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Effect of operating conditions on the dynamic response of thermal sensors with and without analog feedback
Sensors and Actuators A 58 (1997) 129–135
Effect of operating conditions on the dynamic response of thermal sensors with and without analog feedback B.W. van Oudheusden U Faculty of Aerospace Engineering, Delft University of Technology, PO Box 5058, 2600 GB Delft, Netherlands Received 15 February 1996; revised 4 October 1996; accepted 7 November 1996
Abstract The effect of the operating conditions of a thermal sensor on its dynamic response is considered with regard to operation both with and without analog feedback, the latter being the classic solution to improve dynamic response. The effect of aspects such as overheat level, heattransfer rate and feedback linearity are discussed. The thermal behaviour of the system is modelled as a first-order system with a constant time delay in the feedback loop. To provide fundamental insight into the dependencies, a general analysis is first carried out in the thermal domain, to reveal aspects that are independent of any specific electronic implementation. This is followed by investigation of the most commonly employed implementation, that of a self-heating resistive element in a bridge configuration. Keywords: Analog feedback; Dynamic response; Thermal sensors
1. Introduction Thermal sensors find wide application in both the direct sensing of thermal parameters, such as temperature and IR radiation, and that of non-thermal properties through modulation or tandem principles (flow, pressure, composition) [1]. In the modulation principle the heat transfer from an artificially heated sensor is monitored, where the heat-transfer rate contains the information of the desired measurand. In flow-sensing applications [2,3] this principle is commonly referred to as the hot-wire anemometer principle, and has been used in a large variety of implementations at relatively low speeds, i.e., under incompressible flow conditions [4– 6]. The hot-wire anemometer finds application especially for the measurement of very low-speed flows because of the high sensitivity under these conditions, and for the measurement of fluctuating velocities in turbulence research. Originally only the constant-current anemometer (CCA) method was used, but nowadays the constant-temperature anemometer (CTA) is the standard in most low-speed applications. Hotwire measurements at very high velocities require special attention due to the additional thermal effects arising in compressible flows [6–10]. Although this field provides the major motivation of the present study, the discussion will not address the details of the heat-transfer mechanism under these U
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specific flow conditions, but instead will be in rather more general terms in order to elucidate generic characteristics common to many thermal sensors. 1.1. General aspects of thermal sensor operation A first important aspect of the operation of thermal sensors is their fundamental multi-variable dependence. As the heattransfer rate depends on the temperature difference between sensor and ambient, i.e., the overheat of the sensor, this yields at least a two-variable dependence of the sensor operation. For flow measurements these may be conceived of loosely as the flow speed and temperature (for compressible flow in general we need to consider the flow velocity, density and local stagnation temperature [7,8]). As a result the ambient temperature variations must be monitored separately, which can be carried out using a sensitivity-variation method by operating one or several sensors at different conditions to allow a separation of the different variables to be obtained. For flow sensors this is typically done by varying the overheat of the sensor, where the ratio of the sensitivity to velocity fluctuations to that of temperature increases with the overheat level. Elimination of the cross-sensitivity when only one of the variables needs to be measured is commonly achieved by using either a high-overheat CTA for velocity measurements or a low-overheat CCA for temperature measurements (‘cold-wire’ technique).
0924-4247/97/$17.00 q 1997 Elsevier Science S.A. All rights reserved PII S 0 9 2 4 - 4 2 4 7 ( 9 6 ) 0 1 4 0 4 - 5
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A second aspect of consideration is the dynamic response of the sensor. Without any additional means the response of the sensor is limited by its thermal response, which is usually greatly insufficient for measuring the flow fluctuations for which the hot-wire anemometer is applied in particular in flow research. The classic solution to this is to apply an analog feedback loop to keep the sensor temperature (nearly) constant, thus improving the response speed significantly [1,6]. As is well known, the feedback is limited because of the instability occurring due to delay effects in the loop, which may be of both thermal and electronic nature. As long as the temperature variation takes the form of a slow ambient temperature drift, no severe bandwidth demands are placed on the temperature compensation. Monitoring rapid fluctuations, such as occur in non-isothermal high-speed flows, is an entirely different matter, however. Hot-wire measurements in compressible turbulent flows therefore form a subject of special challenge. In addition to the demanding conditions (large and unsteady mechanical loads, short measurement times) the high flow speeds result in very high frequencies in both the velocity and temperature signals, requiring cut-off frequencies typically of the order of 200 kHz. In order to achieve a correct separation of velocity and temperature signals, the sensor frequency performance should be sufficient at all the overheat levels that are used. It is especially this bandwidth demand that poses problems, because the efficiency of the feedback method has been observed to deteriorate with decreasing overheat level [8,9]. This means that with insufficient frequency performance at low overheat levels temperature fluctuations are underestimated, and velocity fluctuations overestimated [11]. The multi-overheat hot-wire methods reported in the literature for use in high-speed flow may employ a CTA but limit the lowest overheat level [12], at the expense of increased error in the separation procedure. Alternatively, others use a CCA method, the frequency response of which does not vary greatly with overheat, in combination with an electronic frequency-compensation circuit to compensate for the thermal inertia of the sensor [9,10,13]. To achieve a correct compensation, however, an additional in situ calibration is required to determine accurately the thermal response of the sensor at the local operating conditions. Earlier studies [10,14,15] have addressed this matter in a direct approach, by considering the thermo-electrical behav-
iour of the complete hot-wire anemometer system. Although this yields a satisfactory description of the characteristics of a particular system, it does not provide insight as to what aspects are primarily of a fundamental thermal nature inherent to the sensing technique, and what, on the other hand, is to be attributed to the particular electronic implementation of the measurement system. For this reason, the present study investigates the thermal behaviour in a more general sense, by studying these effects on the dynamic response first completely in the thermal domain. As stated earlier, for a similar desire for generality the details of the heat-convection mechanism itself are not considered, but rather the effect which the heat transfer has on the sensor operation. This extends the application of the analysis to include other types of thermal sensors as well. 2. Thermal domain analysis 2.1. Thermal model of the sensor operation The thermal structure of the sensor is modelled as a firstorder system, comprising a thermal capacity C and a heat conductance h to the ambient, the latter being representative of, say, the flow velocity. The sensor is heated by electrically supplying a heating power P, resulting in a rise of the sensor temperature Ts above the ambient temperature Tamb. The instantaneous heat balance of the sensor is then given by the following equation [1]: dTs PsC qh(TsyTamb) dt
(1)
As our main concern is with the dynamic behaviour of the system in order to measure rapidly fluctuating flow properties, a linearization of the sensor behaviour around its operating point is applied. Denoting average (or bias) properties by an overbar and fluctuating components by a prime, the averageand small-signal behaviour are expressed as, respectively:
# # # syT# amb) Psh(T
(2)
# s9sP9qhT # amb9yh9(T# syT# amb) (Csqh)T
(3)
where s is the Laplace variable. The dynamic behaviour is illustrated by the signal block scheme in Fig. 1, where the signals represent the fluctuating quantities while bias quan-
Fig. 1. Block scheme diagram of thermal sensor behaviour in the thermal domain.
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tities appear in the diagram blocks (note that overbars and primes have been omitted). The dashed portion represents the feedback circuit. The variation of P is zero in a constant-power operation mode (CPO), or made explicitly a function of the sensor temperature Ts by applying a feedback strategy to compensate temperature variations (constant-temperature operation mode, CTO). Thirdly, P may vary unintentionally due to, e.g., temperature dependence of the way the heating power is generated. This parasitic feedback effect will be seen to play an important role in operation modes that are a simplified implementation of the CPO, like a constant-heating-voltage or -current operation (CVO and CCO). 2.2. Thermal domain analysis of CPO and CTO modes In constant-power operation mode the sensor temperature is the signal representing the measurand, and the sensitivity to variations in the flow velocity (through the heat conductance h) and (ambient) temperature are derived from Eq. (3) to be: ETs Sh(0) flow: Sh(s)s s Eh 1qst0
(4)
ETs ST(0) temperature: ST(s)s s ETamb 1qst0
(5)
where Sh(0) and ST(0) are the common-mode sensitivities and t0 is the uncompensated time constant, given by T# syT# amb Sh(0)sy h#
ST(0)s1
C t0s # h
(6)
For the constant-temperature operation mode the sensor temperature is regulated to be maintained at a nearly constant level by applying feedback to the heating power:
# aTTs9 Psf(TsyTset)sPq
(7)
where Tset is the prescribed target sensor temperature and aTsdP/dTs the linearized thermal feedback sensitivity, which should evidently be negative to achieve the intended temperature compensation. As P now establishes the signal representing the measurand, the sensitivity to variations in the flow velocity and temperature for this case are given by: EP ETs Sh(0) Sh(s)s saT s Eh Eh 1qst1
(8)
EP ETs ST(0) ST(s)s saT s ETamb ETamb 1qst1
(9)
with the common-mode sensitivities Sh(0) and ST(0) and compensated time constant t1 being
aT # # Sh(0)s (TsyTamb) aTyh# aT h# ST(0)sy aTyh#
t1s
C yaTqh#
(10)
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In evaluation of the above results the following observations can be made regarding the fundamental properties of the thermal sensor systems, also with regard to the effect of the different operation modes. 2.2.1. Dynamic response In both CPO and CTO the dynamic response to velocity and temperature variations is governed by a single time constant (t0 and t1, respectively), and applying feedback evidently increases the apparent response speed significantly when aT is large:
tCPO t0 yaT s s1q # tCTO t1 h
(11)
Furthermore, the response time t0 depends on the thermal conductivity h# and decreases with increasing flow velocity. This is a fortunate property, as flow fields with higher velocities will display higher frequency fluctuations as well. Also, the time constants t0 and t1 are seen not to depend directly on the overheat level. In CTO the time constant depends on the feedback sensitivity aT and it is the non-linearity in the feedback that is responsible for the overheat-level dependence in resistive hot-wire anemometry referred to in Section 1. With the feedback voltage usually varying linearly with the bridge voltage (proportional to variation of the sensor temperature) and the heating power being quadratic in the voltage, the feedback sensitivity varies linearly with the feedback voltage and hence with the sensor overheat. 2.2.2. Multi-variable dependence The ratio of velocity to temperature sensitivity is independent of feedback and the same for CPO and CTO, as given by Sh(s) ST(s)
Sh(s) ST(s)
ž / ž / s
CPO
CTO
sy
T# syT# amb h#
(12)
This explains the basic principle of the multi-overheat method, where the relative sensitivity to velocity fluctuations increases with overheat level, while also revealing that the method can be applied in both CPO and CTO modes alike. Comparing Eqs. (6) and (10) shows that (Sh(0))CTO (ST(0))CTO aT h# s sy (Sh(0))CPO (ST(0))CPO aTyh#
(13)
Hence, CTO hot-wire operation at low overheat displays a deteriorated sensitivity in comparison to CPO, not through a fundamental dependence on the overheat level but again due to the non-linearity of the feedback. 2.3. Effect of feedback time delay in the CTO mode Although Eq. (11) appears to suggest that the response speed can be improved indefinitely by increasing the feedback aT, it is well known that a limit exists because of higherorder effects not accounted for in the simplified analysis.
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These higher-order effects can be interpreted as resulting in a time delay in the feedback path, which makes the feedback loop unstable at high aT. The origin of this time delay can be thermal, due to the finite thermal conduction in the sensor material, or caused by the finite speed of the electronic control circuits due to capacitive and inductive effects. For modern high-speed electronics the thermal effect will probably dominate unless very small sensor dimensions are considered. In the present discussion the exact nature of the time delay is not investigated, but rather how this affects the dynamic behaviour of the sensor operation. Therefore, we simply assume a constant time delay td to occur in the feedback path: P(t)sf(Ts(tytd)yTset)
(14)
For thermal delay effects the diffusion of heat is in first approximation independent of the temperature and heat-flow level, hence, the assumption that td does not depend on the operating point appears to be quite plausible. Using Eq. (13) the small-signal behaviour is
# s9saTexp(ystd)Ts9qhT # amb9yh9(T# syT# amb) (Csqh)T (15) The dynamic behaviour in the form of the normalized sensitivity function is given by
Sh(s) aT aT S(s)s s 1y # 1qst0y # exp(ystd) Sh(0) h h
ž /ž
y1
/
(16)
which, under the assumption that yaT4h# , can be written in a scaled parameter form as A S(f)s fqAexp(yf)
(17)
where f and A are the scaled complex frequency and feedback sensitivity, respectively: fsstd
yaTtd yaTtd As # s ht0 C
(18)
The real-valued amplitude characteristic H is defined accordingly as follows: H(F)sNS(jF)Ns
A
x(x cos F) q(F A sin F) 2
2
(19)
where Fsvtd, with v the radial frequency. The root-locus behaviour of this system as a function of the feedback strength A is depicted in Fig. 2, in which three special cases can be distinguished: (1) the creation of a complex pole pair; (2) the case of maximum flatness of H; and (3) the crossing of the imaginary axis. The corresponding frequency character-
Fig. 2. Root-locus (top) and frequency behaviour (bottom) of a first-order system with time-delayed feedback, in terms of non-dimensional complex and radial frequencies fsstd and Fsvtd , and non-dimensional feedback sensitivity AsyaTtd/C. Labels (1)–(3) in the diagrams refer to the operating conditions discussed in Section 2.3.
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istics for these cases are given at the bottom of the Figure and are obtained for, respectively, A1sey1s0.37, A2s0.5 and A3sp/2s1.57, while for the former two the scaled cut-off (y3 dB) frequencies are F1s0.66 and F2s1.12. In summary, for optimum adjustment of the operation control system, say to obtain a maximum flat frequency response, the required feedback sensitivity and the achievable cut-off frequency are inversely proportional to the time delay td. Assuming this value to be approximately constant, then the frequency characteristic deteriorates when a lower overheat is used only due to non-linearity of the feedback (i.e., the variation of aT). Note that this means that this effect can therefore be eliminated if a control system is applied that produces a constant value of aT, where the heating power is increased in proportion to the temperature change of the sensor.
3. Thermal behaviour of self-heating resistive sensors 3.1. Resistor-bridge configurations After the general thermal domain analysis of thermal sensors, we now consider the specific implementation of thermoresitive sensors operated under self-heating conditions. The bridge configuration commonly employed in this respect is depicted in Fig. 3, showing both configurations with and without an explicit feedback system. The ratio R1/R2 is called the bridge ratio, and R2/R3 the resistance ratio of the bridge. The bridge supply voltage and current are denoted by VSS and ISS, respectively. Assuming the resistance to vary (approximately) linearly with temperature, the overheat ratio aw can be written as RsyRs0 aws sb(TsyT0) Rs0
(20)
where Rs0 is the sensor resistance at reference temperature T0, and b is the temperature coefficient of resistivity. For both metal conductors and diffused silicon resistors b is typically of the order of 3–5=10y3 Ky1. Writing the response equation (3) in terms of the fluctuating sensor resistance, the following result is obtained (where for convenience T0 is taken equal to the average value of Tamb):
Rs0 Rs0 b # aRRs9s(1qst0)Rs9qaw # h9ybRs0Tamb9 h h
133
(21)
The left-hand side again represents the thermal feedback effect, with aRsdP/dRs the thermal feedback sensitivity in terms of the sensor resistance, equal to aRsbRs0aT. From this the sensitivity ratio and the effective time constant are derived as Sh(s) aw sy # ST(s) bh
(22)
teff bRs0 s 1y # aR h t0
ž
y1
/
(23)
which correspond directly to Eqs. (12) and (11), respectively. As the dynamic response is concerned, we observe as expected that for a negative feedback (aR-0 while b is positive) the time constant is reduced, while a positive feedback evidently has the opposite effect. These expressions provide a convenient means to analyse the implications for the dynamic behaviour of different operating modes. 3.2. Dynamic response behaviour of different operating modes Instead of a true constant-power operation, usually an electrically simpler implementation is employed in practice, such as a constant-current or -voltage method. Setting the (average) overheat of the sensor is then achieved by adjusting the supply voltage or current, respectively. In the CTO mode the overheat is regulated by the feedback system, and the required overheat is controlled by adjusting one of the resistors in the bridge circuit (typically either R1 or R3). The implications of this, as far as the dynamic response and effect of overheat are concerned, are determined by evaluating the parasitic feedback in each of these cases. Several typical implementations are considered below. 3.2.1. Constant-voltage operation Assuming a constant value of the bridge supply voltage VSS, the parasitic thermal feedback sensitivity is calculated as
bRs0 aR h#
ž
/
CVO
s
R1yRs aw(awq1) R1qRs
(24)
Fig. 3. Schematic configuration of a resistor sensor bridge, (a) without and (b) with temperature control.
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Hence, the feedback can be either positive or negative, depending on the ratio of Rs and R1. Interestingly, the feedback becomes zero when RssR1, which is also the condition for maximum temperature sensitivity of the resistor bridge. Note that this applies only to a single operating condition (Rs changes with temperature and, hence, with the overheat level), unless special adjustment measures are taken. To achieve a constant average overheat for changing average flow conditions VSS needs to be adjusted, while for maintaining a constant resistance ratio of the bridge at changing overheat ratio an adjustment of R1 is required. 3.2.2. Constant-current operation When considering a constant-current operation we may distinguish between the cases where either the bridge supply current ISS or the current Is through the sensor is kept constant. For a large bridge ratio, typically used to reduce power consumption or self-heating effects in the reference bridge arm, these two cases are nearly identical. Assuming constant Is the parasitic thermal feedback is
bRs0 aR h#
ž
/
s
CCO
aw awq1
(25)
making the expression for the time constant, see Eq. (23),
tCCO sawq1 t0
(26)
This shows that the CCO mode displays a positive parasitic feedback which has a time constant that increases with overheat ratio. 3.2.3. Constant-temperature operation The temperature compensation in the CTO mode is commonly achieved by applying a feedback from the bridge voltage to the bridge supply voltage by means of an amplifier, characterized by a voltage gain G and an offset voltage Voff. The latter is required to achieve a finite value of the transconductance amplification gtr [14,15]: 1 dIs Is R3 IsG gtrs sy 1qG 1y fy Is dRs Voff R2qR3 2Voff
≥ ž
/¥
(27)
the latter assuming that G41 and that a bridge resistance ratio of one is used (R2sR3); note also that gtr is negative. The thermal feedback is evaluated as follows:
bRs0 aR h#
ž
bRs0 s # (Is2q2Is2Rsgtr) h CTO
/
aw s q2awRs0gtr awq1
(28)
where the sensor current Is has been substituted from the steady heat balance of the sensor, which reads Is 2Rss h (TsyT0)sawh/b. The first term on the right-hand side of Eq. (28) is the parasitic feedback due to the resistance change
(compare Eq. (25)) while the second term represents the intended feedback due to the transconductance circuit. Assuming the latter is dominant as a result of a strong feedback, the time constant is, hence,
tCTO s(1y2awRs0gtr)y1 t0 aw h# Rs0 awq1 b
≥ ž
s 1qaw
1/2
y1
G Voff
/ ¥
(29)
where the second expression was obtained by substituting the bridge transconductance gtr from Eq. (27).
3.3. Some remarks regarding the effect of using a selfheating sensor The dependence of the system operation on the overheat as expressed in Eq. (29) is rather complicated due to the fact that the sensor is used in a self-heating configuration, where the sensor current Is acts as both the sensing and heating current. As a result, as can be seen from Eq. (28), the feedback sensitivity is cubic in Is, due to the combined effect that the heating effect is quadratic in the current through the resistor and the linear increase of the bridge transconductance with the sensing current, see Eq. (27). In this respect it is enlightening to consider the case where these sensing and heating effects are separated, e.g., by using different elements. We can then define a heating current and voltage, IH and VH, that are related to the sensor only by the explicit control system. If again a resistive heating element RH is employed (assumed independent of temperature), the combination with a transconductance feedback transfer (now defined as gtrsIs y1 dIH/dRs) yields a feedback sensitivity of dIH2RH aRs s2RHIHIsgtr dRs
(30)
whereas when a voltage amplification G is applied the result is dV H2/RH aRs s2IHIsG dRs
(31)
In both cases the feedback sensitivity increases linearly with the heating current IH when a linear amplification is used, the heating power being quadratic in the heating power. In order to achieve a constant thermal feedback sensitivity, a nonlinear amplification would therefore be required. Alternatively, a heating source may be considered which possesses a non-ohmic characteristic, such as a power-dissipating transistor. In that case the heating power can be made to vary linearly with the current (or voltage) output of the amplifier, by maintaining the voltage (current) constant. Then a constant feedback sensitivity is obtained with a linear amplification, as:
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dIH dVH aRsVH sVHIsgtr or: aRsIH sIHIsG dRs dRs
(32)
for transconductance or voltage amplification, respectively.
4. Discussion and conclusions An investigation was made to assess the effect of operating conditions such as overheat level and feedback linearity, on the dynamic response behaviour of thermal sensors. The major motivation for this study was the observed deterioration, as reported in the literature, of the dynamic response of CTO hot-wire systems with decreasing overheat level as employed in compressible flow research to obtain the separation of flow and temperature fluctuations. In order to provide insight into the fundamental dependencies, a general analysis is first carried out in the thermal domain, to reveal aspects that are independent of any specific electronic implementation. The thermal behaviour of the system is modelled as a first-order system with a constant time delay in the feedback loop. The major findings of this analysis illustrate the separation principle, as the ratio of flow to temperature fluctuation sensitivity indeed increases with the temperature difference between sensor and flow. However, no dependence on overheat of the overall time constant was found. Therefore, this has to be accounted to the effect of non-linearity of the feedback in the case of CTO systems, while in implementations of the CPO mode overheat dependence can be introduced through parasitic thermal feedback. This was confirmed and investigated further by considering the most commonly employed implementation, where a selfheating resistive element is used in a bridge configuration. As the wire current acts as both sensing and heating current, a complicated dependence of the dynamic behaviour on the wire overheat ratio aw is found. Therefore, when the dynamic response deterioration at low overheat ratios is to be eliminated, a non-linear transfer of the feedback circuit must be considered in order to achieve a constant thermal feedback sensitivity. Alternatively, when multi-component sensors are considered, this can be obtained more easily by employing separate non-ohmic heating elements.
References [1] G.C.M. Meijer and A.W. van Herwaarden (eds.), Thermal Sensors, IOP Publishing, Bristol, 1994. [2] P. Bradshaw, Thermal methods of flow measurement, J. Phys. E: Sci. Instrum., 1 (1968) 504–509.
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[3] B.W. van Oudheusden, Silicon thermal flow sensors, Sensors and Actuators A, 30 (1992) 5–26. [4] G. Comte-Bellot, Hot-wire and hot-film anemometers, in B.E. Richards (ed.), Measurement of Unsteady Fluid Dynamic Phenomena, Hemisphere Publishing Corporation, Washington, DC, 1977, pp. 123– 162. [5] J.D. Vagt, Hot-wire probes in low speed flow, Prog. Aerospace Sci., 18 (1979) 271–323. [6] H.H. Bruun, Hot-wire Anemometry, Oxford University Press, London, 1995. [7] L.S.G. Kovasnay, The hot-wire anemometer in supersonic flow, J. Aero. Sci., 17 (1950) 565–572. [8] M.V. Morkovin, Fluctuations and Hot-wire Anemometry in Compressible Flows, AGARDograph No. 24, AGARD, Paris, 1956. [9] A.J. Smits and J.P. Dussauge, Hot-wire anemometry in supersonic flow, in A Survey of Measurements and Measuring Techniques in Rapidly Distorted Compressible Turbulent Boundary Layers, AGARDograph No. 315, AGARD, Neuilly-sur-Seine, 1989, Ch. 5. [10] D. Bestion, J. Gaviglio and J.P. Bonnet, Comparison between constantcurrent and constant-temperature hot-wire anemometers in high-speed flows, Rev. Sci. Instrum., 54 (1983) 1513–1524. [11] F.K. Owen, C.C. Horstman and M.I. Kussoy, Mean and fluctuating flow measurements of a fully-developed, non-adiabatic, hypersonic boundary layer, J. Fluid. Mech., 70 (1975) 393–413. [12] R.D.W. Bowersox, Compressible turbulence measurements in a highspeed high-Reynolds-number mixing layer, AIAA J., 32 (1994) 758– 764. [13] P. Dupont, J.F. Debie`ve and J.P. Dussauge, Methods of measurement for compressible turbulence: status of constant-current hot-wire anemometry, ERCOFTAC 2nd SIG-4 Workshop on Compressible Turbulent Flows, Chaˆtillon, France, 19–20 Oct., 1995. [14] P. Freymuth, Feedback control theory for constant-temperature hotwire anemometers, Rev. Sci. Instrum., 38 (1967) 677–681. [15] A.J. Smits and A.E. Perry, The effect of varying resistance ratio on the behaviour of constant-temperature hot-wire anemometers, J. Phys. E: Sci. Instrum., 13 (1980) 451–456.
Biography Bastiaan W. van Oudheusden received the M.Sc. degree in aeronautical engineering in 1985 at the Delft University of Technology, Delft, The Netherlands. His thesis work comprised theoretical and experimental research on transition and turbulence in incompressible boundary-layer flow. In 1985 he joined the Electronic Instrumentation Laboratory of the Department of Electrical Engineering and in 1989 obtained the Ph.D. degree on the subject of silicon-integrated direction-sensitive flow sensors, which resulted in the development of a microelectronic thermal wind meter. Since 1991 he has been a member of the High Speed Aerodynamics Laboratory of the Department of Aeronautical Engineering, where he has been involved in experimental research on non-linear aeroelastic oscillation phenomena and in the compressible flow research and education of the laboratory.
Journal: SNA (Sensors and Actuators A)
Article: 1392
Effect of operating conditions on the dynamic response of thermal sensors with and without analog feedback B.W. van Oudheusden U Faculty of Aerospace Engineering, Delft University of Technology, PO Box 5058, 2600 GB Delft, Netherlands Received 15 February 1996; revised 4 October 1996; accepted 7 November 1996
Abstract The effect of the operating conditions of a thermal sensor on its dynamic response is considered with regard to operation both with and without analog feedback, the latter being the classic solution to improve dynamic response. The effect of aspects such as overheat level, heattransfer rate and feedback linearity are discussed. The thermal behaviour of the system is modelled as a first-order system with a constant time delay in the feedback loop. To provide fundamental insight into the dependencies, a general analysis is first carried out in the thermal domain, to reveal aspects that are independent of any specific electronic implementation. This is followed by investigation of the most commonly employed implementation, that of a self-heating resistive element in a bridge configuration. Keywords: Analog feedback; Dynamic response; Thermal sensors
1. Introduction Thermal sensors find wide application in both the direct sensing of thermal parameters, such as temperature and IR radiation, and that of non-thermal properties through modulation or tandem principles (flow, pressure, composition) [1]. In the modulation principle the heat transfer from an artificially heated sensor is monitored, where the heat-transfer rate contains the information of the desired measurand. In flow-sensing applications [2,3] this principle is commonly referred to as the hot-wire anemometer principle, and has been used in a large variety of implementations at relatively low speeds, i.e., under incompressible flow conditions [4– 6]. The hot-wire anemometer finds application especially for the measurement of very low-speed flows because of the high sensitivity under these conditions, and for the measurement of fluctuating velocities in turbulence research. Originally only the constant-current anemometer (CCA) method was used, but nowadays the constant-temperature anemometer (CTA) is the standard in most low-speed applications. Hotwire measurements at very high velocities require special attention due to the additional thermal effects arising in compressible flows [6–10]. Although this field provides the major motivation of the present study, the discussion will not address the details of the heat-transfer mechanism under these U
Phone: q31 15 270 5349. Fax: q31 15 270 7077. E-mail: [email protected].
specific flow conditions, but instead will be in rather more general terms in order to elucidate generic characteristics common to many thermal sensors. 1.1. General aspects of thermal sensor operation A first important aspect of the operation of thermal sensors is their fundamental multi-variable dependence. As the heattransfer rate depends on the temperature difference between sensor and ambient, i.e., the overheat of the sensor, this yields at least a two-variable dependence of the sensor operation. For flow measurements these may be conceived of loosely as the flow speed and temperature (for compressible flow in general we need to consider the flow velocity, density and local stagnation temperature [7,8]). As a result the ambient temperature variations must be monitored separately, which can be carried out using a sensitivity-variation method by operating one or several sensors at different conditions to allow a separation of the different variables to be obtained. For flow sensors this is typically done by varying the overheat of the sensor, where the ratio of the sensitivity to velocity fluctuations to that of temperature increases with the overheat level. Elimination of the cross-sensitivity when only one of the variables needs to be measured is commonly achieved by using either a high-overheat CTA for velocity measurements or a low-overheat CCA for temperature measurements (‘cold-wire’ technique).
0924-4247/97/$17.00 q 1997 Elsevier Science S.A. All rights reserved PII S 0 9 2 4 - 4 2 4 7 ( 9 6 ) 0 1 4 0 4 - 5
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Article: 1392
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A second aspect of consideration is the dynamic response of the sensor. Without any additional means the response of the sensor is limited by its thermal response, which is usually greatly insufficient for measuring the flow fluctuations for which the hot-wire anemometer is applied in particular in flow research. The classic solution to this is to apply an analog feedback loop to keep the sensor temperature (nearly) constant, thus improving the response speed significantly [1,6]. As is well known, the feedback is limited because of the instability occurring due to delay effects in the loop, which may be of both thermal and electronic nature. As long as the temperature variation takes the form of a slow ambient temperature drift, no severe bandwidth demands are placed on the temperature compensation. Monitoring rapid fluctuations, such as occur in non-isothermal high-speed flows, is an entirely different matter, however. Hot-wire measurements in compressible turbulent flows therefore form a subject of special challenge. In addition to the demanding conditions (large and unsteady mechanical loads, short measurement times) the high flow speeds result in very high frequencies in both the velocity and temperature signals, requiring cut-off frequencies typically of the order of 200 kHz. In order to achieve a correct separation of velocity and temperature signals, the sensor frequency performance should be sufficient at all the overheat levels that are used. It is especially this bandwidth demand that poses problems, because the efficiency of the feedback method has been observed to deteriorate with decreasing overheat level [8,9]. This means that with insufficient frequency performance at low overheat levels temperature fluctuations are underestimated, and velocity fluctuations overestimated [11]. The multi-overheat hot-wire methods reported in the literature for use in high-speed flow may employ a CTA but limit the lowest overheat level [12], at the expense of increased error in the separation procedure. Alternatively, others use a CCA method, the frequency response of which does not vary greatly with overheat, in combination with an electronic frequency-compensation circuit to compensate for the thermal inertia of the sensor [9,10,13]. To achieve a correct compensation, however, an additional in situ calibration is required to determine accurately the thermal response of the sensor at the local operating conditions. Earlier studies [10,14,15] have addressed this matter in a direct approach, by considering the thermo-electrical behav-
iour of the complete hot-wire anemometer system. Although this yields a satisfactory description of the characteristics of a particular system, it does not provide insight as to what aspects are primarily of a fundamental thermal nature inherent to the sensing technique, and what, on the other hand, is to be attributed to the particular electronic implementation of the measurement system. For this reason, the present study investigates the thermal behaviour in a more general sense, by studying these effects on the dynamic response first completely in the thermal domain. As stated earlier, for a similar desire for generality the details of the heat-convection mechanism itself are not considered, but rather the effect which the heat transfer has on the sensor operation. This extends the application of the analysis to include other types of thermal sensors as well. 2. Thermal domain analysis 2.1. Thermal model of the sensor operation The thermal structure of the sensor is modelled as a firstorder system, comprising a thermal capacity C and a heat conductance h to the ambient, the latter being representative of, say, the flow velocity. The sensor is heated by electrically supplying a heating power P, resulting in a rise of the sensor temperature Ts above the ambient temperature Tamb. The instantaneous heat balance of the sensor is then given by the following equation [1]: dTs PsC qh(TsyTamb) dt
(1)
As our main concern is with the dynamic behaviour of the system in order to measure rapidly fluctuating flow properties, a linearization of the sensor behaviour around its operating point is applied. Denoting average (or bias) properties by an overbar and fluctuating components by a prime, the averageand small-signal behaviour are expressed as, respectively:
# # # syT# amb) Psh(T
(2)
# s9sP9qhT # amb9yh9(T# syT# amb) (Csqh)T
(3)
where s is the Laplace variable. The dynamic behaviour is illustrated by the signal block scheme in Fig. 1, where the signals represent the fluctuating quantities while bias quan-
Fig. 1. Block scheme diagram of thermal sensor behaviour in the thermal domain.
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tities appear in the diagram blocks (note that overbars and primes have been omitted). The dashed portion represents the feedback circuit. The variation of P is zero in a constant-power operation mode (CPO), or made explicitly a function of the sensor temperature Ts by applying a feedback strategy to compensate temperature variations (constant-temperature operation mode, CTO). Thirdly, P may vary unintentionally due to, e.g., temperature dependence of the way the heating power is generated. This parasitic feedback effect will be seen to play an important role in operation modes that are a simplified implementation of the CPO, like a constant-heating-voltage or -current operation (CVO and CCO). 2.2. Thermal domain analysis of CPO and CTO modes In constant-power operation mode the sensor temperature is the signal representing the measurand, and the sensitivity to variations in the flow velocity (through the heat conductance h) and (ambient) temperature are derived from Eq. (3) to be: ETs Sh(0) flow: Sh(s)s s Eh 1qst0
(4)
ETs ST(0) temperature: ST(s)s s ETamb 1qst0
(5)
where Sh(0) and ST(0) are the common-mode sensitivities and t0 is the uncompensated time constant, given by T# syT# amb Sh(0)sy h#
ST(0)s1
C t0s # h
(6)
For the constant-temperature operation mode the sensor temperature is regulated to be maintained at a nearly constant level by applying feedback to the heating power:
# aTTs9 Psf(TsyTset)sPq
(7)
where Tset is the prescribed target sensor temperature and aTsdP/dTs the linearized thermal feedback sensitivity, which should evidently be negative to achieve the intended temperature compensation. As P now establishes the signal representing the measurand, the sensitivity to variations in the flow velocity and temperature for this case are given by: EP ETs Sh(0) Sh(s)s saT s Eh Eh 1qst1
(8)
EP ETs ST(0) ST(s)s saT s ETamb ETamb 1qst1
(9)
with the common-mode sensitivities Sh(0) and ST(0) and compensated time constant t1 being
aT # # Sh(0)s (TsyTamb) aTyh# aT h# ST(0)sy aTyh#
t1s
C yaTqh#
(10)
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In evaluation of the above results the following observations can be made regarding the fundamental properties of the thermal sensor systems, also with regard to the effect of the different operation modes. 2.2.1. Dynamic response In both CPO and CTO the dynamic response to velocity and temperature variations is governed by a single time constant (t0 and t1, respectively), and applying feedback evidently increases the apparent response speed significantly when aT is large:
tCPO t0 yaT s s1q # tCTO t1 h
(11)
Furthermore, the response time t0 depends on the thermal conductivity h# and decreases with increasing flow velocity. This is a fortunate property, as flow fields with higher velocities will display higher frequency fluctuations as well. Also, the time constants t0 and t1 are seen not to depend directly on the overheat level. In CTO the time constant depends on the feedback sensitivity aT and it is the non-linearity in the feedback that is responsible for the overheat-level dependence in resistive hot-wire anemometry referred to in Section 1. With the feedback voltage usually varying linearly with the bridge voltage (proportional to variation of the sensor temperature) and the heating power being quadratic in the voltage, the feedback sensitivity varies linearly with the feedback voltage and hence with the sensor overheat. 2.2.2. Multi-variable dependence The ratio of velocity to temperature sensitivity is independent of feedback and the same for CPO and CTO, as given by Sh(s) ST(s)
Sh(s) ST(s)
ž / ž / s
CPO
CTO
sy
T# syT# amb h#
(12)
This explains the basic principle of the multi-overheat method, where the relative sensitivity to velocity fluctuations increases with overheat level, while also revealing that the method can be applied in both CPO and CTO modes alike. Comparing Eqs. (6) and (10) shows that (Sh(0))CTO (ST(0))CTO aT h# s sy (Sh(0))CPO (ST(0))CPO aTyh#
(13)
Hence, CTO hot-wire operation at low overheat displays a deteriorated sensitivity in comparison to CPO, not through a fundamental dependence on the overheat level but again due to the non-linearity of the feedback. 2.3. Effect of feedback time delay in the CTO mode Although Eq. (11) appears to suggest that the response speed can be improved indefinitely by increasing the feedback aT, it is well known that a limit exists because of higherorder effects not accounted for in the simplified analysis.
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These higher-order effects can be interpreted as resulting in a time delay in the feedback path, which makes the feedback loop unstable at high aT. The origin of this time delay can be thermal, due to the finite thermal conduction in the sensor material, or caused by the finite speed of the electronic control circuits due to capacitive and inductive effects. For modern high-speed electronics the thermal effect will probably dominate unless very small sensor dimensions are considered. In the present discussion the exact nature of the time delay is not investigated, but rather how this affects the dynamic behaviour of the sensor operation. Therefore, we simply assume a constant time delay td to occur in the feedback path: P(t)sf(Ts(tytd)yTset)
(14)
For thermal delay effects the diffusion of heat is in first approximation independent of the temperature and heat-flow level, hence, the assumption that td does not depend on the operating point appears to be quite plausible. Using Eq. (13) the small-signal behaviour is
# s9saTexp(ystd)Ts9qhT # amb9yh9(T# syT# amb) (Csqh)T (15) The dynamic behaviour in the form of the normalized sensitivity function is given by
Sh(s) aT aT S(s)s s 1y # 1qst0y # exp(ystd) Sh(0) h h
ž /ž
y1
/
(16)
which, under the assumption that yaT4h# , can be written in a scaled parameter form as A S(f)s fqAexp(yf)
(17)
where f and A are the scaled complex frequency and feedback sensitivity, respectively: fsstd
yaTtd yaTtd As # s ht0 C
(18)
The real-valued amplitude characteristic H is defined accordingly as follows: H(F)sNS(jF)Ns
A
x(x cos F) q(F A sin F) 2
2
(19)
where Fsvtd, with v the radial frequency. The root-locus behaviour of this system as a function of the feedback strength A is depicted in Fig. 2, in which three special cases can be distinguished: (1) the creation of a complex pole pair; (2) the case of maximum flatness of H; and (3) the crossing of the imaginary axis. The corresponding frequency character-
Fig. 2. Root-locus (top) and frequency behaviour (bottom) of a first-order system with time-delayed feedback, in terms of non-dimensional complex and radial frequencies fsstd and Fsvtd , and non-dimensional feedback sensitivity AsyaTtd/C. Labels (1)–(3) in the diagrams refer to the operating conditions discussed in Section 2.3.
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istics for these cases are given at the bottom of the Figure and are obtained for, respectively, A1sey1s0.37, A2s0.5 and A3sp/2s1.57, while for the former two the scaled cut-off (y3 dB) frequencies are F1s0.66 and F2s1.12. In summary, for optimum adjustment of the operation control system, say to obtain a maximum flat frequency response, the required feedback sensitivity and the achievable cut-off frequency are inversely proportional to the time delay td. Assuming this value to be approximately constant, then the frequency characteristic deteriorates when a lower overheat is used only due to non-linearity of the feedback (i.e., the variation of aT). Note that this means that this effect can therefore be eliminated if a control system is applied that produces a constant value of aT, where the heating power is increased in proportion to the temperature change of the sensor.
3. Thermal behaviour of self-heating resistive sensors 3.1. Resistor-bridge configurations After the general thermal domain analysis of thermal sensors, we now consider the specific implementation of thermoresitive sensors operated under self-heating conditions. The bridge configuration commonly employed in this respect is depicted in Fig. 3, showing both configurations with and without an explicit feedback system. The ratio R1/R2 is called the bridge ratio, and R2/R3 the resistance ratio of the bridge. The bridge supply voltage and current are denoted by VSS and ISS, respectively. Assuming the resistance to vary (approximately) linearly with temperature, the overheat ratio aw can be written as RsyRs0 aws sb(TsyT0) Rs0
(20)
where Rs0 is the sensor resistance at reference temperature T0, and b is the temperature coefficient of resistivity. For both metal conductors and diffused silicon resistors b is typically of the order of 3–5=10y3 Ky1. Writing the response equation (3) in terms of the fluctuating sensor resistance, the following result is obtained (where for convenience T0 is taken equal to the average value of Tamb):
Rs0 Rs0 b # aRRs9s(1qst0)Rs9qaw # h9ybRs0Tamb9 h h
133
(21)
The left-hand side again represents the thermal feedback effect, with aRsdP/dRs the thermal feedback sensitivity in terms of the sensor resistance, equal to aRsbRs0aT. From this the sensitivity ratio and the effective time constant are derived as Sh(s) aw sy # ST(s) bh
(22)
teff bRs0 s 1y # aR h t0
ž
y1
/
(23)
which correspond directly to Eqs. (12) and (11), respectively. As the dynamic response is concerned, we observe as expected that for a negative feedback (aR-0 while b is positive) the time constant is reduced, while a positive feedback evidently has the opposite effect. These expressions provide a convenient means to analyse the implications for the dynamic behaviour of different operating modes. 3.2. Dynamic response behaviour of different operating modes Instead of a true constant-power operation, usually an electrically simpler implementation is employed in practice, such as a constant-current or -voltage method. Setting the (average) overheat of the sensor is then achieved by adjusting the supply voltage or current, respectively. In the CTO mode the overheat is regulated by the feedback system, and the required overheat is controlled by adjusting one of the resistors in the bridge circuit (typically either R1 or R3). The implications of this, as far as the dynamic response and effect of overheat are concerned, are determined by evaluating the parasitic feedback in each of these cases. Several typical implementations are considered below. 3.2.1. Constant-voltage operation Assuming a constant value of the bridge supply voltage VSS, the parasitic thermal feedback sensitivity is calculated as
bRs0 aR h#
ž
/
CVO
s
R1yRs aw(awq1) R1qRs
(24)
Fig. 3. Schematic configuration of a resistor sensor bridge, (a) without and (b) with temperature control.
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Hence, the feedback can be either positive or negative, depending on the ratio of Rs and R1. Interestingly, the feedback becomes zero when RssR1, which is also the condition for maximum temperature sensitivity of the resistor bridge. Note that this applies only to a single operating condition (Rs changes with temperature and, hence, with the overheat level), unless special adjustment measures are taken. To achieve a constant average overheat for changing average flow conditions VSS needs to be adjusted, while for maintaining a constant resistance ratio of the bridge at changing overheat ratio an adjustment of R1 is required. 3.2.2. Constant-current operation When considering a constant-current operation we may distinguish between the cases where either the bridge supply current ISS or the current Is through the sensor is kept constant. For a large bridge ratio, typically used to reduce power consumption or self-heating effects in the reference bridge arm, these two cases are nearly identical. Assuming constant Is the parasitic thermal feedback is
bRs0 aR h#
ž
/
s
CCO
aw awq1
(25)
making the expression for the time constant, see Eq. (23),
tCCO sawq1 t0
(26)
This shows that the CCO mode displays a positive parasitic feedback which has a time constant that increases with overheat ratio. 3.2.3. Constant-temperature operation The temperature compensation in the CTO mode is commonly achieved by applying a feedback from the bridge voltage to the bridge supply voltage by means of an amplifier, characterized by a voltage gain G and an offset voltage Voff. The latter is required to achieve a finite value of the transconductance amplification gtr [14,15]: 1 dIs Is R3 IsG gtrs sy 1qG 1y fy Is dRs Voff R2qR3 2Voff
≥ ž
/¥
(27)
the latter assuming that G41 and that a bridge resistance ratio of one is used (R2sR3); note also that gtr is negative. The thermal feedback is evaluated as follows:
bRs0 aR h#
ž
bRs0 s # (Is2q2Is2Rsgtr) h CTO
/
aw s q2awRs0gtr awq1
(28)
where the sensor current Is has been substituted from the steady heat balance of the sensor, which reads Is 2Rss h (TsyT0)sawh/b. The first term on the right-hand side of Eq. (28) is the parasitic feedback due to the resistance change
(compare Eq. (25)) while the second term represents the intended feedback due to the transconductance circuit. Assuming the latter is dominant as a result of a strong feedback, the time constant is, hence,
tCTO s(1y2awRs0gtr)y1 t0 aw h# Rs0 awq1 b
≥ ž
s 1qaw
1/2
y1
G Voff
/ ¥
(29)
where the second expression was obtained by substituting the bridge transconductance gtr from Eq. (27).
3.3. Some remarks regarding the effect of using a selfheating sensor The dependence of the system operation on the overheat as expressed in Eq. (29) is rather complicated due to the fact that the sensor is used in a self-heating configuration, where the sensor current Is acts as both the sensing and heating current. As a result, as can be seen from Eq. (28), the feedback sensitivity is cubic in Is, due to the combined effect that the heating effect is quadratic in the current through the resistor and the linear increase of the bridge transconductance with the sensing current, see Eq. (27). In this respect it is enlightening to consider the case where these sensing and heating effects are separated, e.g., by using different elements. We can then define a heating current and voltage, IH and VH, that are related to the sensor only by the explicit control system. If again a resistive heating element RH is employed (assumed independent of temperature), the combination with a transconductance feedback transfer (now defined as gtrsIs y1 dIH/dRs) yields a feedback sensitivity of dIH2RH aRs s2RHIHIsgtr dRs
(30)
whereas when a voltage amplification G is applied the result is dV H2/RH aRs s2IHIsG dRs
(31)
In both cases the feedback sensitivity increases linearly with the heating current IH when a linear amplification is used, the heating power being quadratic in the heating power. In order to achieve a constant thermal feedback sensitivity, a nonlinear amplification would therefore be required. Alternatively, a heating source may be considered which possesses a non-ohmic characteristic, such as a power-dissipating transistor. In that case the heating power can be made to vary linearly with the current (or voltage) output of the amplifier, by maintaining the voltage (current) constant. Then a constant feedback sensitivity is obtained with a linear amplification, as:
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dIH dVH aRsVH sVHIsgtr or: aRsIH sIHIsG dRs dRs
(32)
for transconductance or voltage amplification, respectively.
4. Discussion and conclusions An investigation was made to assess the effect of operating conditions such as overheat level and feedback linearity, on the dynamic response behaviour of thermal sensors. The major motivation for this study was the observed deterioration, as reported in the literature, of the dynamic response of CTO hot-wire systems with decreasing overheat level as employed in compressible flow research to obtain the separation of flow and temperature fluctuations. In order to provide insight into the fundamental dependencies, a general analysis is first carried out in the thermal domain, to reveal aspects that are independent of any specific electronic implementation. The thermal behaviour of the system is modelled as a first-order system with a constant time delay in the feedback loop. The major findings of this analysis illustrate the separation principle, as the ratio of flow to temperature fluctuation sensitivity indeed increases with the temperature difference between sensor and flow. However, no dependence on overheat of the overall time constant was found. Therefore, this has to be accounted to the effect of non-linearity of the feedback in the case of CTO systems, while in implementations of the CPO mode overheat dependence can be introduced through parasitic thermal feedback. This was confirmed and investigated further by considering the most commonly employed implementation, where a selfheating resistive element is used in a bridge configuration. As the wire current acts as both sensing and heating current, a complicated dependence of the dynamic behaviour on the wire overheat ratio aw is found. Therefore, when the dynamic response deterioration at low overheat ratios is to be eliminated, a non-linear transfer of the feedback circuit must be considered in order to achieve a constant thermal feedback sensitivity. Alternatively, when multi-component sensors are considered, this can be obtained more easily by employing separate non-ohmic heating elements.
References [1] G.C.M. Meijer and A.W. van Herwaarden (eds.), Thermal Sensors, IOP Publishing, Bristol, 1994. [2] P. Bradshaw, Thermal methods of flow measurement, J. Phys. E: Sci. Instrum., 1 (1968) 504–509.
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[3] B.W. van Oudheusden, Silicon thermal flow sensors, Sensors and Actuators A, 30 (1992) 5–26. [4] G. Comte-Bellot, Hot-wire and hot-film anemometers, in B.E. Richards (ed.), Measurement of Unsteady Fluid Dynamic Phenomena, Hemisphere Publishing Corporation, Washington, DC, 1977, pp. 123– 162. [5] J.D. Vagt, Hot-wire probes in low speed flow, Prog. Aerospace Sci., 18 (1979) 271–323. [6] H.H. Bruun, Hot-wire Anemometry, Oxford University Press, London, 1995. [7] L.S.G. Kovasnay, The hot-wire anemometer in supersonic flow, J. Aero. Sci., 17 (1950) 565–572. [8] M.V. Morkovin, Fluctuations and Hot-wire Anemometry in Compressible Flows, AGARDograph No. 24, AGARD, Paris, 1956. [9] A.J. Smits and J.P. Dussauge, Hot-wire anemometry in supersonic flow, in A Survey of Measurements and Measuring Techniques in Rapidly Distorted Compressible Turbulent Boundary Layers, AGARDograph No. 315, AGARD, Neuilly-sur-Seine, 1989, Ch. 5. [10] D. Bestion, J. Gaviglio and J.P. Bonnet, Comparison between constantcurrent and constant-temperature hot-wire anemometers in high-speed flows, Rev. Sci. Instrum., 54 (1983) 1513–1524. [11] F.K. Owen, C.C. Horstman and M.I. Kussoy, Mean and fluctuating flow measurements of a fully-developed, non-adiabatic, hypersonic boundary layer, J. Fluid. Mech., 70 (1975) 393–413. [12] R.D.W. Bowersox, Compressible turbulence measurements in a highspeed high-Reynolds-number mixing layer, AIAA J., 32 (1994) 758– 764. [13] P. Dupont, J.F. Debie`ve and J.P. Dussauge, Methods of measurement for compressible turbulence: status of constant-current hot-wire anemometry, ERCOFTAC 2nd SIG-4 Workshop on Compressible Turbulent Flows, Chaˆtillon, France, 19–20 Oct., 1995. [14] P. Freymuth, Feedback control theory for constant-temperature hotwire anemometers, Rev. Sci. Instrum., 38 (1967) 677–681. [15] A.J. Smits and A.E. Perry, The effect of varying resistance ratio on the behaviour of constant-temperature hot-wire anemometers, J. Phys. E: Sci. Instrum., 13 (1980) 451–456.
Biography Bastiaan W. van Oudheusden received the M.Sc. degree in aeronautical engineering in 1985 at the Delft University of Technology, Delft, The Netherlands. His thesis work comprised theoretical and experimental research on transition and turbulence in incompressible boundary-layer flow. In 1985 he joined the Electronic Instrumentation Laboratory of the Department of Electrical Engineering and in 1989 obtained the Ph.D. degree on the subject of silicon-integrated direction-sensitive flow sensors, which resulted in the development of a microelectronic thermal wind meter. Since 1991 he has been a member of the High Speed Aerodynamics Laboratory of the Department of Aeronautical Engineering, where he has been involved in experimental research on non-linear aeroelastic oscillation phenomena and in the compressible flow research and education of the laboratory.
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