.2 The role of the Time Constant in a Tbmperature Measurement System 1.2.1 The First Order Response Equation The time constant (A) is the parameter in the first order response equation which describes the relationship between the true temperature value at the thermocouple location (To) as a function of the measured temperature value (T;). This equation can be derived from a thermal energy balance for the thermocouple bead: namely -pov- a'r_/a: - n.(r.-rc) + k‘A‘ aT/ax]x:-k,Ax dT/dx] 1 (eq 1.1) x Ihere P and A. are. respectively. the volume and surface area of the bead. k, and k, are the thermal conductivities of the wires connected to the bead at x1 and x,. A3 is the cross sectional area of the wires and h is the conwective heat transfer coefficient. If the wire is sufficiently long with respect to the diameter of the wire (Petit et al 1982 and Bradley and Mnthews 1968). than conduc- tion is negligible. Equation 1.1 then reduces to -pc¥(dTi/dt) - hA'(Ti-T;) (eq. 1.2) which can be written in the form 1(dTi/dt) + Tgf T} (eq. 1.3) where A-chYhA3. For a given wire material. i.e. for given values of p and c, it is seen that A depends upon the ratio of the bead's volume to surface area (FVA‘), and upon the reciprocal of the convection coefficient. nrl. From convective heat transfer considerations. h is a function of the velocity and the thermal properties of the fluid. The latter may be expressed as a function of temperature for the given test section pressure. which is essentially constant for the small overheat values of the present study. Considering the former. h may be approximated as being proportional to nil: for a laminar boundary layer: hence. the time constant 1 would be expected to be proportional to u‘ln. 1.2.2 The Role of 1 in the Data Acquisition Process The true temperature (To) may be determined from the measured temperature (Ti) if the latter measurement is supplemented with a simultaneous evaluation of A and dT;/dt. Specifically. consider that ! high-rate til. 80:10! 0f Th(t) values is available and that the time derivative (dTildt) is evaluated from these data. T; can then be cal- culated from. (1.3). The data samples. so provided, could be used to form a sample population of the temperature values that exist in the flow field. The statistical values of interest can then be determined from this sample population. The general data acquisition procedure. that is considered herein. is for three samples to be acquired in rapid sequence: T.)k-1, Ti)k, T;)k+1, which allows dTi/dt to be defined from a central difference scheme and the corresponding value of T;)k to be computed. The T°)k values are retained as the primitive data for further evalua- tion. It is noteworthy that the mean value. of the T; values so defined. would be independent from- 1 under a relatively non-restrictive assumption. Specifically. consider that the velocity magnitude (u) is simultaneously measured with the T; value. The cor- rected temperature (To) is then given by 1.3 where 1-1(u) is used for the time constant. Using an over-bar to denote the mean of the sample population and a prime to denote the deviation (i.e.. difference between a given realization and its mean value). the equation for the mean value of the corrected temperature of the semple population is: To - ‘11-. + 1'(a'r./a:)'+ Marl/at) (eq. 1.4) For a stochastic process. (dT‘Idt)lo and‘TgiT; if there is no correla- tion between the l and (dTgldt) deviations. The variance of the sample population is. however. clearly affected by the time constant value. This can be shown as follows. Subtracting 1.4 from.I.3 yields T3): - To)? Tc - In)? T. + hurl/ank- fldTn/dt) (eq 1.5) It will be assumed that the correlation: 1(dTi/dt) is zero for this analysis. Given this assumption. the variance of the sample population is To” - I: + 2T;)klk(dTn/dtk)+1;(dTlldt)’ («1 1.6) The second term. r.h.s. of (1.6) is not expected to have a signifi- cant value: the third term is. however. always positive and hence the sample variance for the corrected temperature will exceed that of the measured temperature if A ) 0. The following chapters of Part I identify the physical tempera- ture measurement system and the data acquisition scheme. Chapter 2 provides results for. and a description of the method used to deter- mine. the time constant values for all thermocouples. A.brief discussion of the velocity dependence of the time response is also included. The measured temperature value is digitally corrected for the time constant of the thermocouple: this correction scheme is explained in Chapter 3. CHAPTER 2 TEMPERATURE MEASUREMENT SYSTEM 2.1 THE PHYSICAL SYSTEM 2.1.1 Thermocouples and Support Array A schematic representation of the present thermocouple probe is shown in Figure 1a. The diameter of the probe body is 1.58mm and the overall length of the probe is 153mm. The micro-fine wire thermocou- ples (7.62 um die.) ere supported by .235mm dis. prongs separated by 1.59mm (see Figure 1b). The thermocouples used in this study were type B which is made up of a positive conductor of nickel-chromium (chromel) and a negative conductor of copper-nickel (constantan). the sensitivity of the type B thermocouple is 42.5 n volts/'F (Doebelin 1966). The 72 thermocouples are supported in the array shown in Figures 2 and 3. The frame is 146mm square. There are 18 modular elements with four thermocouples supported in each modular element as shown in Figure 3. The 18 modular elements are connected by "forks” with two 10 11 of the corner elements secured to the frame. The area blockage at the measurement point is 1.5%. and at a downstream distance of 102mm. the area blockage is 42*. Figure 2.14 in Schlicting (1968) shows that the affect on the velocity field at the measurement point would be negli- gible even if the forks and modular elements created a 100% blockage. 2.1.2 Reference Junctions and Assembly The 72 reference junctions for the thermocouples are located in the boundary layer bleed passage of the Free Shear Flow Laboratory (FSFL) flow facility (Figure 4). The reference junctions sense T; and they have a relatively large time constant since the wire diameter is large (.8mm). The thermocouples and reference junctions are connected via 72 twisted pair shielded cables. The cables are 35 feet in length. Extra lengths of chromel and constantan were welded on to the leads of the thermocouple probes. as shown in Figure 2 . to ensure that no second thermocouple effect would be present in the measure- ments: i.e.. if the chromel/copper or constantan/copper junctions were subjected to a temperature above the ambient value. T;, gn gdditiongl emf would be induced. 2.1.3 Electronic Processing Units A schematic reprsentation of one of the four electronic process- ing boards is shown in Figure 5. Each processing board has 20 sample and hold units (detail shown in Figure 6). one multiplexer with 32 12 channels and 20 amplifiers. The resistors used to amplify the thermo- couple signal were metal film with a 1% tolerance: their values were selected to give a nominal gain of 500. The reference junctions were mounted on the back of the processing boards thereby reducing 60 Ex noise pickup by the leads connecting the reference junctions and pro- cessing boards. Placement of the processing boards in the FSFL flow facility can be seen in Figure 4. The processing boards were designed and built by Sigmon.Electronr ics. 2.1.4 Data Acquisition System The input to the processing boards is a voltage corresponding to the temperature difference between the thermocouple probe and the associated reference junction. T;fT;. The signal is amplified. sam- pled and held. multiplexed and presented by the processing boards to a four channel TSI 10751 analog to digital converter. The multiplexers on the processing boards are controlled by a DEC DRVll interface board which allows the user to pick the starting channel and the number of channels on each board to be read. The 12 bit analog to digital con- verter (AID) has a 0-+5 volt range: therefore. the resolution of the AID is 1.2 millivolts. By connecting all channels of the AID to a common signal. it was found that the accuracy of the AID was 12.4 mil- livolts. The four channels have matched SOkBs input filters and are sampled simultaneously. The AID is controlled by a direct memory 13 access interface board (DRVllB) which is installed in a Charles River Data Systems PDP1123 microcomputer. 2.2 System Performance Evaluation 2.2.1 Evaluation of the processing boards Several pertinent characteristics of the processing boards were evaluated prior to the connection of the thermocouples. The charac- teristics checked were i) the gain for each channel. ii) simultaneous sampling of all channels and iii) the sampling rate threshold of the multiplexers. Since all 80 pairs of resistors are not identical. the amplification of the thermocouple voltages will not be identical for all channels. The evaluation of the gain (6) for each channel was performed as follows. Known d.c. voltages (E1) were applied to the inputs (points 2.3 of Figure 6) for all channels and the previously discussed data acquisition system was used to sample the output (Eo) of each channel. For the transfer function: where Buff - offset voltage. the gain (0) was obtained by a linear regression fit to Equation 1.7 for the data pairs: (E1,Eb). The offset value, determined by a separate procedure as described in chapter 3,. was performed by giving the channels a sequence of DC vol- tages and using the previously discussed data acquisition system to sample all channels. A linear relationdhip exists between the thermo- 14 couple reading and the input DC voltage: namely. the thermocouple reading is equal to the channel offset plus the DC voltage multiplied by the channel gain. By using a linear regression routine. the value for the gain for every channel was found. To determine if all channels were sampled simultaneously. a com- mon signal was input to each of the channels and the channel outputs were compared. Specifically. a nominally 200 Fr sine wave from a sig- nal generator was applied to the channels and a visual comparison of the outputs. from.various channels. showed that the sample and hold units were sampled simultaneously. It was observed that the multiplexers would sometimes get "lost" at high sampling rates: i.e.. it seemed that the multiplexers on the processing boards did not start on the user specified starting chan- nel. This hardware problem was compensated for by the data acquisition software. as described in the following chapter. 2.2.2 Thermocouple Time Constant Evaluation The experimental configuration. to determine the time constant values. consisted of placing a Sum diameter tungsten hot-wire probe directly upstream of the subject thermocouple. The hot-wire probe was positioned easily and precisely by means of a traversing mechaniem. This is shown schematically in Figure 7. 15 The data acquisition system discussed above was used to sample the subject thermocouple and the hot-wire output. During the time period that the AID is sampling. the hot-wire anemometer is switched from operate to stand-by. thereby causing an impulsive decrease of the heating current to the hot-wire. The hot-wire has a sufficiently fast response that the thermocouple essentially senses a step change in temperature. Approximately five runs at a constant flow speed (= 7mps) were performed for each thermocouple. A schematic representation of a thermocouple's response (with 1 = Smsec) to the hot-wire can be seen in Figure 8. The initial flat por- tion of the thermocouples' response is attributed to the separation distance between the hot-wire and thermocouple. and the convection velocity. The asymptotic value of the thermocouples' response would be the laboratory temperature (1;) for this case. The solution to equation 3 can be written as follows: ln[(T.-T.)I(Ti-T.)] - 4'1: (eq. 1.8) The terms in equation 4 were evaluated from the time constant data as follows. T3 was the initial value of the thermocouple just before the hot-wire anemometer was switched from operate to standby. T;’ was the measured value at the sequence of semple times t. and T. was the steady state value reached by the thermocouple after the passage of the trailing edge of the hot-wires' thermal wake. A linear regression routine was then used to determine 1 (-I -slope'1) when the data were 16 fit to equaton I.8. An average value for 1 was determined based on nominally five data runs per thermocouple. Consistent values of A .per thermocouple. were found when the hot-wire probe was placed directly upstream of the thermocouple probe. This proper placement resulted in a relatively large Tb-I;(=13 'C) and a low standard deviation of the data when fit to equation 4. Oscilloscope traces of the thermocouples response were also observed to be very smooth. The procedure described above proved to be a good check on the integrity of the thermocouples. This check revealed 66 good thermo- couples. for which the variability of 1 at 7mps was found to be 2.0 msec to 4.7 msec. A nominal uncertainity of 1.5 msec is associated with the A value for a given thermocouple. 2.2.3 Reynolds Number Dependence of Time constants In addition to the data runs at 7mps. time constant values for four thermocouples were also found for the range of velocities: 2mps to lamps. The 1(Re) results can be found in Figures 9 and 10. Figure 9 is a representation of A vs. u and Figure 10 is a plot of A vs 11'“2 where u is proportional to Re for a given diameter and the noni- nally constant kinematic viscosity values (6% difference betweenv‘nu and “mink 17 The 1(u) results appear to approach an asymptotic value of 1 for large n. The experimental results of Figure 10 support the observa- tions made in 2.2.2: specifically that A is proportional to uFl/z. CHAPTER.3 DATA scours ITION PROCEWRE 3.1 Offset Determination The voltage. that is sempled by the AID represents the net emf: [Et c.1y"’-3ref]' plus the offset associated with the electronic com- ponents for that channel. The offset for each channel must be subtracted from the voltages sampled by the AID before any other pro- cessing steps can be performed: therefore. determination of the 66 offsets is an important part of the data acquisition procedure. By placing the thermocouple array in the ambient temperature flow field of the FSFL flow facility. the temperature sensed by the thermo- couples (Ti) and reference junctions (T;) will be approximately equal. Discrepancies between the two temperatures will exist insofar as there are thermal variations within the room: these thermal variations will hereafter be referred to as "thermal noise". The voltages sampled by the AID will then simply be the offset values for the 66 channels. note that [Et c.(y.z.)-- Er.f]=0 for offset determination. It is important to note that a stabilization period is required for the offsets. Apparently this stabilization period is needed to bring the 18 19 processing boards to a steady state temperature value once the boun- dary layer bleed suction is activated. 3.2 Smmpling Rate Considerations Referring back to equation 3 one can see that the quantity dTi/dt is essential in determining the corrected temperature value (To). Evaluation of dTi/dt is performed using a central difference techni- que. therefore a high sampling rate is required. 'hen choosing a sampling rate. the rate threshold of the multiplexers must be considered (refer to Part 1 Chapter 2). It was found that at the highest sampling rate possible for the AID(3.125 kHz for 80 channels) the multiplexers would get "lost": i.e. they would not start on the user prescribed starting channel and hence. the order in which the data was stored in memory would not be correct. At the next highest sampling rate (1.56 kEx) the multiplexers would start on the prescribed starting channel only a portion of the time. Therefore a check is performed in software to determine if the order that the data is stored in memory is correct. If correct. then the data run will be further processed (as will be explained in the following sec- tion) and if incorrect then the values are deleted and another data run is taken. The "lost” condition of the multiplexers improves as the sampling rate decreases and the user can choose one of six sam- pling rates between 20 Ba and 1.56 kHz. 3.3 Time Constant Correction and Data Storage 20 The modes of data storage are available to the user of the present temperature measurement system. A. time series of data is required for studying the instantaneous behavior (e.g. instantaneous isothermal maps) of the flow field in question. and a histogram. comr posed of statistically independent samples. is used to determine statistical quantities at the discrete locations in space occupied by the thermocouples. The data which are sampled and stored as a time series. are taken at a high sampling rate (1.56kBs) so that the measured temperature value can be corrected as in equation 1.3. This high sampling rate (.64msec) is appropriate when considering the time constants of the thermocouples (24.5msec at 2mps) The value for the time constant need in equation I.3 is based on a user defined velocity or it can be based on a user defined function of velocity with temperature. As explained in the previous chapter. A values were found for all thermocouples at a convection velocity of 7mps. Using these results. and if one assumes a common slope of 2 5(msec)l(lps)1/2 (Figure 10) for all ther- mocouples. the value of 1 for any velocity in the range 2 S u S 10mps can be found for each thermocouple. As noted in the Introduction. the first order correction of the measured temperature values needs to be performed in order to obtain accurate values for statistical quantities of the data. The corrected temperature value T’ is used to build a histogram for each thermocou- ple. The pregram is written such that the user defines the minimum. the maximum and the number of intervals for the Te distribution. For 21 each data run a total of seven points per thermocouple are sorted into the correct interval of the appropriate histogram. Although there are approximately 96 kBytes of memory used for the measured temperature values per data run. only seven statistically independent samples are kept. This seemingly excess amount of raw data is required because of the high sampling rate (.64 msec) necessary for the central difference scheme. The user specifies the number of points desired to develop the histograms and the appropriate number of data runs will be taken under software control. PART II JET IN A CROSS FLW EXPERIMENT CHAPTER 1 INTRODUCTION A jet exiting into a cross flow is an example of a complex three dimensional flow field. The interaction of the jet fluid with cross stream fluid results in two large counter rotating structures which are one of the dominant features of this flow field (Figure 12). These structures are responsible for the distribution of entrained cross stream fluid within the jet. 1 The interaction of the jet with cross stream fluid results in high pressures on the upstream surface of the jet column. The down- stream face of the jet is characterized by low pressure values and strong entrainment of the ambient fluid. A qualitative discussion of the flow field. including surface topology effects. is presented by Foss(1980). The deflection of the jet makes it useful to define a system of jet coordinates (§.n.{). § follows the jet trajectory. n is perpen- dicular to g and parallel to Y. and f is perpendicular to both E and n. Figure 12 shows this system of coordinates and the lab coordinates 22 23 X.Y.and Z. The important parameter in this problem is the momentmn flux ratio (J-PjVj’Ip.Uo’). lhen the cross stream and jet fluid have the same density. the velocity ratio (R-FJIUO) is often used to character- ize the problem. Some of the physical applications of a jet exiting into a cross flow are i) the discharge from a chimney stack. ii) waste discharge in rivers. and iii) the cooling of combustion gases. The latter is the motivating application for the present study. The study of a jet exiting into a cross flow has been the subject of numerous investigations. [offer and Baines (1962) present velocity measurements at a large number of points in the flow field. for the velocity ratio values VjIUb of 2.4.6.8. and 10. Isobars for the velo- city ratio values of 2.2 to 10 can be found in Fearn and Weston (1975). Ramsey and Goldstein (1971) used a large diameter thermocour ple (.13cm) and obtained temperature profiles of a heated jet exiting into a cross stream at low ijjIp.U. values (.1 to 2) Remotani and Greber (1971) provide a substantial foundation for the present work. Their study was also motivated by the combustor cooling problem and they provide velocity and mean temperature infor- mation in planes that are perpendicular to the jet axis. Extensive reference to the detailed considerations in their report are made herein. Andreopoulos (1983) in a recent publication. provides infor- 24 mation regarding the mean and fluctuating thermal field for Ji4.0. These previous studies have been performed with a relatively low disturbance cross flow. The flow field in a combustor is. however disturbed and it is this cross stream disturbance effect on the dynam- ics of a jet in a cross flow which is the primary focus of the present study. The present study uses thermal energy to mark the jet fluid. The temperature measurement system described in Part I is used to investi- gate the temperature field downstream of the jet exit. The cross stream disturbance effect is investigated by comparing the results obtained for a jet exiting into a disturbed cross flow with those for a jet exiting into an undisturbed cross flow for a given.momentmm flux ratio. The momentum flux ratios (selected to be the same as those of Kamotani and Greber (1971)) and three jet overheat values are used in the present experiment. CHAPTER.2 EXPERIMENTAL EQUIPMENT AND PROCEDURE 2.1 Experimental Equipment 2.1.1 Facility for the Cross Flow A schematic representation of the'FSFL wind tunnel can be seen in Figure 12. This flow facility provides a large.planar shear layer for use in the disturbed cross flow case ‘of the present study. Specifically the jet exhausts into the free shear layer at a location Of Eyuref - .25 at the end of the three .meter test section. The 3IUr°t and turbulence intensity profiles based on both the free stream and local velocities can be seen in Figures 13.14 and 15. The iIUin = .25 (y380cm) location in the free shear layer was chosen based on the relatively small velocity gradient and the relatively high turbu- lence intensity values existing at that point (Figures 13 and 15). It is pertinent to note that. based on the energy spectrum results at y-80cm (Figure 16). the high turbulence intensity values are caused by very low frequency fluctuations. For the undisturbed cross flow case. a "false wall" added to the FSFL flow facility (shown as a dotted line 25 26 in Figure 4) resulted in a quiescent flow field at the jet exit loca- tion. The turbulent intensity at this location.was 2.6% and the energy spectrum results can be seen in Figure 17. A boundary layer plate. the leading edge of which has a parabolic profile. was positioned 203.2mm below the top of the Tbst Section Extension (T.S.E.) (Figure 18). An adjustable diffuser flap.for the parallel alignment of the leading edge stream line. was attached to the downstream edge of the boundary layer plate. (Figure 19). 2.1.2 Jet Delivery System and Exit Conditions A Spencer blower is used to provide the necessary flow rate for the jet. The exhaust from the blower is ducted into a 136cm by 101cm plenum. This is shown schematically in Figure 18. Flow enters the jet delivery tube through a 6.35mm dia. sharp edge orifice. At a downstream distance of 10mm from.the entrance orifice. a static pres- sure tap is located in the wall of a 25mm I.D. copper pipe. The static pressure from this tap. minus that of the plenum. was used to measure the flow rate. After the right angle bend. a 50mm I.D. galvanized pipe is used to deliver the flow to the jet exit. The jet exits through a 10mm dia. sharp edge orifice (Figure 18). Care was taken to ensure that the exit plane of the jet was flush with the lower surface of the boundary layer plate. The center of the exit orifice was located 260mm downstream from the leading edge 27 of the boundary layer plate. as shown in Figure 19. Figures 20 and 21 are plots of the cross stream boundary layers. just upstream from the jet exit orifice. for the undisturbed and disturbed cross flow condi- tions respectively. Also shown in figures 19 and 20. are the reference curves for a turbulent boundary layer in a zero pressure gradient flow. via..'HIU; - (ylb)1’7. and the Blasius solution for a laminar boundary layer. 2.1.3 Jet Beating Considerations A Superior Electric powerstat was used to supply a controlled voltage level. to a flexible resistance strip heater. The strip heater was wrapped around the copper delivery pipe in the plenum above the T.S.E.. Fiberglass insulation. 220mm in dia.. was placed around both the strip heater/copper pipe and the galvanised delivery pipe to protect from heat loss to the surrounding plenum and/or cross flow (Figure 18). A reference thermocouple (wire die of .254mm) is located 10mm upstream fromithe jet exit and was used to monitor the jet tem- perature. The leads of the thermocouple extend through the sides of the pipe and are connected via one of the shielded cables. to a chan- nel on the processing boards. 2.2 Experimental Procedure 2.2.1 Velocity and Jet Temperature Determination 28 The cross stream velocity. (U0), '.3 dat.rnin°d' for the undisturbed cross flow case. by using a pitot-static pressure probe placed in the free stream of the FSFL flow facility. For the dis- turbed 02088 flow study, the U0 value was 1/4 of the velocity calculated from the pressure probe reading. The mass flow rate through the delivery tube was determined using the static pressure (downstream from the entrance orifice) and the plenum pressure. The discharge coefficient. (Cd). which is required to correct for the non-uniform velocity profile at the orifice. was known a-priori as a function of pressure drOp across the orifice. A thermometer located in the plenum. provided for the density value used in the flow rate calculation. The average jet velocity (Vj) ... determined from the calculated mass flow rate. The output from the reference thermocouple. used to monitor the jet temperature. is sampled using the previously discussed data acqui- sition system. Knowing the sensitivity of the type E thermocouple. 76.5umvoltsI°C. an output voltage corresponding to the desired jet temperature can be calculated. The desired output from the reference thermocouple is obtained by adjusting the voltage level of the power- Sttts It was found that a period of approximately one hour was required for the jet temperature to stabilise. however a period of three hours was required for the jet mass flow rate to stabilise. The latter was a direct result of the initial transient period of the Spencer blower. 29 2.2.3 The Temperature Measurement System The results of Kamotani and Greber (1971) were used to determine an appropriate position of the thermocouple array with respect to the jet exit location. Their results include the Vj/Uo values of interest (4 and 8) for the present study. The thermocouple array was posi- tioned in XId ($0.5) corresponding to the chosen {Id value. The lid position ($0.7) was chosen such that the maximum amount of temperature field information.would be obtained. (The YId (10.5) Placement was to simply center the array with respect to the jet exit.) The array was mounted on a pair of dove tail traverses. allowing for X and Y posi- tioning. which were mounted on an aluminum plate positioned in Z by a scissors jack (see Figure 19). The measurement plane of the present study was located at XID - 3.9 for the J-l6 results and at XID - 3.5 for the J-64 results. The data acquisition procedure. discussed in Part I Chapter 3. is used to acquire the data for the present study. The following features are specific to the present experiment. i) The offsets asso- ciated with the channels of the processing boards require a stabilisation period (as noted in Part 1 Chapter 3). which was found to be approximately 45 minutes for the present study. ii) The sam- pling rate of 1.56 kHs (.64msec) is appropriate when considering the central difference scheme used to evaluate the term dTh/dt: that is. .128 jet diameters of fluid will be convected downstream every .64msec. This estimate of the convected distance is based on a con- vection velocity of 2mps which is the value of the free stream velocity for all cases. 30 CHAPTER.3 DISCUSSION OF EXPERIMENTAL RESULTS 3.1 Introduction to Discussion of Results The primary motivation for this experimental program was to determine the effects of cross stream disturbance on the jet in a cross flow problem. A secondary body of results is also presented: thpse results derive from the use of three overheat jet temperatures: 13-1;-22.2,41.7.sna 61.1 'c and they indicate the influence of 3.: temperature on the dynamics of the jet in a cross flow. This secon- dary body of results will be discussed after the general features of the measurements are identified. The influence of the disturbed cross stream will then be considered. The influence of assuming that time constant values for each thermocouple could be taken as 1-1(2mps). was evaluated by processing one (high-rate time series) data set with the 1 values: A-A(5mps) and 1-0. The former represents an upper bound for the expected velocities at the lid plane of the measurements (Kamotani and Greber (1971)) and the latter represents the absence of a time constant correction. From the considerations in article 1.1.2.2. it is expected that negligible 31 32 differences in the mean values of the measured (A-0) and the corrected: A(2mps) and A(5mps) should be obtained. Also. it is expected that the rms temperature values should vary is T" (A-O) < T:3 (A(5mps)) < Tl: (A(2mps)). Using one of the time series data sets for: 1364. TB-Igp51,1'c , and a disturbed cross flow. the results shown in the following table were obtained. TABLE II.1 Influence of A on measured temperature values 1'30.) - Egon...» . 7;; 5127mm...» min median max min median max A-O -0.63 0.05 0.73 1.65 6.0 17.86 A-5 -0.15 0.03 0.19 0.84 2.0 7.0 The relatively small differences between the 2 and 5 mps time constant conditions support the inferrence that the use of a constant A value does not exert a significant influence on the present results. The temperature field results are most easily interpreted if the conduction of energy through the nossle plate. and the corresponding thermal contamination of the boundary layer fluid. can be neglected. The magnitude of this contamination can be conservatively estimated by assuming that a thermal boundary layer began at the juncture of the nossle plate and the boundary layer plate (Li). A measure of the con- tamination is provided by the assumed two-dimensional boundary layer 33 at the location of the jet centerline. Using the apapropriate heat transfer relationship for this laminar boundary layer (e.g.. Gebhart (1971)): q - .664 1: (1,-1.1 (0.1.)1’2 (1,1’2 - 1.11”) (eq. 11.1) and equating this to the flux of thermal energy carried by the boun- dary layer: q . I Pop (T T. To) u dy (.q II.2) one can solve for the ”non-dimensional thermal contamination measure": I [ (1—1.)/(1,-1.) ] (up...) ama) - .664 (klpop)I(U.d)(U./v)1’2 ((L,)1’2-(L,_)1’2) - 1.4 x 10" (sq. 11.3) for U; - 2mps and L3-260mm and L1 - 213mm. Hence. it is inferred that the boundary layer heating effect is of negligible importance for this flow field. 3.2 Thermal Energy Considerations Applying the energy equation to the control volume shown in fig- 34 ure 21 one obtains d-ts-a/azc.vjwl’lznui) paw“ '.I(V13/2+gs+3+plp)pY-ndA (11.4) Assuming i) steady state. ii) heat-transfer rate and work rate between system and surroundings - 0. and iii) that the kinetic energy term is small compared with the enthalpy term. (h-p/p-I-E). equation 11.4 reduces to 1.0.8., pcpT Van dA - pcpT U-n dA (eq. 11.5) c.s., The above integral quantities if evaluated. would provide a good check on the experimental data; however. velocity information is not avail- able from.the present study. The present results provide contours of constant temperature (isotherms) for both the mean flow field and the instantaneous flow field. These results show that. at the Xrlocation of the thermocouple array. both the mean and instantaneous tempera- tures existing in this flow field are substantially lower than the initial jet temperature. Namely. the peak temperatures do not exceed the value: 0.25(T}-T;). Equivalently. this result shows that substan- tial diffusion (i.e. molecular transfer) of thermal energy has occured between the jet exit and the observation plane since this is the sole agent that can reduce the energy state of a given fluid ele- ment. From (II.5). and for jet velocities which are approximately equal to the cross stream velocity. it is apparent that the contamina- tion field at c.s. 2 must be much larger than the area of the jet orifice. This characteristic of the isotherms is quite apparent as 35 noted below. 3.3 Jet temperature considerations For the present experiment. it was desired to use thermal energy as a passive scalar contaminant with which to mark the jet fluid. It was found however. that at the jet temperatures investigated. the thermal energy had a dynamic influence on the flow field. This can be seen in figures 22-33. These figures represent the mean isotherms for the momentum. flux ratio (J) of 16 and 64 and for three different overheat conditions: Tj-L-22.2.41.7.and 61.1 'c for both :1. undis- turbed and disturbed cross flow cases. These contours were obtained using the Surface 11 contouring package on the Cyber 750 at Michigan State University. The + signs on the figures represent the positions occupied by the thermocouples. The coordinates of all contours are those of the thermocouple array (s and t). Listed in the caption of each figure are the transformation equations between the array coordi- nates and the jet exit coordinates. The numerical values of the isotherms represent 1000x(T°-T;)l (13-1;) - Th. The mean isotherms show that as the jet temperature increases (I-constant) the centroid of the temperature field moves away from the boundary layer plate. (It is pertinent to note that the position of the thermocouple array was not changed as the jet temperature was changed for a given I value.) Figure 34a is a plot of the s component of the centroid as a function of overheat for the several cases inves- tigated. The centroid represents an integral measure of the 36 temperature field; in this sense it represents a smoothing of the dis- crete data samples. The centroid was calculated by the equation sco‘o-E 31A! I 2 AI 0 tc.‘.'§ tIAI I 2 AI (eq. 11.6) where s1 is the s component of the centroid for each isotherm and AI represents the area of each isotherm and was calculated using the digitizer on the Prime computer at Michigan State University. An alternative method of calculating the centroid is to consider the measured temperature as a discrete "mass" point and to compute the centroid of the distributed field of such "mass" points. Specifically. the centroid was calculated using the equation 3c.g. - 2 'iTR/ 2T3 . tea, . 2 “In 2 T3 (eq. 11.7) where 31.t1 are the coordinates for a given thermocouple. The results of this technique are not considered to be as valid a measure of the thermal field: however. this calculation is dramatically easier to execute and it will be employed where the use of the digitized isotherm contours would be impractical. The centroid results. using this method. are presented in Figure 34b. It is pertinent to note that the centroids. inferred from the isotherms. show a much larger variation. and a more regular dependence upon. the overheat tempera- ture values than the centroids calculated from the discrete mass points. 37 The increased jet penetrationlwith jet temperature is opposite to a buoyancy effect: specifically. for the present experiment. buoyancy would act to shift the jet trajectory closer to the boundary layer plate as jet temperature was increased. The effects of buoyancy are expected to be negligible since the Richardson number (xi-wrj-ma/uo‘rr) for the present study 1. ...11 (111-.005). see Townsend (1976) . Kamotani and Greber (1971) present mean isotherms for a jet exit- ing into a low disturbance cross flow. The authors found that "for a given momentum flux ratio. increasing the jet temperature causes less penetration of the jet temperature centerline". This qualitatively opposite trend. compared with the present results. is considered to be significant: however. several factors must be noted to place this observation in proper context. It can first be noted that their results are also contrary to a buoyancy effect. The Kamotani and Greber (1971) results are derived from data which are taken in planes normal to the jet centerline (f-n plane). whereas the present data are taken in the 1-2 plane. The jet nozzle configurations for the two studies are rather different: a contoured nossle (Kamotani and Greber (1971)) vs. a sharp-edge edge orifice for the present study. The Kamotani and Greber (1971) results are for two overheat ratios: 41.7 and 177.8 'C: the latter is substantially larger than those of the present study. The Kamotani and Greber (1971) centerline is defined as the maximum temperature in the {-n plane. whereas the present result is for the centroid of the temperature field in the 191 plane. The present measurement grid is too coarse to allow the maximum. tem- 38 perature position to be precisely determined; however. to the extent that it is known. this measure of the temperature field shows a weak dependence on the overheat value. Specifically. the position of the maximum mean temperature moves away from the boundary layer plate with increasing overheat. 'hcn comparing the isotherms of Kamotani and Greber with the present contours. it is also pertinent to keep in mind that Kamotani and Greber used a jet that exits from the floor unlike the present jet which exits from the ceiling into the cross flow. Kamotani and Greber (1971) explained their results in terms of i) the buoyancy force which would act to shift their jet away from.their boundary layer plate and ii) the increased momentum flux in the x-direction resulting from the increased rate of entrainment of cross flow fluid caused by the decrease of the jet density. This latter effect would act to shift the temperature centerline toward the boundary layer plate as noted in the following discusson. Ricou and Spalding (1961) show that an azisymmetric jet exiting into a quiescent ambient entrains fluid by the following relation Mina-hound)(.../.3)“: (011. 11.8) This relation shows that as the jet temperature increases (95 decreases) the mass flux for a given x increases. If one applies this to the jet in a cross flow problem. it would be expected that increas- ing the jet temperature would lead to the increased entrainment of 39 cross stream fluid. Since the momentum of the cross stream fluid is initially directed in the x-direction. it would then be expected that (for the experiment conducted by Kamotani and Greber (1971) and for the present experiment) this effect would act to shift the temperature centerline toward the boundary layer plate. This effect is observed for the Kamotani and Greber (1971) experiment but not for the present study. As was mentioned earlier. the maximum mean temperature decreases with increasing overheat. This is consistent with the idea of increased entrainment: namely. the increased entrainment of lower tem- perature ambient fluid will act to decrease the mean temperature values in the jet. This decrease in maximum mean temperature can be seen in the 'mean isotherms for both the disturbed and undisturbed cross flow conditions (Figures 22-33). The overheat influence can also be seen when looking at the his- tograms obtained for all thermocouples in the thermocouple array. A selected few of these histograms can be seen in figures 35-42. Figures 35.37.39.and 41 represent the histograms for a thermocouple located in approximately the center of the jet while figures 36.38.40.and 42 are the histograms for thermocouples located farther from the boundary layer plate. Ihen comparing the overheat trends of thermocuples located in the center with those located farther away from the boundary layer plate it can be seen that the jet penetration increases as jet temperature increases. Namely. the overheat trend in the center of the jet acts to decrease the mean temperature. while 40 farther away from the boundary layer plate. increasing the jet tem- perature acts to increase the mean temperature sensed by the thermocouple. This overheat trend can be quite dramatic as is indi- cated in figures 36 and 38. Ihen increasing the jet temperature. the jet velocity was also increased such that the momentum flux ratio (1) was held constant. In order to ensure that the increased jet penetration with increased overheat was not a result of the increased jet velocity. the results for the three overheat conditions were examined for the case where the jet and cross stream velocity were held constant (RIVjIVOrconstant-4) as the jet temperature was increased. The contours for this case are Inot included in this document; however. the jet displacement with overheat can be seen in Figure 34b. The results for Reconstant show that the centroid of the temperature field moves farther away from the boundary layer plate as the jet temperature is increased. It has been shown that neither a buoyancy effect nor the increased entrainment effect is solely responsible for the influence of jet temperature on the present results. Also the qualitatively opposite trends between the present results and those of Kamotani and Greber (1971) should be kept in the proper context. as was discussed above. It is expected that. for high jet temperatures. buoyancy effects would cause the jet penetration to decrease with increasing jet temperature for a jet exiting from.the ceiling. and an experimen- tal program will be carried out at I.8.U.. in the near future. which will provide this information. 41 3.4 Comparison of Present Results with Kamotani and Greber Significant differences can be found when comparing the mean isotherms of Kamotani and Greber (1971) with those of the present study. The absence of kidney shaped isotherms is one factor albeit this may relate to the vertical vs. the jet-axis-normal plane of the data. Compounding this difference in observation planes is the effect of an increased jet penetration. Figures 43a and 43b are taken from Kamotani and Greber (1971). The placement of the present thermocouple array for the J-16.64 (294.8 Khmotani and Greber) cases. and the a component centroid results for T3-1;,. 41,1'c (Figure 34s) have been added to Figures 43a and 43b. An approximate value. for the location of the maximum temperature. was inferred from the mean isotherms and this value has also been added to the figure to provide a direct com- parison with the Kmmotani and Greber results. The increased penetration of the jet for the present study is attributed to the higher effective momentum flux ratio which results from using the average velocity exiting from the sharp edge orifice. The velocity profile at the exit of the nossle used by Kamotani and Greber (1971) is inherently more uniform than that at the exit of a sharp edge ori- fice and the mmmentum flux ratio. based on an average velocity. will be less for their nozzle. Another important difference between the two experiments is the cross stream boundary layer thickness compared with the jet exit diameter; bld < .1 for lemotani and Greber. s/a a 1.3 for the present experiment. 3.5 Comparison of undisturbed with disturbed cross flow conditions Figures 28-33 are contours of mean isotherms for the case where 42 the jet exits into a disturbed cross flow. The shapes of these con- tours are very similar to those for the undisturbed cross flow case. (Figures 22-27); however. the maximum mean values for the disturbed cross flow case are significantly lower than those for the undisturbed cross flow case. Additional differences are reflected in the contours of constant temperature standard deviations (Figures 44-55) and the associated histograms (Figures 35-42). The contours of constant standard deviation show drematic differ- ences between the disturbed and undisturbed cross flow conditions. The values of the standard deviations are larger for the disturbed cross flow condition and the temperature standard deviation field is larger than that for the undisturbed case. The histograms reveal a great deal of information regarding the differences between the undisturbed and disturbed cross flow cases. For example. compare figures 35 and 39. These two figures represent the histograms for thermocouples located near the maximum contour level for 1-16 for the undisturbed and disturbed cross flow conditions respectively. The bimodal characteristic for the disturbed cross flow case. shows that ambient (cross stream) temperature fluid occupied this point in space for a significant fraction of time. Similar his- tograme exist for the 1-64 condition; see Figure 37 and 41. These suggest that the jet trajectory excursions are a significant fraction of the jet width for the disturbed cross flow cases. Six instantaneous time series. each approximately .8 seconds in 43 length. were taken and stored for the T}-T;-61.1'C overheat cases: I-l6 and 64. disturbed and undisturbed cross flow conditions. These time series were formed from.periodic (At-0.64msec) and simultaneous samples of the 64 thermocouples. The centroid (s of the c.s.‘tc.g.) instantaneous temperature field was determined using equation II.7 and representative time series for the four cases are shown in Figures 56-59. (Note that the two coordinates of the centroid: 'c.g. and tc.g.' are shown separately). The increased movement of the jet column for the disturbed cross flow case is clearly seen in these fig- ures. The following table shows the results using all six of the time series for the disturbed cross flow case and three of the time series for the undisturbed cross flov case. J 6"c.g. ctc.g. K't undisturbed c.f. 16 .341 .253 .067 undisturbed c.f. 64 .233 .233 .0.13 disturbed c.f. A 16 1.84 1.45 +0.33 disturbed c.f. 64 1.16 1.12 -0.45 TmBLB II.2 Cross stream disturbance effect on centroid of temperature field The correlation coefficient (I.t-:Zl(o‘ot) results presented in the above table show that the T and Z motions of the jet are signifi- cantly correlated for the disturbed cross flow case. This correlation is considered to be representative of the cross flow itself rather the dynamics of a jet in a disturbed cross flow. That is. the 5: correla- tion. that is suggested by the Kat values. would be expected from the large-scale secondary motion. for the related problem of a bounded 44 jet. as documented by Holdeman and Foss (I975). The time series records. Figures 56-59. indicate a low frequency translation of the centroid. This is qualitatively similar to the (hot-wire anemometer derived) energy spectrum results presented in Figure 16. Instantaneous isotherms can also be generated from the time ser- ies taken at the high sampling rate. A selected few of these isotherms are shown in Figures 60-67. These isotherms were selected based on the centroid time series shown in Figures 56-59. Referring to figures 56 and 57 (1-16). one can see that at approximately .2 and .65 seconds there are peak excursions of the jet centerline for the disturbed cross flow case. The isotherms for both the disturbed and undisturbed cross flow case at these two instants in time are shown in Figures 60-63. At the discrete points in time of approximately .3 and .58 seconds. figures 58 and 59 (1'64) show peak excursions of the jet centerline. The corresponding contours can be seen in Figures 64-67. The migrating jet column is clearly seen‘when comparing the dia- turbed cross flow isotherms. For the disturbed cross flow. 1564. contours shown in Figures 66 and 67. the excursion is so great that the resulting two temperature fields hardly overlap. This is also true for the J-l6 contours seen in Figures 62 and 63. The migration of the jet column for the undisturbed cross flow case is not as severe as can be seen in Figures 60.61.64.and 65. Comparing the instantaneous contours with the mean contours. one can see that the differences are greater for the disturbed cross flow 45 case. The maximum values for the instantaneous contours of the dis- turbed cross flow case are much larger than those of the mean contours. The maximmm instantaneous values for the disturbed cross flow case do not differ significantly from those for the undisturbed cross flow case. The mean temperature values are much lower however. because of the jet centerline excursions. CHAPTER 4 CONCLUSIONS The following conclusions are based on the results of the present study. i) Substantial diffusion of thermal energy has occurred between the exit plane and measurement location. since the maximum tempera- tures recorded were <.25(T3.¢-T.) for both the undisturbed and disturbed cross flow cases. ii) For the jet temperatures investigated. T}-1;,- 22.2.41.7 and 61.1 'C. it was found that thermal energy had a dynamic influence on a jet exiting into both a disturbed and undisturbed cross flow; specifi- cally the calculated centroid of the temperature field moved away from the boundary layer plate as jet temperature increased. iii) The present results show that the centroid of a heated jet has much larger excursions. for the jet exiting into a highly dis- turbed cross flow than for a jet exiting into an undisturbed cross flow. 46 47 iv) For both the undisturbed and disturbed cross flow cases. an instantaneous isotherm pattern can be significantly different from the mean isotherm pattern and this difference is more dramatic for the disturbed cross flow case. Specifically. the instantaneous maximum temperatures for the disturbed flow are similar in magnitude to those of the undisturbed case whereas the maximum mean temperature is sub- stantially less for the disturbed cross flow compared with the undisturbed cross flow case. 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In... 75 0p (K and G) .——--—- Jet Velocity Centerline (K and G) I location of a component centroid (.1-64) T.-Tu, = 41.7°C ‘3 approximate location of the maximum tempgrature ‘ SJ-Gf) 1T1?” 8. 413700. -' . . . . 1 5 10 15 UP Figure 43b Location of Temperature Centerline (R=8) from Kamotani and Greber (1971) 93 Figure 44. Undisturbed Cross Flow (u.c.f.) Contours of a Temperature Standard Deviation: J = 16, Tjet - Ta = 22.2°C NOTE: Values shown are 1000X[Tc(s,t) - Terms/(Tj - Tm) s/d and t/d as defined for the mean temperature isotherms 12 94 10 .p co 12 Figure 45. u.c.f. Contours of Constant Temperature Standard Deviation: J = 16, Tjet - Tm = 41.7°C NOTE: Values shown are 1000X[Tc(s,t) - Terms/(Tj - Tm) s/d and t/d as defined for the mean temperature isotherms 12 95 12 Figure 46. u.c.f. Contours of Constant Temperature Standard Deviation: J = 16, Tjet - Ta = 6l.l°C NOTE: Values shown are l000X[Tc(s,t) - Terms/(Tj - Tm) s/d and t/d as defined for the mean temperature isotherms 96 Figure 47. u.c.f. Contours of Constant Temperature Standard Deviation: J = 64, Tjet - Tco = 22.2°C NOTE: Values shown are lOOOXETc(s,t) - TermS/(Tj - Tm) s/d and t/d as defined for the mean temperature isotherms 97 Figure 48. u.c.f. Contours of Constant Temperature Standard Deviation: J = 64, Tjet - T°° = 41.7°C NOTE: Values shown are lOOOXETc(s,t) 'le1rms/(Tj - Tm) s/d and t/d as defined for the mean temperature isotherms 98 12 10 .p m Figure 49. u. c. f. Contours of Constant Temperature Standard 6l. 1° C Deviation: J = 64, Tjet- T = NOTE: Values shown are lOOOXETC(s,t) - Tmes/ /(TJ - Ta) s/d and t/d as defined for the mean temperature isotherms 99 Figure 50. Disturbed Cross Flow (d.c.f.) Contours of Constant Temperature Standard Deviation: J = l6, Tje - T0° = 22.2°C t NOTE: Values shown are lOOOXETC(s,t) - Terms/(Tj - Tm) s/d and t/d as defined for the mean temperature isotherms 12 100 12 + o l _+ 0?! Figure 5T. d.c.f. Contours of Constant Temperature Standard Deviation: J = 16, Tjet - Tm = 4l.7°C NOTE: Values shown are lOOOXETC(s,t) - Terms/Tj - Tm) s/d and t/d as defined for the mean temperature isotherms lOl Figure 52. d.c.f. Contours of Constant Temperature Standard Deviation: J = l6, Tjet - T0° = 61.l°C NOTE:. Values shown are lOOOX[TC(s,t) - TermS/Tj - Tm) s/d and t/d as defined for the mean temperature isotherms 102 Figure 53. d.c.f. Contour of Constant Temperature Standard .. 0 Deviation: J = 64, Tjet - T°° — 22.2 C NOTE: Values shown are lOOOXETc(s,t) - TMerS/Tj - Tm) s/d and t/d as defined for the mean temperature isotherms 103 Figure 54. d.c.f. Contour of Constant Temperature Standard Deviation: J = 64, Tjet - Ton = 4l.7°C NOTE: Values shown are lOOOX[Tc(s,t) - Terms/Tj - Tm) s/d and t/d as defined for the mean temperature isotherms 104 Figure 55. d.c.f. Contour of Constant Temperature Standard Deviation: J = 64, Tjet - T0° = 61.1°C NOTE: Values shown are TOOOXETC(s.t) - Terms/Tj - Tm) s/d and t/d as defined for the mean temperature isotherms ---disiurbed 105 -‘~ '0 ‘n. I ‘1’ -‘.~ 2 " o- -.' ~-‘ 3 r . O’O‘.:’- ‘3 J ‘1’ 3 O’OOC'.-' -.. 0" o’- 48" c" . --~..-‘ - r .O" .0- “.-..-- 0’. «‘1‘ - t’;’ --cc' ‘- --’ 0 ..-.--~ ,7 v. - ofi" 0:- “...‘ 'CO".. ‘0 -..-..‘CO .5: \g‘ a" Q \ Q... o". .\ 6‘-‘ 0.50 4.50 5 . 0 (en) SQQ‘ECJ. I -3.50 0.40 0.80 time (ml 0.20 0.00 16, Tjet - Tm = 6].] C Variation of 5 Component of Centroid with Time J Figure 56. 8 mm. oo_._o u a - o .e .m. n a wave new: vwogpcmu so peacoQEoo a mo cowuw_cm> .Nm wczmwm .93. 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(U >"D co LO Q) S. 3 01 .‘F' LL I 9'0_ ”4‘ ' fit. . ‘n. uo_._o u a» - “owe .ao n a week saw: uwocuemu so ucmcoasou a so copumwnm> .mm mc=m_m auouv OE: QW.G 8*.8 QN.G 8.8 108 ’ ~ 0 _ _ _ h _ _ _ _ _ _ _ _, _ _ _ _ _ _ nmmgwu. Hui—umflmvl «w. y .1. . . c s. as: . ..I Po. 7 M... :23..." «so... .... A...) .... H .... ......fi . . .... .... a. I . . ”a ...-w . ”I am 8'. Jo er. ... a!“ o I AEUV .sw 1.00.— . a. .n I. ems ” .......... . .. m .... " ... coo s. u... ‘un “K.” ”.01. H Mam m. a a .m» unw._n:wsw .... M 33535:: 3’... rl amim $03535 uuuuuuuu a r: smd 12 109 o 4 a 12 an: 4» + + + + ‘I" F1 + + + 4 + + + + + + + - a + + + d + + + + + + + \ a +Q+ + 0‘ O 0 + 70 + i’ w 4' +' i' ‘30 -+ .+ + + + + + + ‘ 0 6 ‘ i J 3 ‘ 12 ' .JL (I Figure 60. Undisturbed Cross Flow (u.c.f.) Instantaneous Temperature Isotherms, J = l6, Tjet - T0° = 6l.l°C, Time = .2 sec T -T o m X 1000, s/d and t/d as defined for 'the mean temperature isotherms NOTE: Contours shown are 110 12 12- 9.. + 4.5 +. 0!. .L. 6 Figure 6l. u.c.f. I stantaneous Temperature Isotherms J = 16, T. - T = 61.1°C, Time = .65 sec get a To-Ton NOTE: Contours are T _ X 1000, s/d and t/d as defined for jet w the mean temperature isotherms (LIV. 12 lll 0 12 112 ... r + s f3 4- i + :. L 4F h:w + + + + + -F 4F 4 + + + "' + a. .+ -F 4- +_ 1 4 +. + + it -+ it + + + + q -F 4- + + 4- -F + + "I" 1 0 6 ' i L a ‘ 12 .1. d Figure 62. d.c.f. Instantaneous Temperature Isotherms J=16,T. -T =6l.l°C,Time= .2 sec Jet m To-Ton NOTE: Contours are-T——e:T— X lOOO, s/d and t/d as defined for jet m the mean temperature isotherms “I“ 112 Figure 63. d.c. J =1 NOTE: Instantaneous Temperature Isotherms f. _ = o ' = 6, Tjet Ton 6l.l C, Time .65 sec T -T Contours are T 0 _; X 1000, s/d and t/d as defined for jet m the mean temperature isotherms 12 113 12 r + L + + L 'F ’ + + L «f 0 Figure 64. u.c.f. I stantaneous Temperature Isotherms J = 64, T. - T = 6l.l°C, Time = .3 sec Jet m To-T0° NOTE: Contours are T~——:f— X lOOO, s/d and t/d as defined for jet w the mean temperature isotherms 12 al.. 114 . Instantaneous Temperature Isotherms Figure 65. c. 05—h u. J 4, T. = ° ' = get - T0° 6l.l C, Time .58 sec. NOTE: Contours are T o _? X lOOO, s/d and t/d as defined for jet w the mean temperature isotherms 12 115 0 4 8 12 -12 + + + + + 4. .p ‘T -+ + + + + 4p 6 Figure 66. Disturbed Cross Flow (d.c.f.) Instantaneous Temperature Isotherms, J = 64, Tjet - Ton = 61.l°C, Time = .3 sec. T -T ° ” x 1000, s/d and t/d as defined for the mean temperature isotherms NOTE: Contours are 116 12 + + + + + + .p + .+ 4. + ‘ + + + + 4p + -t. -F _+ at + + 1 l A: ‘ 5 1 ° ..t. d Figure 67. d.c.f. Instantaneous Temperature Isotherms J = 64, T. - T = 61.l°C, Time = .58 sec. jet m TO-Tm NOTE: Contours are T_——:T_ X lOOO, s/d and t/d as defined for jet w the mean temperature isotherms 12 WCES REFERENCES Peterson, C. H., (1979) "A Survey of the Utilitarian Aspects of Advanced Flowfield Diagnostic Techniques." AIAA J. 17:1252-1360. Doebelin, E. 0., (1966) "Measurement System: Application and Design." McGraw-Hill. Bradley, D. and Matthews, K. J., (1968) "Measurements of High Gas Temperatures with Fine Hire Thermocouples." J. Mech. Eng, Sci. 10:299-305. Moffat, R. J., (1958) “Designing Thermocouples for Response Rate." Trans. ASME 80:257-62. Petit, C., Gajan, P., Lecordier, J. C., and Paranthaen, P., (1982) "Frequency Response of Fine Hire Thermocouple." J. Phys. E:Sci. 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