Detection of direct and indirect noise generated by synthetic hot spots in a duct

Sound waves in a combustor are generated from fluctuations in the heat release rate (direct noise) or the acceleration of entropy, vorticity or compositional perturbations through nozzles or turbine guide vanes (indirect or entropy noise). These sound waves are transmitted downstream as well as reflected upstream of the acceleration point, contributing to the overall noise emissions, or triggering combustion instabilities. Previous experiments attempted to isolate indirect noise by generating thermoacoustic hot spots electrically and measuring the transmitted acoustic waves, yet there are no measurements on the backward propagating entropy and acoustic waves. This work presents the first measurements which clearly separate the direct and indirect noise contributions to pressure fluctuations upstream of the acceleration point. Synthetic entropy spots are produced by unsteady electrical heating of a grid of thin wires located in a tube. Compression waves (direct noise) are generated from this heating process. The hot spots are then advected with the mean flow and finally accelerated through an orifice plate located at the end of the tube, producing a strong acoustic signature which propagates upstream (indirect noise). The convective time is selected to be longer than the heating pulse length, in order to obtain a clear time separation between direct and indirect noise in the overall pressure trace. The contribution of indirect noise to the overall noise is shown to be non ∗Corresponding author Email address: fd314@cam.ac.uk (Francesca De Domenico*) Preprint submitted to Journal of LTEX Templates December 5, 2016 negligible either in subsonic or sonic throat conditions. However, the absolute amplitude of direct noise is larger than the corresponding fraction of indirect noise, explaining the difficulty in clearly identifying the two contributions when they are merged. Further, the work shows the importance of using appropriate pressure transducer instrumentation and correcting for the respective transfer functions in order to account for low frequency effects in the determination of pressure fluctuations.

measurements which clearly separate the direct and indirect noise contributions to pressure fluctuations upstream of the acceleration point. Synthetic entropy spots are produced by unsteady electrical heating of a grid of thin wires located in a tube. Compression waves (direct noise) are generated from this heating process. The hot spots are then advected with the mean flow and finally accelerated through an orifice plate located at the end of the tube, producing a strong acoustic signature which propagates upstream (indirect noise). The convective time is selected to be longer than the heating pulse length, in order to obtain a clear time separation between direct and indirect noise in the overall pressure trace. The contribution of indirect noise to the overall noise is shown to be non

Introduction
Acoustic perturbations arising from the heat release in combustion devices are a topic of increasing concern due to stricter noise regulations. The introduction of lean premixed pre-vaporised combustors, which produce low NO x emissions, but are more sensitive to fuel flow rate and thus pressure fluctuations, 5 has increased noise emissions and the potential for catastrophic instabilities [1].
In the last decade, a significant effort has been undertaken to understand and reduce noise and instabilities whilst maintaining emissions benefits through EUfunded research programmes such as ICLEAC, TIMECOP-AE and RECORD [2,3,4]. Pressure perturbations generated in combustors have traditionally 10 been classified into direct and indirect combustion noise. The first is caused by isentropic pressure waves that are produced by the unsteady heat release and propagate towards the turbine [5]. In the second mechanism, local regions of hot gas (hot spots or entropy spots), vortical structures [6] and composition inhomogeneities [7] are produced and then advected toward the turbine with 15 the mean flow. These entropy, vorticity and compositional waves are not directly associated with any pressure fluctuations in the linear regime. However, as they convect through regions with mean flow gradients (such as through turbine vanes or exhaust nozzles) acoustic waves are created, generating indirect combustion noise. These waves travel both upstream into the combustor as well 20 as downstream through the turbine. The upstream-travelling acoustic waves may couple with the acoustics of the system, stabilising or destabilising the original flame oscillation [8,9]. Marble and Candel [10] originally developed a one dimensional analytical model, deriving expressions for the magnitude of both direct and indirect noise in the low frequency limit, and more recent work 25 has revisited the issue [8,9,11,12].
One of the main obstacles in the investigation of entropy noise is the lack of unambiguous data linking entropy and pressure fluctuations, owing to the to the complex dynamics of flames in combustion chambers [13]. To overcome this issue, simplified laboratory scale experiments have been designed, in which the 30 flame is replaced with a more easily controlled unsteady source.
Bohn, Zukoski et al. [14,15,16] reported some of the first experiments attempting to isolate indirect noise by generating entropy spots synthetically using an electrical heater. However, due to the small temperature increase achieved (1 K) and the poor resolution of the data acquisition system available then, 35 direct and indirect noise could not be separated. This method of generating hot spots was applied more recently in the Entropy Wave Generator (EWG) rig developed at DLR Berlin, to study indirect combustion noise [17,18]. Acoustic waves resulting from the unsteady electrical heating of thin wires were measured downstream of a convergent-divergent nozzle both in the subsonic and super- 40 sonic regime. The DLR experiment generated interest in the community and prompted multiple theoretical and numerical endeavours to explain the experimental results [18,19,20,21,12,22,13]. In the case of the supersonic nozzle the signal was attributed to indirect noise and acoustic reflections [21]. In a study simulating numerically the operation of the EWG under subsonic condi-45 tions, Duran et al. [12] suggested that the pressure signal obtained was instead mainly due to direct noise. In contrast, according to their model, Lourier et al. [22] concluded that direct noise was nearly 6-7 times lower than indirect noise.
In all the simulations performed, the acoustic boundary conditions applied had a large influence in the interpretation of the results. 50 Due to the difficulties in explaining the results of the DLR EWG experiment and the differing interpretations in subsequent analytical and numerical simu-lations, further experiments have been developed to investigate the phenomena in depth. The Osney Thermo Fluid Laboratory at the University of Oxford has produced an Entropy Wave Generator Test Rig [23] where hot spots are 55 also generated via electrical heating. At Politecnico of Milan a new concept of Entropy Wave Generator has been developed, based on the alternating injection of hot and cold air upstream of a high pressure turbine [24,25]. Recent experiments have also been performed in the Hot Acoustic Test rig at DLR to investigate the sound generation and propagation due to accelerated cold spots 60 in a nozzle [26].
The aim of all these experiments has been to generate and isolate transmitted entropy noise in a clean and traceable way, without the complications induced by flames or vorticity, so that appropriate models can be suitably validated. To date, there have been no measurements of the upstream entropy noise generated 65 by the acceleration of synthetic hot spots: the experimental data reported so far refers only to the transmitted acoustic waves (acquired downstream of the nozzle). Yet the impact of the backward propagating waves is clear, as they can adversely affect the flame leading to instabilities [8,9,27].
The present study aims to investigate the physical mechanisms involved 70 in the generation of direct and indirect noise in a controlled environment.
The experiment produces a very simple geometric situation, amenable to onedimensional modelling. Synthetic hot spots are generated via the Joule effect and accelerated via an orifice plate. The acoustic signal is acquired upstream rather than downstream of the acceleration point; therefore, the results are Finally, we discuss an important issue which has not been previously reported, regarding the inadvertent use of condenser microphones in the low fre-90 quency range typical of entropy spot experiments. In the ultra low frequency range, they behave as a high pass filter, leading to potentially erroneous outputs.

Theoretical background
The theoretical underpinnings of the generation of acoustic waves via entropy spots in a flow have been discussed in a number of papers [28,10], and further 95 developed more recently [9,12,29]. Most theoretical studies consider the one dimensional case of hot spots generated from a heating source at rest and then convected through a compact nozzle. A schematic layout of this scenario is represented in Figure 1, where acoustic (P + 1 and P − 0 ) and entropy waves (σ) are generated in an unsteady heat release zone. The heat release zone is considered 100 compact, meaning that its length is much smaller than all the wavelengths considered here (i.e. low frequency waves). These waves manifest themselves as fluctuations of pressure p , velocity u and density ρ relative to the mean flow pressure, velocity and density (p,ū,ρ), and can be represented by their respective amplitudes in the downstream (+) and upstream (-) direction, where 105 (0) and (1) denote the regions upstream and downstream of the heat release interface: If one assumes negligible incoming waves (P − 1 = P + 0 = 0), one can derive expressions for the amplitudes of the waves generated at the heat release zone from the conservation of mass, enthalpy and entropy [12]: where M is the mean Mach number and q is the non-dimensionalised value of the fluctuating heat releaseQ (q =Q /ṁC pT ). These acoustic waves are referred to as 'direct' noise, as they are a direct result of the unsteady heat release. The acoustic waves thus generated propagate at the speed of soundc relative to the mean flow, and are reflected at the inlet and outlet of the duct 115 having acoustic reflection coefficients R i,a and R o,a , respectively ( Figure 1).
The entropy spots are advected downstream with the mean flow without generating an acoustic signature in the linear approximation [28]. If these waves are accelerated, they generate sound waves which propagate both downstream and upstream of the outlet. Marble and Candel [10] derived expressions for 120 the amplitude of a single backward-propagating (or 'reflected') wave due the acceleration of an hot spot for a compact nozzle (P − s ) under subcritical and supercritical (choked) isentropic conditions, between two sections with Mach numbers M 1 and M 2 , respectively: Under critical conditions, we have M 2 = 1, so that: The acoustic waves generated in this manner are referred to as 'indirect' 125 noise, as they are only indirectly related to the unsteady heat release upstream.
In this paper, the terms 'indirect noise' and 'entropy noise' are used interchangeably to indicate acoustic waves generated from the acceleration of entropy spots both upstream and downstream of the nozzle. From Marble and Candel [10], the reflected indirect noise is a negative perturbation relative to the mean, whereas In the absence of acoustic reflections at the boundaries, in an idealised one dimensional situation, the shape of the direct and indirect acoustic waves in the time domain is expected to be identical to that of the heat fluctuation q at the 135 heating grid and at the nozzle respectively (e.g. a square heat pulse should lead to a square acoustic pulse). Dispersive effects owing to molecular or turbulent diffusion alter the original shape of the non-uniformity, thus affecting the final pressure perturbation [30]. (0) Temperature measurement

Instrumentation
The experimental set-up is shown in Figure 2. Air flows through a tube at a controlled rate. Hot spots are produced synthetically by pulsing current through a heating device, generating a heat release pulse via the Joule effect.
The air flow exits through an orifice plate, which can be operated in subsonic The tube has an inner diameter of 42.6 mm and is made from sections of PVC and stainless steel 316. The PVC tube inner diameter is slightly larger than the steel tube by 0.2%, so the discrepancy is assumed to be negligible. The Two orifice plates are used: one with a 6.6 mm diameter hole (8 mm thickness), and a second with a 3 mm diameter hole (5 mm thickness). An orifice plate is easier and cheaper to manufacture than a convergent nozzle but the two are expected to behave in the same way regarding both the direct and the 190 indirect noise generated. In a first approximation, the flow through a generic area decrease interface can be assumed to be isentropic [31]. Additionally, both the orifice and the nozzle are expected to behave as a compact sources in the frequency range of the experiment.
The air temperature is determined using thin K-type thermocouples (fine 195 gauge exposed welded tip thermocouples type K, 0.076 mm wire diameter, labelled T i in Figure 2), whose time constant is found experimentally to be around

Flow rate measurements and conditions at the throat
The flow meter/controller records the volumetric flow rate (Q), mass flow rate (ṁ), temperature T f and pressure at the flowmeter P f at a sampling rate of 20-30 Hz. The bulk flow velocityŪ is calculated as: where A is the inner cross-sectional area of the tube,P andT are the measured pressure and temperature in the tube and R is the gas constant for air. In the 215 present analysis, the mean temperature in the tubeT is assumed to be identical to that acquired at the flow meter T f since the difference between these two temperatures is expected to be lower than 1%.
The Mach number at the orifice plate throat is necessary to estimate the 220 intensity of the entropy noise, yet it is difficult to measure it directly in subsonic conditions. A calculated value for the Mach number M T at the throat can be obtained by assuming isentropic expansion from the measured mean pressure in the straight section of the tube,P , to the pressure at the throat, estimated to be atmospheric pressure (P T = P a ).
The upstream pressureP is measured using the Kulite absolute pressure transducer, and the upstream Mach numberM is calculated from the bulk velocity and mean temperature (M =Ū / γRT ).
The markers in Fig. 4(a) show the upstream pressureP and velocityŪ measured in the tube at several operating points for the 3 mm (red dots) and 6.6  V, and the excess energy is dissipated. However, in the first few milliseconds of the pulse, the capacitor in the driving system leads the power supply to release a higher current, before it auto-adjusts the current to its maximum nominal limit. The initial peak in the delivered current makes the wires warm up faster than they would do with a square pulse. It can be observed that there is no

Temperature measurements
Accurate information regarding the temperature and shape of the hot spots generated by the heating device is crucial to understand and model the exper- where τ tc is the time constant of the thermocouple. voltage variation ∆E can be expressed as [32]: where T W is the temperature of the hot wire (T W ∼330 • C). For small tempera-290 ture increases, the change in the output voltage of the anemometer is in a first approximation proportional to the change in the air temperature. Assuming that the anemometer captures the shape of the temperature pulse without distortion or attenuation, the shape of the output voltage of the anemometer is used to represent of the shape of the hot spot.

295
The different measurements of the air temperature are kept as consistently as possible, but there is an estimated uncertainty of ±2 K in the determination of the absolute value of the air temperature rise. This is due to: (i) difficulties in accessing the correct location for some measurements (i.e. as close as possible to the heating grid and to the nozzle), (ii) internal differences between the trans-

Pressure transducer characteristics
Piezoresistive pressure transducers and microphones convert an acoustic signal into an electrical signal. Piezoresistive transducers rely on the piezoresistive 310 effect that occurs when the electrical resistance of a material changes in response to applied mechanical strain [33]. They offer a flat frequency response and zero phase shift even at very low frequencies. Microphones translate pressure fluctuations into a voltage via a diaphragm or a cantilever beam exposed to the incident sound pressure, using cavities and vents as pressure equalisation 315 channels. Microphones therefore act as differential pressure measurements with capacitance, so that the sensors only respond to dynamic pressure fluctuations, unlike pressure transducers [34,35]. The added capacitance means that at low frequency they behave as a high pass filter, with lower gain and shift in phase.
On the other end, capacitive microphones are capable of higher sensitivity and 320 dynamic range than piezoresistive pressure transducers.
The transfer function F p (f ) of a condenser microphone such as the G.R.A.S.
40bp has been shown to be well represented by that of a high pass filter function [33,34]: where f 0 is the cut-on frequency of the microphone and G is the frequencyindependent sensitivity of the microphone, called open-circuit voltage [33]. In the present experiment we calibrate the response of the condenser microphone to show that its corrected response can yield the original pressure data. The differences in gain and phase between the signals acquired by the two 335 G.R.A.S. microphones and the Kulite reference transducer are shown in Figure   7. As expected, the signals displayed by the G.R.A.S. transducers are attenuated ( Fig. 7(a)) and phase shifted ( Fig. 7(b)). The two G.R.A.S. transducers behave slightly differently at low frequencies. The cut-on frequency was experimentally determined as 1.02 Hz, with a phase shift of π/4. This is consistent with the

Results
The response of the system to the generation and convection of synthetic    The forward and backward waves in the tube nearly cancel out, explaining why the pressure in the tube oscillates around zero. In the long tube data (Fig. 9a), the oscillation frequency f 38 Hz corresponds to a quarter of wave modes (λ/4 L), which is consistent with the fact that the inlet of the tube behaves as a closed wall (R i,a +1).

Case C: Accelerated flow (subsonic)
In these experiments, the downstream end of the tube is terminated by the 6.6 mm orifice plate, through which the air flow accelerates. The experimental 435 conditions tested are listed in Table 2. It was experimentally determined that the bulk flow velocity required to choke the flow with the 6.6 mm orifice is 4.2 m/s (see Figure 4 in Sec. 3.2) therefore the flow through the orifice is subsonic in the test conditions listed.    Table 2. Two thermocouples are located in the orifice to detect the arrival of hot spots at the outlet of the tube. Figure 12 zooms on Case C-3 (Table 2) to identify the characteristic components of the acoustic signal.   Therefore, these negative peaks are attributed to the acceleration of hot spots through the orifice plate, the so-called indirect noise. A third contribution to the acoustic signal can be seen in the pressure signal in Figure 12: after the direct noise peak, the pressure fluctuation does not return to zero, but becomes negative (negative oscillation labelled P N ). This effect may arise from the mean 475 lower density of the flow, but requires further investigation.  [17,18], Oxford EWG [23] and [40]), condenser microphones rather than pressure transducers were used, without mentioning if any correction was applied to the output of the microphones.
In [42] the issue of the microphone transfer function was brought up. How-535 ever, the cut-on frequency obtained in [42] from numerical considerations is 12 Hz, 10 times larger than the cut-on frequency experimentally determined in this work and reported in the specifications of G.R.A.S. microphones [36]. Therefore, we suggest that in the future, all such low frequency measurements need to be verified for accuracy according to the calibration suggested here, or that 540 piezo sensors be exclusively used for such low frequency experiments. However, when they superpose, both the positive and the negative peaks seem to decrease and the slope of the signal changes.

Short tube
As shown in the case of the long tube (Fig. 13), the amplitude of the direct noise is nearly four times higher than that of the indirect noise, and extracted from the overall pressure trace, even if its influence as a change of the decay rate of the curve is clear. Another important result is the need to carefully account for the pressure transducer response at the very low frequencies typical of such rigs, which are limited by the cooling time of the wires. Condenser microphones behave as high pass filters, which significantly attenuate the pressure signal and lead to a phase shift at frequencies below about 10 Hz, and are unable to follow static pressure increases or decreases. This generates non-physical ringings in the displayed output, which can lead to a misinterpretation of the results. Once the transfer functions of the microphones are taken into account, their outputs can 665 be brought to a good agreement with piezoresistive transducers.