Mathieu Chalnot

Anthony Coustou

Hervé Aubert

Patrick Pons

Maylis Lavayssière

Alexandre Lefrançois

Jérôme Luc

Wireless Transmission of Friedlander-type Signals for the Dynamic Measurement of Blast Pressure

Keywords: Wireless transmission, explosive, detonation, air blast, radiofrequency, dynamic pressure measurement

During explosive detonation or air blast experiments, long cables are commonly used for transmitting signals delivered by pressure sensors to the safe place of the acquisition unit. While constant efforts are undertaken for enlarging the bandwidth of sensors in order to improve the measurement precision of the peak pressure, the limitations of the wired transmission of blast pressure signals delivered by these sensors are not addressed. We discuss here such limitations and propose a wireless new solution for the dynamic measurement of Friedlandertype signals delivered by ultra-wideband sensors (> 10 MHz). Contrary to the wired solution, the distance between the sensor and the acquisition unit does not limit the measurement bandwidth of the wireless setup. Experimental results are reported for validation purposes and pave the way of the dynamic measurement of blast pressure variations occurring at the heart of the fireball generated during explosions.

Introduction

During a high explosive detonation, a rapid amount of energy is released, generating a supersonic shock wave, with discontinuities in pressure, gas density, temperature and particle velocity across the wave front. At the shock wave front, the pressure reaches quasi-instantaneously the so-called peak pressure 𝑃𝑃 𝑚𝑚𝑚𝑚𝑚𝑚 and then, it decays rapidly back to ambient pressure 𝑃𝑃 𝑚𝑚 during the time 𝑇𝑇 (typically a few hundreds microseconds) of the so-called positive phase. This phase is often followed by the negative phase, during which the pressure is below the ambient pressure. Such pressure-time profile is usually modeled by the Friedlander function displayed in Figure 1 (see, e.g., [START_REF] Baker | Explosions in Air[END_REF][START_REF] Ismail | Study of the Blast Wave Parameters from Small Scale Explosions[END_REF][START_REF] Formby | Blast characteristics and TNT equivalence values some commercial explosives detonated at ground level[END_REF][START_REF] Goel | An Abridged Review of Blast Wave Parameters[END_REF][START_REF] Rigby | Validation of semi-empirical blast pressure predictions for far field explosions -is there inherent variability in blast wave parameters?[END_REF]). Structure vulnerability studies and high explosive characterization need an accurate estimation of the pressure to compare with hydrocode numerical simulations (see, e.g., [START_REF] Fickett | Detonation: Theory and Experiment[END_REF]).

In a typical air blast experimental setup, high-precision pressure sensors are used for measuring the pressuretime profile [START_REF] Chaudhary | Pressure Sensors for Blasts and Shock Waves: State of Art[END_REF][START_REF] Bauer | PVDF shock sensors: applications to polar materials and high explosives[END_REF], and constant efforts are undertaken for enlarging the bandwidth of such sensors. Nowadays, commercially available piezoelectric sensors [START_REF]Piezoelectric transducers for high frequency measurements[END_REF] can give signals with rise time of about 40 ns. Since sooner or later, the measurement of shorter rise times will be made possible, we address in this paper the issue of transmitting ultrafast signals delivered by wideband (> 10 MHz) pressure sensors. Long cables are commonly used during explosive detonation or air blast experiments for transmitting Friedlander-type signals from pressure sensors to the safe place of the acquisition unit (see, e.g., [START_REF] Silver | Evaluation of Air Blast Measurement Techniques, 75th Shock and Vibration Proceedings[END_REF]). However, as shown in Section II, bandwidth limitation will make this standard and well-known wired technique unsuitable for transmitting over long distances. Moreover, extreme conditions involved during explosions (temperature over 1000 degrees Celsius with intense light, vibrations, ionized gases, etc.) may degrade the functionality of conventional wired measurement setups.

In order to overcome the limitations of the wired technique for transmitting signals delivered by sensors during high explosive detonations, a wireless experimental setup is proposed in this paper. The voltage at the pressure sensor output is used here for the analog frequency-modulation of a radiofrequency carrier signal. The resulting frequency-modulated signal is next wirelessly transmitted to the acquisition unit, which proceeds to the digital demodulation. Very preliminary results investigating this solution were reported by us in [START_REF] Fourmann | Wireless Sensors for the Incident Pressure Measurement in Air Blast[END_REF]. It is shown here for the first time that the proposed wireless technique allows transmitting higher signal bandwidth than standard wired transmission setups and consequently, may be useful for remotely measuring Friedlander-type signals delivered by ultra-wideband sensors. Moreover, contrary to the wired setups, it is shown that the distance between sensors and the acquisition unit does not limit the bandwidth of the proposed wireless measurement setup.

The paper is organized as follows: Section II highlights the limitations of the wired setup commonly used for transmitting signals from the sensors output to the acquisition unit during air blast experiments. Section III details the design of the proposed wireless setup to overcome these limitations. From experimental results, Section IV validates that, contrary to the wired solution, the distance between sensors and the acquisition unit does not limit the measurement bandwidth of the wireless setup. Moreover, Section IV reports the dynamic measurement of blast pressure variations occurring within the fireball generated during a controlled explosion. Finally, Section V gives the conclusion and proposes future work.

Wired Setup for the Dynamic Measurement of Blast Pressure: Description and Limitations

During an explosive detonation (see Figure 2), a shock wave is generated and moves supersonically, creating an overpressure. Nowadays, for dynamically measuring the blast pressure during such an event, sensors (or gauges) are distributed around the charge to be characterized, and long coaxial cables (> 50 m) are used for transmitting the Friedlandertype signal delivered by sensors to the safe place of an acquisition unit. The typical wired setup is shown in Figure 3. Piezo-electric pressure sensors with high output impedance (~1 GΩ) are often used for such experiment [START_REF] Silver | Evaluation of Air Blast Measurement Techniques, 75th Shock and Vibration Proceedings[END_REF]. During the explosion, when the shock wave front impinges on the sensor, an amount of electric charge is produced at the sensor output, depending on the mechanical stress induced by the pressure on the piezoelectric crystal. The conditioning circuit converts the charge quantity into a voltage by using a common-drain Metal Oxide Semiconductor (MOS) amplifier. At the output port of this circuit, the impedance does not exceed 100 Ω and a direct current (DC) voltage of typically few tens of Volts is generated due to the biasing current 𝐼𝐼 𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 of the amplifier. In order to avoid any current leakage, this DC voltage is filtered by using a series capacitor 𝐶𝐶 𝐷𝐷𝐷𝐷 of few μF (here, 𝐶𝐶 𝐷𝐷𝐷𝐷 = 15 μF).

Figure 3.

Standard wired setup for the dynamic measurement of the blast pressure. This setup allows the remote estimation of the aerial pressure peak 𝑃𝑃 𝑚𝑚𝑚𝑚𝑚𝑚 occurring just after the explosive ignition. 𝑍𝑍 𝑂𝑂𝐵𝐵𝐷𝐷 denotes here the input impedance of the digital oscilloscope used for the direct measurement of the baseband signal transmitted through long RG58 coaxial cable (typically of 50 m or more).

The DC power unit of the sensor is usually located in a shelter close to the explosion (at a distance of about 10 m). The RG58 coaxial cable of few tens of meters long (typically of 50 m or more) is commonly used for transmitting the baseband signal generated at the sensor output to the safe place of the acquisition unit. In this unit, the digital oscilloscope allows the direct measurement of the received signal. This conventional wired setup exhibits poorly documented issues for the dynamic measurement of the blast pressure and especially, for the high-precision measurement of the pressure peak occurring just after the explosion.

First, as the series capacitor 𝐶𝐶 𝐷𝐷𝐷𝐷 is connected to a long transmission line loaded by the high (but finite) input impedance of the digital oscilloscope 𝑍𝑍 𝑂𝑂𝐵𝐵𝐷𝐷 (typically 1 MΩ shunted by 10 pF), an undesirable high-pass filtering of the transmitted baseband signal occurs in the wired setup. If the corresponding cut-off frequency is not sufficiently low, the measured late temporal variation of the received signal may not reproduce the voltage at the sensor output. Furthermore, due to the shunt capacitance of transmission cables (~100 pF/m for the RG58 coaxial cable) combined with the input impedance of the digital oscilloscope, a low-pass filtering of the transmitted baseband signal occurs. Since the cut-off frequency of this low-pass filtering does not exceed in practice few tens of MHz, the rejection of higher frequencies in the received signal takes place. The longer the coaxial cable, the lower the cut-off frequency and as a result, the narrower the transmission bandwidth of the wired setup. This undesirable effect of bandwidth reduction is illustrated in Figure 4. This latter displays the voltage at the output port of RG58 coaxial transmission cables, when a Heaviside step voltage of 1 V is applied at their input port. As expected, the longer the transmission cables, the higher the rise time of the output voltage (see Table 1). Such frequency bandwidth limitation is the major weakness of the conventional transmission line setup for transmitting over long distances the burst signals delivered by the wideband (>10 MHz) sensors. Moreover, as the input impedance 𝑍𝑍 𝑂𝑂𝐵𝐵𝐷𝐷 ( 1 MΩ shunted by 10 pF ) of the oscilloscope does not match the characteristic impedance 𝑍𝑍 𝐷𝐷 (about 50 Ω over the bandwidth of interest) of the coaxial transmission lines, the transmitted baseband signal is reflected by the oscilloscope input impedance, and propagates back to the cable input. Next, this signal is reflected again, as the impedance 𝑍𝑍 𝑖𝑖𝑖𝑖 connected to the cable input differs generally from the characteristic impedance 𝑍𝑍 𝐷𝐷 of the coaxial line. Consequently, the steady state value is reached after signal roundtrips between input and output of the cable, whose duration depends on the cable length and level of impedance mismatches. For the sake of illustration, the voltage at the output port of RG58 coaxial cable is displayed in Figure 5 for 𝑍𝑍 𝑖𝑖𝑖𝑖 = 47.5Ω, when the Heaviside step voltage of 1 V is applied at the cable input. As shown in Table 2, the longer the coaxial cable, the larger the time required by the output voltage to reach the steady state value. Such undesirable effect of inevitable impedance mismatches at the input and output ports of cables over the wide bandwidth of interest is the second major weakness of conventional wired setups for transmitting the aerial pressure signal delivered by ultra-wideband sensors. Let the so-called Friedlander-type voltage 𝑉𝑉 𝐹𝐹 (𝑡𝑡) be applied at the input port of a transmission cable. This voltage is defined as follows:

𝑉𝑉 𝐹𝐹 (𝑡𝑡) = 𝑉𝑉 𝑚𝑚𝑚𝑚𝑚𝑚 𝑡𝑡 𝜏𝜏 for 0 ≤ 𝑡𝑡 ≤ 𝜏𝜏 (1-a) = 𝑉𝑉 𝑚𝑚𝑚𝑚𝑚𝑚 �1 - 𝑡𝑡-𝜏𝜏 𝑇𝑇 � 𝑒𝑒 -𝜆𝜆 𝑡𝑡-𝜏𝜏 𝑇𝑇 for 𝑡𝑡 > 𝜏𝜏 (1-b)
Eq. ( 1) may be used to model the voltage delivered by a pressure sensor during an explosion, where 𝜏𝜏 denotes the time required by the voltage to reach its maximum value 𝑉𝑉 𝑚𝑚𝑚𝑚𝑚𝑚 , 𝑇𝑇(≫ 𝜏𝜏) is the duration of the positive phase, and 𝜆𝜆 designates a positive constant. Figure 6 displays the simulated voltage at the output port of RG58 coaxial cables, when the voltage-time profile of Eq. ( 1) is applied at the input. As expected from the above analysis, the higher the cable length, the larger the discrepancies between the input and the output voltage profiles. Since the measurement of blast effects generated by explosives requires long distances (and therefore, long cables) for transmitting the sensor signals to the safe place of the acquisition unit, the derivation of the pressure peak 𝑃𝑃 𝑚𝑚𝑚𝑚𝑚𝑚 from the measurement of the peak voltage 𝑉𝑉 𝑚𝑚𝑚𝑚𝑚𝑚 may suffer from high inaccuracy.

In order to overcome the above-mentioned limitations of standard wired setups for the dynamic measurement of blast pressure signal, a wireless solution is proposed in the next Section.

(a) (b) Figure 6: Simulated voltage at the output port of RG58 coaxial transmission cables, when the Friedlander-type voltage 𝑉𝑉 𝐹𝐹 (𝑡𝑡) defined by Eq. ( 1) is applied at the input port of the cables, with 𝑉𝑉 𝑚𝑚𝑚𝑚𝑚𝑚 = 1 V, 𝑇𝑇 = 100 μs, 𝜆𝜆 = 1 and 𝜏𝜏 = 40 ns (using the commercial off-the-shelf pressure sensor reported in [START_REF]Piezoelectric transducers for high frequency measurements[END_REF], 𝜏𝜏 may actually reach 40 𝑛𝑛𝑛𝑛) and for different cable lengths : (a) between 250 m and 1 km and (b) between 25 m and 150 m. The impedance 𝑍𝑍 𝑖𝑖𝑖𝑖 of the voltage source at the input of the cable is of 50 𝛺𝛺, and simulations results are performed by using Advanced Design System software.

Wireless Setup for the Dynamic Measurement of Blast Pressure

Signal: Design Methodology

Operating principle

To transmit the signal delivered by a pressure sensor during an explosive detonation or a blast experiment, the proposed wireless setup performs: i. the analog frequency modulation of the radiofrequency (RF) carrier signal with the voltage 𝑉𝑉 𝑚𝑚𝑚𝑚𝑚𝑚 delivered at the output port of the sensor conditioning circuit (see Figure 7(a)). Ideally, this voltage depends linearly on the pressure existing at the sensor location;

ii. the wireless propagation of the frequency-modulated (FM) signal through the propagation channel;

iii. the estimation of instantaneous frequencies embedded in the received FM signal from the digital microwave frequency counter (see Figure 7(b)). From these frequencies, the time-variation of the modulating voltage 𝑉𝑉 𝑚𝑚𝑚𝑚𝑚𝑚 (𝑡𝑡) delivered at the output port of the conditioning circuit is estimated; iv. Finally, knowing the sensitivity of the pressure sensor, the derived signal 𝑉𝑉 𝑚𝑚𝑚𝑚𝑚𝑚 (𝑡𝑡) allows the estimation of the pressure profile 𝑃𝑃(𝑡𝑡) at the sensor location. The Tx-unit converts the voltage variations 𝑉𝑉 𝑚𝑚𝑚𝑚𝑚𝑚 (𝑡𝑡) at the output of the conditioning circuit into a frequency deviation of the RF carrier signal by using a Voltage Controlled Oscillator (VCO). The resulting analog FM signal is wirelessly transmitted to the Rx-unit by using the Tx-antenna. In the Rx-unit, the received FM signal is first amplified and then low-pass filtered in order to remove eventual aliasing spectrum effect. The sampling is performed by using an Analog-to-Digital Converter (ADC) device, and the variation of the instantaneous radio-frequency 𝑓𝑓(𝑡𝑡) of this signal at any time 𝑡𝑡 is derived from Fast Fourier Transform (FFT).

Calibration process

The VCO device in the Tx-unit converts ideally a voltage variation ∆𝑉𝑉 𝑚𝑚𝑚𝑚𝑚𝑚 into the instantaneous frequency shift ∆𝑓𝑓 = 𝐾𝐾 0 ∆𝑉𝑉 𝑚𝑚𝑚𝑚𝑚𝑚 , where 𝐾𝐾 0 is called the sensitivity coefficient of the VCO. In practice, this coefficient is not constant and depends, for example, on the ambient temperature [13]. Hence, the calibration of the wireless setup is required for taking into account the eventual deviation from the ideal linear conversion law.

The proposed calibration process is driven as follows: before the explosive detonation, a controlled periodic voltage 𝑉𝑉 𝑐𝑐𝑚𝑚𝑐𝑐 (𝑡𝑡) is applied at the input port of the VCO device (a saw tooth signal is used in this work). The resulting FM signal is wirelessly transmitted through the propagation channel to the Rx-unit, and the instantaneous frequency 𝑓𝑓 𝑐𝑐𝑚𝑚𝑐𝑐 (𝑡𝑡) of the received FM signal is measured. Since the calibration voltage 𝑉𝑉 𝑐𝑐𝑚𝑚𝑐𝑐 (𝑡𝑡) is periodic, each given voltage 𝑉𝑉 𝑐𝑐𝑚𝑚𝑐𝑐 is applied many times to the VCO input during the calibration process. Due to electronic noise, identical (or very close) voltages do not generate identical 𝑓𝑓 𝑐𝑐𝑚𝑚𝑐𝑐 . The polynomial regression of 𝑓𝑓 𝑐𝑐𝑚𝑚𝑐𝑐 on 𝑉𝑉 𝑐𝑐𝑚𝑚𝑐𝑐 is performed in this study. At the end of the calibration process, any modulating voltage 𝑉𝑉 applied at the input of the VCO can be remotely estimated from the measurement of the instantaneous frequency 𝑓𝑓 embedded in the received FM signal.

Key descriptors of the wireless transmission setup and design methodology

One key descriptor of the proposed wireless solution is the 3 𝑑𝑑𝑑𝑑 bandwidth of the setup. This bandwidth is mainly limited by three following components: (1) the sensor bandwidth 𝑑𝑑 𝐵𝐵 , (2) the bandwidth of the VCO device 𝑑𝑑 𝑉𝑉𝐷𝐷𝑂𝑂 and, (3) the bandwidth of the digital microwave frequency counter 𝑑𝑑 𝑐𝑐𝑚𝑚𝑐𝑐𝑖𝑖𝑡𝑡 . The bandwidth 𝑑𝑑 𝑉𝑉𝐷𝐷𝑂𝑂 is required to include 𝑑𝑑 𝐵𝐵 , and the output impedance of the conditioning circuit must match the input impedance of the VCO device. Moreover, the bandwidth 𝑑𝑑 𝐹𝐹𝐹𝐹 of the transmitted FM signal, which is given by Carson rule 2𝑑𝑑 𝐵𝐵 (1 + 𝑚𝑚 0 ) where 𝑚𝑚 0 denotes the modulation rate [START_REF] Smith | The Scientist & Engineer's Guide to Digital Signal Processing[END_REF][START_REF] Carson | Notes on the theory of modulation[END_REF], must be included in the bandwidth of all RF devices of the wireless setup. Furthermore, the amplitude of the received FM signal must be amplified for taking advantage of the maximal full-scale range offered by the ADC device. After amplification, the received FM signal is sampled with a sampling rate 𝑓𝑓 𝑠𝑠𝑚𝑚𝑚𝑚𝑠𝑠 which must be higher than 2𝑓𝑓 0 to satisfy the Shannon criterion, where 𝑓𝑓 0 denotes the RF carrier frequency.

In order to measure the instantaneous frequency 𝑓𝑓(𝑡𝑡 𝑖𝑖 ) in the received FM signal at any time 𝑡𝑡 𝑖𝑖 , a time-windowing of duration 𝑇𝑇 𝑚𝑚𝑚𝑚𝑚𝑚𝑠𝑠 (< 1 2𝑑𝑑 𝐵𝐵 ⁄

) and starting at time 𝑡𝑡 𝑖𝑖 , is performed to the signal. Next, FFT is applied to the windowed signal for deriving the set of spectral amplitudes for 𝑁𝑁 = 𝑇𝑇 𝑚𝑚𝑚𝑚𝑚𝑚𝑠𝑠 𝑓𝑓 𝑠𝑠𝑚𝑚𝑚𝑚𝑠𝑠 frequencies. Following [START_REF] Rife | Single-Tone Parameter Estimation from Discrete-Time Observations[END_REF], we assume here that the frequency for which the spectral amplitude of FFT takes its highest value provides the estimation of the instantaneous frequency 𝑓𝑓(𝑡𝑡 𝑖𝑖 ) in the FM signal at time 𝑡𝑡 𝑖𝑖 . Since the frequency resolution of the FFT does not exceed 1 𝑇𝑇 𝑚𝑚𝑚𝑚𝑚𝑚𝑠𝑠 ⁄ = 𝑓𝑓 𝑠𝑠𝑚𝑚𝑚𝑚𝑠𝑠 𝑁𝑁 ⁄ , and as the principal source of noise is the quantization error variance 𝜎𝜎 𝑞𝑞 2 of the ADC device (𝜎𝜎 𝑞𝑞 2 = 𝑞𝑞 2 12 ⁄ , where 𝑞𝑞 is the quantization error given by 2 𝑉𝑉 𝐹𝐹 2 𝑁𝑁 𝐷𝐷 -1 ⁄ ), it can be derived from [START_REF] Rife | Single-Tone Parameter Estimation from Discrete-Time Observations[END_REF] that the standard deviation of the estimated instantaneous frequency is lower bounded by 𝜎𝜎 𝑚𝑚𝑖𝑖𝑖𝑖 given as follows:

𝜎𝜎 𝑚𝑚𝑖𝑖𝑖𝑖 = 2 -𝑁𝑁 𝐷𝐷 𝜋𝜋 𝑉𝑉 𝑀𝑀 𝑉𝑉 𝑅𝑅𝑅𝑅 𝑓𝑓 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 �𝑁𝑁(𝑁𝑁 2 -1) (2)
where 𝑁𝑁 𝐷𝐷 and 𝑉𝑉 𝐹𝐹 denote, respectively, the effective digital resolution and the maximum input voltage of the ADC device, and 𝑉𝑉 𝑅𝑅𝐹𝐹 designates the voltage applied to the input of ADC device. In practice, N should be then chosen so that 𝜎𝜎 𝑚𝑚𝑖𝑖𝑖𝑖 is close to the standard deviation of the calibration signal 𝑉𝑉 𝑐𝑐𝑚𝑚𝑐𝑐 (𝑡𝑡). Moreover, by applying the zero-padding technique [START_REF] Smith | The Scientist & Engineer's Guide to Digital Signal Processing[END_REF], which consists of adding a number 𝑍𝑍 of zero-valued samples in the time-windowed FM signal, the number of frequency samples is finally given by 𝑁𝑁 + 𝑍𝑍. This technique does not enhance the frequency resolution of the ADC, but it allows improving the resolution of the FFT. The number 𝑍𝑍 should be then chosen so that 𝑓𝑓 𝑠𝑠𝑚𝑚𝑚𝑚𝑠𝑠 (𝑁𝑁 + 𝑍𝑍) ⁄ ≈ 𝜎𝜎 𝑚𝑚𝑖𝑖𝑖𝑖 . Finally, it can be observed from Eq. ( 2) that the measurement resolution of the instantaneous frequency at any time 𝑡𝑡 𝑖𝑖 may be enhanced by: i. improving the effective digital resolution of the ADC device;

ii. enlarging the bandwidth of the digital microwave frequency counter 𝑑𝑑 𝑐𝑐𝑚𝑚𝑐𝑐𝑖𝑖𝑡𝑡 from which the measurement duration -or equivalently, the number of frequency samples in the FFT-can be derived;

iii. increasing the received RF power 𝑃𝑃 𝑅𝑅𝑅𝑅 for rising the voltage applied to the input of ADC device. Moreover, the lowest RF power 𝑃𝑃 𝑅𝑅𝑅𝑅 𝑀𝑀𝑀𝑀𝑁𝑁 required at the ADC input, called the sensitivity of the ADC, depends on the minimum carrier-to-noise power ratio 𝐶𝐶𝑁𝑁𝐶𝐶 𝐹𝐹𝐵𝐵𝑁𝑁 required for ensuring the FM demodulation. 𝐶𝐶𝑁𝑁𝐶𝐶 𝐹𝐹𝐵𝐵𝑁𝑁 is found to be about 10, whatever the modulation rate [START_REF] Wojnar | Exact Threshold Location in Analog FM Systems[END_REF]:

𝐶𝐶𝑁𝑁𝐶𝐶 𝐹𝐹𝐵𝐵𝑁𝑁 = 𝑃𝑃 𝑅𝑅𝑅𝑅 𝑀𝑀𝑀𝑀𝑁𝑁 𝑃𝑃 𝑁𝑁𝑁𝑁𝑀𝑀𝑁𝑁𝑁𝑁 ≅ 10 (3)
where 𝑃𝑃 𝑁𝑁𝑂𝑂𝐵𝐵𝐵𝐵𝑁𝑁 denotes the noise power in the carrier signal. This power is estimated from the quantization error variance 𝜎𝜎 𝑞𝑞 2 of the ADC device. From Eq.( 3), the sensitivity of ADC device is then derived as follows:

𝑃𝑃 𝑅𝑅𝑅𝑅 𝑀𝑀𝑀𝑀𝑁𝑁 = 10 3 2 -2𝑁𝑁 𝐷𝐷 𝑉𝑉 𝐹𝐹 2 (4)
Consequently, according to the link budget based on Friis Equation (see, e.g., [START_REF] Balanis | Antenna Theory: Analysis and Design 3rd[END_REF]), the received power 𝑃𝑃 𝑅𝑅𝑅𝑅 is higher than the ADC sensitivity when the transmitted power 𝑃𝑃 𝑇𝑇𝑅𝑅 is larger than 𝑃𝑃 𝑇𝑇𝑅𝑅 𝑀𝑀𝑀𝑀𝑁𝑁 given by:

𝑃𝑃 𝑇𝑇𝑅𝑅 𝑀𝑀𝑀𝑀𝑁𝑁 = 𝑃𝑃 𝑅𝑅𝑅𝑅 𝑀𝑀𝑀𝑀𝑁𝑁 𝜌𝜌 𝐺𝐺 𝑠𝑠𝑠𝑠𝑠𝑠𝑎𝑎𝑎𝑎 𝐺𝐺 𝑇𝑇𝑅𝑅 𝐺𝐺 𝑅𝑅𝑅𝑅 𝐺𝐺 𝑠𝑠𝑝𝑝𝑝𝑝𝑠𝑠𝑠𝑠 (5)
where 𝐺𝐺 𝑇𝑇𝑅𝑅 and 𝐺𝐺 𝑅𝑅𝑅𝑅 are the gains of respectively the Tx-and Rx-antennas, 𝐺𝐺 𝑠𝑠𝑝𝑝𝑚𝑚𝑠𝑠𝑚𝑚 is the path loss in the propagation channel at the carrier frequency 𝑓𝑓 0 , 𝐺𝐺 𝑚𝑚𝑚𝑚𝑠𝑠𝑐𝑐𝑖𝑖 is the gain of the RF power amplification in the Rx-unit (see the block diagram of Fig. 7(b)), and 𝜌𝜌 is the efficiency due to the eventual polarization mismatch between the Tx-and Rxantennas.

Wireless and Analog RF Setup for the Dynamic Measurement of Blast Pressure Signal: Experimental Validation

Figure 8 shows the block diagrams of the experimental setup which was designed for transmitting Friedlander-type signals over long distances, while Table 3 reports the key descriptors of this setup derived from the design methodology detailed in Section III. Before transmitting signals of interest, the calibration voltage 𝑉𝑉 𝑐𝑐𝑚𝑚𝑐𝑐 (𝑡𝑡) shown in Figure 9(a) is used as the modulating voltage in the Tx-unit. For each voltage 𝑉𝑉 𝑐𝑐𝑚𝑚𝑐𝑐 at time 𝑡𝑡, the instantaneous frequency 𝑓𝑓 𝑐𝑐𝑚𝑚𝑐𝑐 is estimated at a distance of 140 m. As displayed in Figure 9(b), the resulting scattered plot of 𝑓𝑓 𝑐𝑐𝑚𝑚𝑐𝑐 versus 𝑉𝑉 𝑐𝑐𝑚𝑚𝑐𝑐 is obtained and the linear regression of 𝑓𝑓 𝑐𝑐𝑚𝑚𝑐𝑐 on 𝑉𝑉 𝑐𝑐𝑚𝑚𝑐𝑐 is performed (we assume here that uncertainty on voltage is negligible compared with one on the The regression law 𝑓𝑓 𝑐𝑐𝑚𝑚𝑐𝑐 = 𝛼𝛼 + 𝛽𝛽 𝑉𝑉 𝑐𝑐𝑚𝑚𝑐𝑐 is then derived, with 𝛼𝛼 = 5.55 GHz and 𝛽𝛽 = 0.12 GHz V ⁄ with the coefficient of determination 𝐶𝐶 2 of 0.9997. Therefore, any voltage 𝑉𝑉 𝑚𝑚𝑚𝑚𝑚𝑚 applied at the input of the VCO device can be remotely estimated from the measurement of instantaneous frequency 𝑓𝑓 and the application of the relationship: 𝑉𝑉 𝑚𝑚𝑚𝑚𝑚𝑚 = (𝑓𝑓 -𝛼𝛼) 𝛽𝛽 ⁄ .

Table 3: Key descriptors of the wireless setup of Figure 8. Once the calibration process is complete, the Heaviside step voltage of amplitude 1 𝑉𝑉 and rise time 5 𝑛𝑛𝑛𝑛 is used as the modulating voltage 𝑉𝑉 𝑚𝑚𝑚𝑚𝑚𝑚 (𝑡𝑡). For comparison purpose, the same step voltage is simultaneously applied at the input of the 100 m long RG58 coaxial cable. Figure 10 displays the voltage received by using the wired and wireless setups. It can be observed that:

i. When using the wired setup, the measured rise time (10% to 90%) of the received voltage is (100 ± 6) 𝑛𝑛𝑛𝑛 (with a 95 % confidence interval) and consequently, is found significantly larger than the rise time (5 𝑛𝑛𝑛𝑛) of the step voltage applied at the cable input. As highlighted in Section II, the reason of this discrepancy originates in the lowpass filtering of the transmitted baseband signal due to the shunt capacitance (~100 pF/m) of the RG58 coaxial cable and to the input impedance (1 MΩ shunted by 16 pF) of the digital oscilloscope. Moreover, the time required by the output voltage to reach ± 2% of the steady state value is 1.15 μs. As discussed in Section II, this long reaction time originates in the impedance mismatches at the input and output ports, despite the use of a signal generator of output impedance 𝑍𝑍 𝑂𝑂𝑂𝑂𝑇𝑇 = 50𝛺𝛺;

ii. When using the wireless setup, the measured rise time (about 10 ns) of the signal received at a distance of 140 m is found to be significantly shorter than the one obtained from the wired setup. Moreover, as expected, the time required by the output voltage to reach ± 2% of the steady state value is very short (< 28 ns). Another experimental demonstration of the benefit of the proposed wireless solution compared with the wired setup consists of transmitting the Friedlander-type signal with 𝑇𝑇 = 100 µs and 𝜏𝜏 = 5 ns. This signal, generated by using the programmable Tektronix AFG3102, is used here to simulate the voltage delivered by an ideal ultrawideband pressure sensor located at 50 cm of a 500 𝑔𝑔 Semtex explosive. It can be observed from Figure 11 that the signal received by the wired setup requires 1 µs to reach its peak value, while only 10 ns are needed when using the wireless setup. Consequently, the wireless setup allows a time of arrival and reaction time of the shock wave estimation with higher measurement accuracy than the one provided by the wired setup. Moreover, contrary to the wired setup, the proposed wireless solution gives the direct measurement of the peak value 𝑉𝑉 𝑚𝑚𝑚𝑚𝑚𝑚 , without requiring any post-processing on measurement data (see, e.g., [START_REF] Goel | An Abridged Review of Blast Wave Parameters[END_REF] for details on the limitations of such post-processing usually applied on the measurement data for estimating the peak value 𝑉𝑉 𝑚𝑚𝑚𝑚𝑚𝑚 in wired setups). Furthermore, the effect of the impedance mismatches at the input and output ports of the coaxial transmission cable is clearly apparent in Figure 11, and negatively impacts the measurement accuracy of 𝑉𝑉 𝑚𝑚𝑚𝑚𝑚𝑚 . This issue related to impedance mismatches does not arise in the wireless setup. In the last but not least experiment, the wireless setup is used to transmit and receive the pressure signal delivered by the piezoelectric PCB 113A34 sensor [START_REF]Model 113A34 High frequency Invar ICP® pressure probe[END_REF] during an explosion. The sensor is located at 50 cm of aluminized TriNiTrotoluene (TNT) explosive of 600 g (see Figure 12). When the sensor, VCO device (located at 1 m from the explosive) and Tx-antenna are inside the fireball, it is demonstrated here that the carrier frequency of (5.3 ± 0.1) GHz chosen in this last experiment allows the wireless transmission of the pressure signal with very low distortion. In Table 4 are summarized the key descriptors for this experiment. The other descriptors are reported in Table 3. The distance between the Rx-and Tx-antennas is set to about 30 m. The explosion occurs 65 μs after the end of the calibration signal. For comparison purpose, the pressure signal delivered by the sensor is also applied at the input of a RG58 coaxial cable of 60 m long. Figure 13 displays the pressure obtained from the signal received by the wired and wireless setups (the pressure is derived here from multiplying output sensor voltage by the sensor sensibility of about 73 mV/bar [START_REF]Model 113A34 High frequency Invar ICP® pressure probe[END_REF]). The VCO and its antenna are inside the fireball generated by the explosion from at most 300 µs after the peak overpressure. The wired and wireless estimations of pressure are found in very good agreement, and both the wired and wireless setups require 4 μs for reaching the pressure peak of 35.3 bar. In this experiment the bandwidth is not limited by the transmission channel, but mainly by the sensor bandwidth. As the shock wave front is here normally incident upon the PCB 113A34 sensor surface, this bandwidth is found to be of about 100 kHz. This experiment demonstrates that the wireless transmission of the pressure is possible through the fireball of the explosion, even if some unexpected spikes are detected (see, e.g., at time t = 45 μs in Figure 13). These spikes (whose interpretation remains to be found) could be eventually removed by enhancing the radiofrequency link budget. This could be easily done by adding a power amplifier in the Tx-unit. (2) by the wireless setup (in blue). During 300 µs, the VCO and the Tx-antenna are inside the fireball generated by the explosion when wirelessly transmitting this pressure signal. A polynomial of order 𝟑𝟑 was used in the calibration process for the regression of 𝒇𝒇 𝒄𝒄𝒄𝒄𝒄𝒄 on 𝑽𝑽 𝒄𝒄𝒄𝒄𝒄𝒄 . This order is required due to the non-linearity of the VCO response in the large full-scale range of the measured pressure.

Compared with the state-of-the-art [START_REF]Piezoelectric transducers for high frequency measurements[END_REF], the piezoelectric PCB 113A34 sensor used in this last experiment has a low reaction time of few µs and consequently, cannot highlight the benefit of the wireless setup compared with the wired setup for short transmission channel of few ten meters. However, this sensor demonstrates that the calibration performed few microseconds before the fireball formation, with a propagation channel different, is still usable when the VCO is inside the fireball.

Conclusion

A wireless setup based on the analog frequency-modulation technique and using a digital frequency microwave meter was proposed for transmitting and receiving signal variations delivered by pressure sensors. It allows measuring the blast pressure within a fireball generated by an explosion.

Two experiments have demonstrated that, contrary to the wired solution, the distance between the sensor and the acquisition unit does not limit the measurement bandwidth of the wireless setup. This makes the reported wireless technique suitable for transmitting ultrafast variations of pressure inside the fireball of explosions.

The two main drawbacks associated with the proposed wireless set up are the following ones:

(1) The extension of the approach for the remote analysis of explosive detonation occurring in cluttered environments is not straightforward. As a matter of fact, electromagnetic propagation with multi-path and multiple reflections may degrade the signal-to-noise ratio and consequently, cause a disadvantageously impact on the measurement accuracy of the overpressure peak;

(2) Due to the limited electromagnetic susceptibility & immunity of electronic devices in the wireless setup, the electromagnetic power level radiated by the sensors must be sufficiently low in order to avoid any eventual malfunction in these devices. This constraint limits the separation distance between sensors and the reader to few tens meters in practice. This highest achievable distance may be not sufficient for some long-range applications. Ongoing works are devoted to the development of a wireless solution based on the direct sampling of the received FM signal and the application of the so-called direct detection technique. Moreover, frequency bandwidth about 1 GHz is, at least in principle, achievable by using the proposed wireless architecture. Thanks to large bandwidth, multiple FM signals may be simultaneously transmitted and processed using the proposed wireless technique. Extension of this work to the simultaneous wireless transmission of FM signals from multiple sensors is in progress.

Figure 1 .

 1 Figure 1. Profile of the Friedlander signal used for modeling the pressure generated by blast waves. 𝑃𝑃 𝑚𝑚𝑚𝑚𝑚𝑚 and 𝑃𝑃 𝑚𝑚 denote respectively the peak pressure and the ambient pressure.

Figure 2 .

 2 Figure 2. (a) The fireball during an explosion at various duration t after explosive ignition: (a) t = 556 μs; (b) t = 972 μs; (c) t = 1.389 ms; (d) t = 2.639 ms; (e) t = 5 ms, and (f) t = 20 ms. The plain circle indicates the fireball expansion, while the dotted circle indicates the shock wave front.

Figure 4 :

 4 Figure 4: Simulated voltage at the output port of RG58 coaxial cables (𝑍𝑍 𝐷𝐷 = 50𝛺𝛺 [12]) loaded by 𝑍𝑍 𝑂𝑂𝐵𝐵𝐷𝐷 (1 MΩ shunted by 10 pF) for different cable lengths between 250 m and 1000 m, when the Heaviside step voltage of 1 V is applied at the input port. Simulations are performed by using Advanced Design System software.

Figure 5 :

 5 Figure 5: (a) Simulated voltage at the output port of RG58 coaxial cables coaxial cables (𝑍𝑍 𝐷𝐷 = 50𝛺𝛺 [12]) loaded by 𝑍𝑍 𝑂𝑂𝐵𝐵𝐷𝐷 (1 MΩ shunted by 10 pF) for different cable lengths between 25 m and 200 m, when the Heaviside step voltage of 1 V is applied at cable input port. Simulations are performed by using Advanced Design System software.

Figure 7 :

 7 Figure 7: Block diagrams of the (a) transmission unit (Tx-unit) and the (b) reception unit (Rx-unit). The voltage 𝑉𝑉 𝑚𝑚𝑚𝑚𝑚𝑚 (𝑡𝑡) indicated in the Tx-unit is called the modulating voltage, and is estimated at any time 𝑡𝑡 from the measurement in the Rx-unit of the instantaneous frequency 𝑓𝑓(𝑡𝑡) of the received frequency-modulated signal.

Figure 8 :

 8 Figure 8: Block diagrams of the experimental setup used for wirelessly transmitting Friedlander-type signals over long distances: (a) Tx-unit, and (b) Rx-unit.

Figure 9 :

 9 Figure 9: (a) Portion (from 𝟓𝟓𝟓𝟓𝟓𝟓 𝛍𝛍𝛍𝛍 to 𝟓𝟓𝟓𝟓𝟓𝟓 𝛍𝛍𝛍𝛍) of the signal used for calibration voltage 𝑽𝑽 𝒄𝒄𝒄𝒄𝒄𝒄 (𝒕𝒕), with period of 𝟒𝟒 𝛍𝛍𝛍𝛍 and total duration of 𝟓𝟓 𝐦𝐦𝛍𝛍; (b) transmitted instantaneous frequency as a function of the calibration voltage 𝑽𝑽 𝒄𝒄𝒄𝒄𝒄𝒄 (in blue). The frequencies embedded in the transmitted signal are measured at the distance of 𝟏𝟏𝟒𝟒𝟓𝟓 𝐦𝐦 from the Txantenna. The linear regression (in red) is used here for deriving the regression of 𝒇𝒇 𝒄𝒄𝒄𝒄𝒄𝒄 on 𝑽𝑽 𝒄𝒄𝒄𝒄𝒄𝒄 .

Figure 10 :

 10 Figure10: Heaviside step voltage of 𝟏𝟏 𝑽𝑽 (from 𝟓𝟓. 𝟓𝟓 𝑽𝑽 to 𝟏𝟏. 𝟓𝟓 𝑽𝑽) and rise time of 𝟓𝟓 𝒏𝒏𝒏𝒏 received by using the wired setup (in red) and the proposed wireless setup (in blue). The wireless transmission is carried out over 𝟏𝟏𝟒𝟒𝟓𝟓 𝐦𝐦, while the wired transmission uses a RG58 cable of 100m long loaded by the input impedance 𝒁𝒁 𝑶𝑶𝑶𝑶𝑶𝑶 (𝟏𝟏 𝐌𝐌𝐌𝐌 shunted by 𝟏𝟏𝟓𝟓 𝐩𝐩𝐩𝐩) of the serial data analyzer LECROY SDA 813Z.

Figure 11 :

 11 Figure 11: Friedlander-type signal with 𝑻𝑻 = 𝟏𝟏𝟓𝟓𝟓𝟓µ𝒏𝒏 and 𝝉𝝉 = 𝟓𝟓 𝐧𝐧𝛍𝛍, received by the wired setup at a distance of 𝟏𝟏𝟓𝟓𝟓𝟓 𝐦𝐦 (in red), and received at a distance of 𝟏𝟏𝟒𝟒𝟓𝟓 m by the proposed wireless setup (in blue). During the calibration process, a polynomial of order 𝟑𝟑 was used for the regression of 𝒇𝒇 𝒄𝒄𝒄𝒄𝒄𝒄 on 𝑽𝑽 𝒄𝒄𝒄𝒄𝒄𝒄 .

Figure 12 :

 12 Figure 12: Photograph of the experimental setup (detail). The piezoelectric PCB 113A34 sensor (4) is placed at 𝟓𝟓𝟓𝟓 𝐜𝐜𝐦𝐦 of aluminized TriNiTrotoluene (TNT) spherical explosive charge of 6𝟓𝟓𝟓𝟓 𝐠𝐠 (2). The VCO device (HMC587) and Tx-antenna (half-wave dipole) (1) are located at 𝟏𝟏 𝐦𝐦 from the center of the spherical charge. The rest of the Tx-unit is placed inside the bunker (3). The acquisition unit and Rx-unit are placed in a second bunker (not shown here) located at 𝟑𝟑𝟓𝟓 𝐦𝐦 from the charge.

Figure 13 :

 13 Figure 13: Overpressure as a function of time obtained from the signal received (1) by the wired setup (in red) and(2) by the wireless setup (in blue). During 300 µs, the VCO and the Tx-antenna are inside the fireball generated by the explosion when wirelessly transmitting this pressure signal. A polynomial of order 𝟑𝟑 was used in the calibration process for the regression of 𝒇𝒇 𝒄𝒄𝒄𝒄𝒄𝒄 on 𝑽𝑽 𝒄𝒄𝒄𝒄𝒄𝒄 . This order is required due to the non-linearity of the VCO response in the large full-scale range of the measured pressure.

Table 1 . Rise time derived from Figure 4 of the output voltage as a function of the cable length. The rise time is defined as the time required by the voltage to reach for the first time 90% of the steady state value (1 V) from 10% of this value.

 1

	Length of R58	Rise time
	transmission cable
	250 m	0.79 µs
	500 m	2.14 µs
	1000 m	7.40 µs

Table 2 .

 2 Reaction time derived from Figure5as a function of the cable length. The reaction time is defined here as the time required by the output voltage to reach ±2% of the steady state value.

	Length of R58	Rise time
	transmission cable
	25 m	251 ns
	50 m	525 ns
	100 m	1243 ns
	200 m	2585 ns

Table 4 :

 4 Key descriptors of the wireless setup for the experiment with aluminized TNT explosive of 600 g.

	bandwidth of the transmitted FM signal (𝑑𝑑 𝐹𝐹𝐹𝐹 )	100 kHz
	duration of time-windowing (𝑇𝑇 𝑚𝑚𝑚𝑚𝑚𝑚𝑠𝑠 )	50 ns
	sampling rate of the ADC device (𝑓𝑓 𝑠𝑠𝑚𝑚𝑚𝑚𝑠𝑠 )	20 GS/s
	gain of Tx-antenna (𝐺𝐺 𝑇𝑇𝑅𝑅 )	2 dBi
	gain of Rx-antenna (𝐺𝐺 𝑅𝑅𝑅𝑅 )	16 dBi
	Transmiited power	4 dBm

Acknowledgements

The authors thank Fabrice Mathieu for the help during the development of the high bandwidth conditioning circuit and the Occitanie Regional Council in France for contributing to the financial support of this work.


T Marchal

D Henry

P Pons

H Aubert

Wireless Measurement of the Pressure from the Ka-Band Radar Echo of a 3D-Printed Microfluidic Depolarizing Sensor

Keywords: Passive sensors, wireless sensors, additive technology, microfluidic technology, field depolarization, remote sensing

In this paper, we report the remote measurement of the pressure from the Radar interrogation of a novel microfluidic passive sensor. This sensor includes a microfluidic band-pass filter, whose transmission coefficient in the Ka-band depends on the applied pressure, and two cross-polarized Rx-and Tx-antennas connected to the terminals of the filter for enhancing the full-scale measurement range of the sensor's Radar echo level. The filter is 3D-printed via the Sintering Laser Melting technique. For a Radar-to-sensor distance of 3 meters, a high full-scale measurement range of 8dB on the echo level is reported with a measurement sensitivity of 0,03dB/mbar for applied pressure ranging from 350 mbar to 640 mbar.

I. INTRODUCTION

Wireless and passive (or zero-power) sensors are commonly used for the short-range remote reading of physical quantities (such as, the temperature, humidity and pressure). The remote sensing can be performed by using well-known Radio Frequency Identification (RFID) or Surface Acoustic Waves (SAW) sensor tags. Because they are chipless and batteryless, these sensor tags are suitable for applications involving, e.g., extreme temperatures and/or very high pressures. However, the short reading range of passive wireless sensors (typically lower than 3 meters [START_REF] Islam | Aperture coupled UWB microstrip patch antenna array for mm-Wave chipless RFID tag reader[END_REF][START_REF] Schumacher | Passive chipless wireless pressure sensor for Harsh and reflective environments[END_REF][START_REF] Marindra | Chipless RFID Sensor Tag for Metal Crack Detection and Characterization[END_REF]) can be a strong limitation to their systematic application in harsh environments. For example, the reader might be degraded in extrem conditions such as by temperature or radioactivity.

To achieve both the reading and identification of passive sensors for large reader-to-sensor distances, the use of Frequency-Modulated Continuous-Wave (FMCW) Radars was proposed very recently in [START_REF] Henry | Classification of Radar Echoes for Identification and Remote Reading of Chipless Millimeter-Wave Sensors[END_REF]. Up to now, this Radar-based technique requires the fabrication of millimeter-wave sensing devices from costly clean room technological facilities (see, e.g., [START_REF] Philippe | In-Situ Wireless Pressure Measurement Using Zero-Power Packaged Microwave Sensors[END_REF]). In order to reduce the fabrication cost, we investigate here the feasibility of designing such devices from using a 3D printing additive technology. The proof of concept is illustrated in this paper from the design, fabrication and Radar interrogation of a Ka-band microfluidic pressure sensor. The sensor is composed of a microfluidic band-pass filter, whose transmission coefficient in the Ka-band depends on the applied pressure. The filter is fabricated by using the Sintering Laser Melting technique.

The paper is organized in two sections. The first section described the microfluidic 3D-printed pressure sensor. In the second section, the sensor is remotely interrogated from a 24 GHz FMCW Radar for various applied pressures.

II. MICROFLUIDIC 3D PRINTED KA-BAND PRESSURE SENSOR

The pressure sensor is designed to operate in the modulation bandwidth [22.8-24.8 GHz] of a FMCW Radar. It is composed of a band-pass rectangular waveguide (WR28 -3.556 mm x 7.112 mm) filter connected to a vertically (V) polarized antenna at one port (Rx, port 1) and to a horizontally (H) polarized antenna at the second port (Tx, port 2). A polytetrafluoroethylene (PTFE) circular channel (relative permittivity of 2.1, with inner and outer diameters of 300 µm and 800 µm, respectively) crosses the waveguide in the region where the electric field magnitude of the fundamental TE10 mode is maximum (see Figure 1 A liquid (here we use water, with relative dielectric permittivity of 38 and loss tangent of 1 [START_REF] Philippe | In-Situ Wireless Pressure Measurement Using Zero-Power Packaged Microwave Sensors[END_REF]) flows inside the channel. As the pressure increases, the liquid level moves inside the channel and gradually modifies the transmission coefficient S21 of the bandpass filter. As a result, the electromagnetic power received by the V-polarized Rx-antenna of the sensor is more or less attenuated, depending on the liquid level in the channel, which in turn is a function of the applied pressure at one end of the channel. The electromagnetic power is then re-radiated by the H-polarized Tx-antenna of the sensor, and part of this power is received by the Rx-antenna of the Radar. Following [START_REF] Schumacher | Passive chipless wireless pressure sensor for Harsh and reflective environments[END_REF], the electric fields received and re-radiated by the sensor are cross-polarized for mitigating the impact of the electromagnetic clutter on the measurement accuracy of sensor's Radar echo level. For this specific reason, the sensor is called here a depolarizing sensor.

The filter is fabricated via the Sintering Laser Melting technique (manufacturing precision of 40 µm and surface roughness of 20 µm). The metal is stainless steel (316L, conductivity of 3 10 6 S/m). As it can be observed from Figure 1(a), the filter is composed of a (unique) resonant cell with triangular metallic diaphragms in order to be compliant with the additive technological process. Figure 1(b) shows the fabricated microfluidic tunable band-pass filter used as a pressure sensing device (or transducer). The liquid displacement in the PTFE channel is controlled by adjusting the pressure at one end of the channel (with the Fluigent EZ-MFCS pressure controller), while the other end is closed. The applied pressure ranges from 0 bar to 1 bar (by step of 10 mbar) and the corresponding fluid level ranges from 0 to 15 mm inside the channel.

Let Tmean be the mean-value of the transmission coefficient |S21| in the modulation bandwidth [22,8 GHz-24,8 GHz] of the FMCW Radar, which will be used in Section III for the remote interrogation of the pressure sensor. Figure 2 reports the measured values of Tmean as a function of the liquid level inside the channel. The measurement sensitivity is found to be 2.3 dB/mm and the full-scale measurement range ∆Τmean is of 9.4 dB.

III. WIRELESS MEASUREMENT OF THE PRESSURE FROM THE RADAR ECHO OF THE 3D-PRINTED PASSIVE SENSOR

The indoor experimental setup for the remote measurement of the pressure is shown in Figure 3. It is located in a room of our Laboratory. The wireless interrogation is performed by using a 24GHz FMCW Radar (model DK-sR-1030e from IMST GmbH [START_REF] Kaatze | The Dielectric Properties of Water at Microwave Frequencies[END_REF]) which transmits a frequency modulated signal (or chirp) at a carrier frequency of 23.8 GHz. The modulation bandwidth is [22.8 GHz -24.8 GHz] and consequently, the theoretical range resolution is of 7.5 cm.

The front-end of the Radar uses one Tx-antenna and two Rx-antennas. The Tx-antenna is a V-polarized lens antenna (gain of 30 dBi) and following [START_REF] Henry | Classification of Radar Echoes for Identification and Remote Reading of Chipless Millimeter-Wave Sensors[END_REF], two horn antennas (gain of 20 dBi) are used to receive the frequency-modulated (FM) fields re-radiated and backscattered by the 3D-printed sensor:

(i) one Rx-antenna is H-polarized for deriving the pressure from the electric field re-radiated by the sensor;

(ii) the second Rx-antenna is V-polarized for locating the sensor from the electric field backscattered in this polarization by the sensor.

Moreover, in order to separate the time-of-arrival of the re-radiated and backscattered FM fields, delay lines (electrical length of 1.5m) are placed between the two ports of the filter and the sensor's Rx-and Tx-antennas, as shown in Figure 3(b). The distance between the Radar and the sensor is set here to 3 meters.

For each applied pressure, the Radar transmits a V-polarized FM electric field, which is received by the V-polarized Rx-antenna of the sensor, and is then re-radiated by the H-polarized Tx-antenna of this sensor. Before the re-radiation, the received FM field propagates inside the filter and is subjected to an attenuation, which depends on the pressure-dependent fluid level in the channel. The re-radiated FM field, whose magnitude is dependent on the applied pressure, is finally received by the Rx-antennas of the Radar. In Figure 4 are displayed the mean value (over 100 measurements) and standard deviation of the echo level received by the Hpolarized Rx-antenna of the Radar. For an applied pressure at one end of the microfluidic channel ranging from 350 mbar to 640 mbar, the liquid level varies inside the waveguide. Outside this range (adjustable by design), the channel is empty or is completely filled with liquid. A convenient linear variation of the echo level (in dB) is obtained as the applied pressure varies. Fig. 4. Measured cross-polarized (V-to-H) Radar echo level of the 3D-printed microfluidic sensor as a function of the applied pressure. For pressure ranging from 350 mbar to 640 mbar the liquid level varies inside the waveguide. For a fixed applied pressure, the mean value and standard deviation of the Radar echo is computed from 100 successive echo measurements.

For a Radar-to-sensor distance of 3 meters, a high full-scale measurement range Δe of 8dB on the echo level is obtained with a measurement sensitivity of 0.03dB/mbar for applied pressure ranging from 350 mbar to 640 mbar. The precision of the measurement is derived from the calculated standard deviation. We obtain a maximal standard deviation of 0.07dB for an applied pressure of 550 mbar. Hence, the standard deviation represents the precision of the measurement according to the signal-to-noise ratio of the radar. Knowing the sensitivity of the pressure sensor, the precision of the measurement is 3 mbar. This precision obtained at a Radar-tosensor distance of 3m may be degraded at a higher range of interrogation, or if a mechanical beamscanning is performed [START_REF] Henry | Classification of Radar Echoes for Identification and Remote Reading of Chipless Millimeter-Wave Sensors[END_REF]. The sensitivity of the proposed sensor can be compared with the one obtained in [START_REF] Henry | Classification of Radar Echoes for Identification and Remote Reading of Chipless Millimeter-Wave Sensors[END_REF]. With identical reader and antennas and a reading distance of 4,2m, the current sensor had a sensitivity ten times higher and a dynamic range more than two times higher. Moreover, we have observed (not shown in this paper) that reading range up to 22m is reachable by using the fabricated 3D-printed microfluidic sensor, but at the expense of lower measurement sensitivity. Anyway, these results are very encouraging and prove that additive technologies (such as the Sintering Laser Melting technique) can be advantageously used to manufacture wireless chipless sensors in Ka-Band.

IV. CONCLUSION

In this paper, we investigated the feasibility of designing wireless and chipless sensors in the Ka band from using a 3D printing additive technology. We demonstrate that a 3D-printed microfluidic sensor allows the remote measurement of the pressure. A pressure measurement sensitivity of 0,03dB/mbar is obtained for a pressure variation of 290 mbars and sensor-to-reader distance of 3 meters.

Additive technology (Sintering Laser Melting technique) in addition with microfluidics brings a promising solution for manufacturing cost-effective wireless passive sensors in the Ka-band. The next step consists of manufacturing millimeter-wave 3D sensors (combining microfluidic filters and antennas) from this technology and demonstrates the feasibility of their long-range wireless reading in various harsh environments.

  (a)).

Fig. 1 .

 1 Fig. 1. Microfluidic pressure sensor (without its cross-polarized Rx-and Tx-antennas): (a) 3D view of the microfluidic tunable band-pass filter used as a pressure sensing device (dimensions are in millimeter) and, (b) Photo of the 3D-printed microfluidic filter fabricated via additive technology. Two SpaceK T28-K WR28to-coax adapters are used here to connect the V-polarized Tx-antenna at port 1 and H-polarized Rx-antennas at port 2.

Fig. 2 .

 2 Fig. 2. Mean-value Tmean of the measured transmission coefficient |S21| of the microfluidic filter in the FMCW Radar modulation bandwidth [22.8 GHz -24.8 GHz] as a function of the liquid (water) level inside the channel. As the pressure increases, the liquid progressively fills the PTFE channel crossing the waveguide section (in the region where the magnitude of the TE10-mode electric field is maximum) and gradually modifies the transmission coefficient of the filter.

Fig. 3 .

 3 Fig. 3. (a) Photo of the indoor experimental setup and (b) Photo of pressure sensor combining the 3D-printed microfluidic filter, the two cross-polarized Tx-and Rx-antennas and the delay lines.


Julie Mendret

Antonin Azaïs

Thibault Favier

Stephan Brosillon

Antonin Azais

Urban wastewater reuse using a coupling between nanofiltration and ozonation: Techno-economic assessment

Keywords: nanofiltration, ozonation, wastewater reuse, economic analysis

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

2

Highlights:

Nanofiltration is a possible alternative to reverse osmosis for wastewater reuse Nanofiltration combined to ozonation is a competitive process for wastewater reuse Nanofiltration is a barrier for micropollutants with reasonable operating costs Coupling nanofiltration and ozonation results in cost saving due to reuse possibility

Introduction.

Water resources management is a major challenge in economic development and public health. The demographic growth and associated economic development will further exacerbate the situation in the next twenty years by increasing water demand while discharging more and more polluted effluents. It is therefore necessary, in addition to the draft of very strict regulations, to protect the quality of the resource, to challenge the marine or brackish resources desalination by developing cost-effective systems, and also to define new and relevant treatment processes for urban wastewaters allowing direct wastewater reuse and improvement of water resource protection. This concept of wastewater treatment allowing direct recycling is an issue already tackled and resolved in part in the industrial environment and in some "early bird" countries (Singapore for drinking water and Tunisia, California and Florida for irrigation water) [START_REF] Wintgens | The role of membrane processes in municipal wastewater reclamation and reuse[END_REF]. However, it is still secondary in densely populated urban environments, where the major concern is to comply with standards imposed with regards to the fragility or constraints of the receiving environment. Nevertheless, this reuse becomes one of the essential points in optimal management of a freshwater resource, especially when considering its global cost, less than half the cost of desalination (Cote et al., 2005).

After massive investment in energy-intensive desalination processes which increased the global production capacity of desalinated water by 67% to 52 million m³.d -1 (GWI, 2009), governments are now looking at overall water efficiency and start to prioritize water reclamation and reuse as a solution to water scarcity since water reclamation requires only a third to a fourth of the energy needed for reverse osmosis (RO) desalination. While the combined approach of seawater desalination and water reuse has proven to be successful in a number of coastal sites such as Barcelona, Singapore, land locked cities have to focus completely on water reuse for irrigation or aquifer recharge, sometimes even accepting direct potable reuse as practiced in Windhoek, Namibia (Bunani et al., 2015, Bellona et al;, 2012). With a closed water loop, land locked cities require high-quality water reuse systems mostly based on membrane technology as affordable and efficient barrier.

Municipal wastewater is an alternative water source but increasingly contaminated with toxic organic pollutants [START_REF] Schwarzenbach | The Challenge of MPs in Aquatic Systems[END_REF]. The occurrence of organic micropollutants (OMPs) in the aquatic environment, often called 'emerging pollutants' as they became increasingly detectable since the last two decades, has been identified as a global issue. Research has shown the ubiquitous presence of a broad range of pharmaceuticals, personal care products and industrial chemicals in the water cycle, particularly in the effluent of wastewater treatment plants (WWTP) and surface waters in low concentrations from ng.L -1 to μg.L -1 [START_REF] Jorgensen | Drugs in the environment[END_REF][START_REF] Heberer | Occurrence, fate, and removal of pharmaceutical residues in the aquatic environment: a review of recent research data[END_REF][START_REF] Wode | Search for over 2000 current and legacy micropollutants on a wastewater infiltration site with a UPLC-high resolution MS target screening method[END_REF][START_REF] Hermes | Quantification of more than 150 micropollutants including transformation products in aqueous samples by liquid chromatographytandem mass spectrometry using scheduled multiple reaction monitoring[END_REF]. Also, important concerns have been raised regarding that continuous discharge of antibiotics and anti-microbial products into aquatic environment may facilitate the development or proliferation of resistant strains of bacteria [START_REF] Kim | Potential ecological and human health impacts of antibiotics and antibioticresistant bacteria from wastewater treatment plants[END_REF]. Indeed, the emergence and spread of antibiotic resistant bacteria have been classified by the World Health Organization as one of the three biggest threats to public health in the 21st century. Moreover, chronic toxicity effects have been reported for aquatic organisms exposed to OMPs at trace concentrations.

Current technologies in existing WWTPs struggle to eliminate OMPs or to limit their concentration and toxicity sufficiently to comply with the thresholds in new regulations. These evolutions are driving the urban wastewater treatment to come up with advanced technologies like RO or activated carbon (AC) are able to effectively remove OMPs without chemicals addition and limiting byproducts formation [START_REF] Gomez | Determination and occurrence of organic micropollutants in reverse osmosis treatment for advanced water reuse[END_REF][START_REF] Paredes | Integrating granular activated carbon in the post-treatment of membrane and settler effluents to improve organic micropollutants removal[END_REF]. Nonetheless, RO is expensive because of high operating pressure and is very sensitive to fouling thus requires a high level of water pretreatment or works best on groundwater or low solids surface water. AC could be efficient but its performances are greatly affected by variations in pH, temperature, and flow rate as it could release or desorb [START_REF] Benstoem | Performance of granular activated carbon to remove micropollutants from municipal wastewater-A meta-analysis of pilot-and large-scale studies[END_REF]. To recover fresh reusable water from urban wastewater treatment, efficient additional treatment processes which are economically viable are required and thus must be developed. Nanofiltration (NF) has been proved to be efficient as a tertiary treatment as it enables high rejections of small organic molecules (around 200-300 Da) due to size exclusion and electrostatic or hydrophobic interactions. Moreover, this membrane technology requires operation pressure significantly lower than traditional RO processes and without the need of further permeate remineralization. Hence, NF provides an interesting alternative to RO for wastewater reuse with a number of advantages: lower energy consumption due to lower pressure requirement, less chemical additives, lower rejection of monovalent salts and thus less problematic membrane concentrates and finally less heavy post treatment of re-mineralization [START_REF] Bellona | Viability of a low-pressure nanofilter in treating recycled water for water reuse applications: A pilot-scale study[END_REF]. However, two main limitations of NF application in WWTP are i) membrane fouling which affects directly process performances and costs; and ii) the disposal of retentates which contains a wide range of concentrated organic pollutants. Indeed, NF applied to a polluted water provides a large volume of practically clean water (permeate) that can be reused immediately and a concentrated stream that requires further treatment. The recovery ratio for NF is normally 50-85% which corresponds to a volume reduction factor (VRF) of 2 -7 and results in a waste stream which could be returned to the biological treatment or could be discharged or treated depending on regulations and possibilities.

However, retentate recirculation upstream of the biological treatment is not possible in the long term as salinity greater than 5 g.L -1 may inhibit biological activity [START_REF] Reid | Effect of high salinity on activated sludge characteristics and membrane permeability in an immersed membrane bioreactor[END_REF]. In addition, the recirculation of NF concentrates within a MBR significantly increases its clogging [START_REF] Kappel | Impacts of NF concentrate recirculation on membrane performance in an integrated MBR and NF membrane process for wastewater treatment[END_REF]. Finally, direct discharge into surface or marine waters is not easy to encourage given the average composition of the urban retentates i.e. conductivities of 2 to 20 mS.cm -1 , CODs ranging from 20 to 55 mg.L -1 and levels of organic micropollutants multiplied by 3 to 7 [START_REF] Benner | Ozonation of reverse osmosis concentrate: kinetics and efficiency of beta blocker oxidation[END_REF][START_REF] Solley | Managing the reverse osmosis concentrate from the Western Corridor recycled water scheme[END_REF]. Hence, treatment of membrane concentrates is recommended.

With this view in mind, ozonation was found to degrade efficiently most OMPs present in treated wastewater through the strong oxidative properties of ozone (applied dose: 3-8 mg O3.L -1 ) and of the hydroxyl radicals produced spontaneously during its decomposition. AOP based on ozonation could thus be used to treat membranes rejection streams (retentate) containing high concentration of harmful organics. The general advantages of the combined process NF/AOP or AOP/NF with recirculation of the concentrate over direct treatment would be, depending on the configuration: (i) lower ozonation treatment time, (ii) more efficient reagent consumption, (iii) treatment of lower flow rate, (iv) higher permeate flow [START_REF] Van Geluwe | Ozone oxidation of nanofiltration concentrates alleviates membrane fouling in drinking water industry[END_REF][START_REF] Park | Pre-ozonation for high recovery of nanofiltration (NF) membrane system: Membrane fouling reduction and trace organic compound attenuation[END_REF]. Concentration of OMPs can be reduced to a desired level by NF or ozonation separately, but only few researches took advantage of these two wastewater treatment process to produce high quality effluent.

Over past years, objective of our researches is to prove that the combination of NF and ozonation could be a promising, efficient and affordable solution for OMPs and global toxicity removal from urban wastewater while reducing costs and limitations occurring when the two processes are carried out separately, making wastewater reuse possible and safe for various applications (Azais et al., 2014;Azais et al., 2016;[START_REF] Azaïs | Ozonation as a pretreatment process for nanofiltration brines: Monitoring of transformation products and toxicity evaluation[END_REF]. The final objective is to design novel integrated process schemes combining NF and ozonation with structural (flow-sheet) and parameters optimization of these processes. One of the design objectives of the integrated processes should be the minimization of liquid wastes, thus reducing the load of the following waste treatment stage. Any new NF membrane plant needs an evaluation of the membrane performance in order to evaluate the number of NF elements and type of membrane, this is essential in the prediction of the initial cost of the plant. In addition, costs of emerging processes have to be evaluated. To our knowledge, this has never been done for such coupling applied to wastewater reuse. In this way, the specific objective of this paper is to present an economic and technical evaluation of the proposed coupling between NF and ozonation where ozonation is used to treat retentate from nanofiltration. Reverse Osmosis System Analysis (ROSA) software developed by Filmtec (Dow Water and Process Solutions, 2011) was applied in this study to simulate the proposed filtration design. The effect of membrane choice on power consumption in terms of specific energy consumption (kWh.m -3 ), capital, operation and maintenance (O&M) costs and scale potential was investigated. Interest of the use of NF instead of RO was analyzed by comparing both processes. A process analysis and a comparative economic analysis of capital and operating costs for both technologies were performed. Cost of ozonation was estimated based on experimental results concerning ozonation of real wastewater matrice concentrated by nanofiltration (Azais et al., 2016a). Thus, ozone doses are known for this effluent. Finally, impact of the treatment of concentrates by ozonation on the treatment costs was considered.

Material and methods.

Cost of nanofiltration

ROSA 9.0 software model was applied to predict water quality and flow rate for different membrane system configurations. ROSA software is a model designed by Nisan in 2005, applied to design and manipulate RO and NF systems taking into account effects of concentration polarization factor and hydrodynamic pressure drop in the concentrate-side on the membrane performance [START_REF] Nisan | A new method for the treatment of the reverse osmosis process, with preheating of the feedwater[END_REF]. This software is often used in research work to simulate designs using reverse osmosis or nanofiltration plants (Yangali-Quintilla et al., 2010 ;[START_REF] Haryati | Process intensification of seawater reverse osmosis through enhanced train capacity and module size -Simulation on Lanzarote IV SWRO plant[END_REF].

The main inputs of the model include the amount of feed water and its chemical characteristics including the SDI range, feed water and concentrate feed pressures, temperature and pH. Then, setting up of the number of membranes, pressure vessels, type of membrane, and if needed booster pumps, is performed by ROSA. Depending upon the system, the goal is to minimize feed pressure and membrane costs whilst maximizing permeate quality and recovery. After performing calculations, ROSA produces a report predicting among others the water quality and flow rate.

Feed water whose characteristics were implemented in ROSA was the one used in previous studies (Azais et al., 2014;Azais et al. 2016 a), 2016 b), Azais et al., 2017). It is a real secondary effluent from a municipal WWTP located in the south of France (Baillargues) with a SDI=2.5 which is inferior to 3 as recommended for a direct use of the effluent as feed water for NF, without pretreatment. The membrane bioreactor (MBR) system incorporates immerged ZeeWeed 500 (GE Zenon) ultrafiltration (UF) membranes in polyvinylidene difluoride (PVDF) which have a pore size of 0.035 microns. The total membrane surface area is about 7 605 m² and produces approximately 1 500 m 3 of permeate per day while operating at a mixed liquor total suspended solids (TSS) concentration of between 4 and 7 g L -1 . Summary of major constituents of the secondary effluent is presented in table 1 with intervals given with 95% confidence.

COD mg L -1 18 ± 3 DOC mg L -1 6 ± 2 NO3 --N mg L -1 2.0 ± 0.6 Total Nitrogen (TN) mg L -1 4.1 ± 1.6 PO4 3--P mg L -1 0.11 ± 0.08 Na + mg L -1 152 ± 14 K + mg L -1 22 ± 3 Ca 2+ mg L -1 160 ± 20 Mg 2+ mg L -1 6.6 ± 0.8 Cl - mg L -1 267 ± 35 SO4 2- Ionic strength mg L -1 mM 89 ± 13 22 ± 5
No nitrites were detected in the effluent so that the value of TN could be due to the presence of ammonia because of incomplete nitrification. Regarding water pH and ionic composition, ROSA estimates Langelier Saturation Index (LSI) which is a measure for the saturation of CaCO3 in water.

The LSI should be used for low Total Dissolved Solids (TDS) ranges (<10 000 ppm). At the pH of saturation (pHS), the water is in equilibrium with CaCO3. To avoid calcium carbonate scaling by acid addition alone, the LSI in the concentrate stream must be negative. If a high quality scale inhibitor is used, the LSI in the concentrate stream can be increase up to 1.5. This will reduce or eliminate the acid consumption. Many inhibitors allow operation up to an LSI of < 1.8 in the concentrate. In this study the water is hard, so acid (H2SO4) was added. Finally, the low value of SDI will reduce fouling problems due to particulate matters which tends to accumulate at the membrane surface resulting in a membrane flux decline.

Capital cost of a NF plant is directly impacted by the design of the system. This issue should be taken into account into the system design as most companies try to reduce the capital cost. Moreover, maintenance cost of NF system can be reduced because of lower propensity to fouling of elements when correctly chosen. Thus, balance has to be found between design and maintenance costs to meet both economic and technical requirements.

A two or three stage configuration with a decreasing number of pressure vessels in parallel allows respecting the minimum concentrate flow rate constraint and other required hydraulic conditions in nanofiltration process. Consequently, this kind of configuration was chosen in this study in order to reach high conversion rates (> 80 %), obtain a reliable permeate quality without a severe fouling risk The average flux of the entire system, i.e. the system permeate flow rate related to the total active membrane area of the system, is a characteristic parameter of a given design. The system flux is a useful number to quickly estimate the required number of elements for a new project. In this study, the feed water flow of Baillargues wastewater treatment plant (125 m 3 .h -1 ) was chosen as inlet feed flow in ROSA. Tested recovery rates (Y) were chosen as they correspond to VRF reached in a previous study (Azais et al., 2016 a)).

Among elements proposed by ROSA, NF 90-400 was first chosen. NF90-400 element is a high area, high productivity element designed to remove a high percentage of salts, nitrate, iron and organic compounds. The high active area membrane combined with high permeability of the membrane allows the removal of these compounds at low operating pressure. The membrane active area is 400 square feet; the diameter and length are respectively 7.9 and 40 inch. Then, same calculation were performed for NF 270-400 (same dimensions as NF 90-400) and for BW 30-400 (brackish water reverse osmosis membrane, same dimensions as NF 90-400).

Cost of NF 90-400 element and pressure vessel was estimated to respectively 850 and 1 500 $.

Cost of ozonation

Economic evaluation of NF retentate ozonation is necessary so as to define an optimal conversion rate which assures a compromise between permeate flux and retentate treatability. This economic evaluation was done on the basis of transferred ozone dose in concentrated real wastewater which guarantees a 90% elimination of three pollutants among the four chosen in our previous studies (see Azais et al., 2016 a)).

As only little ozone doses are required to treat retentates of this study, on site oxygen generation using Pressure Swing Absorption (PSA) was chosen. This is ideally suited to supply an ozone generator with medium frequency (60 to 1 000 Hz). Specific energy for ozone production was estimated to 10 kWh.kgO3 -1 [START_REF] Rosenfeldt | Comparison of the efficiency of •OH radical formation during ozonation and the advanced oxidation processes O3/H2O2 and UV/H2O2[END_REF]. According to [START_REF] Margot | Treatment of micropollutants in municipal wastewater: Ozone or powdered activated carbon?[END_REF], the transfer efficiency of ozone into the dissolved phase in ozonation pilot plant is between 70 to over 90% depending on the gas flow [START_REF] Margot | Treatment of micropollutants in municipal wastewater: Ozone or powdered activated carbon?[END_REF]. In this study, it was fixed to 95%. Investment cost was taken equal to 100 $.gO3 -1 .h -1 as suggested by ozone water treatment plants manufacturers and suppliers. The operational cost was then evaluated in this study. Finally, as cooling water is used in a close loop system, this item of expenditure was neglected.

Considering the different input parameters (economic as well as process design and performance data)

and their variability in the cost assessment, the maturity level is fixed to 5 (corresponding to 10 % of complete definition) with an accuracy range of -50 % to 50 % according to the AACE (American Association of Cost Engineering) cost estimate classification matrix. A narrow accuracy range was defined since the approach developed in this study could easily lead to a feasibility study or even to a pre-budget authorization (maturity level 4 or 3) as the membrane and ozonation technologies are mature and controlled.

Results and discussion

Optimization of nanofiltration design for NF-90

To verify that the chosen configuration (figure 1) is well adapted to the targeted conversion rates, simulations were done by imposing the three recovery rates for different configuration (one, two or three stages). For this, value of the number of pressure vessel in first stage (N) was modified between 10 and 30. At first approximation, number of elements in a pressure vessel was fixed to 7 as usually encountered at industrial scale ( [START_REF] Van Der Meer | Only two membrane modules per pressure vessel? Hydraulic optimization of spiral-wound membrane filtration plants[END_REF]. For each simulation, total power to be supplied by the pumps was noticed so as to determine specific energy consumption (kWh/m 3 ) of each configuration. In addition, the rejection of total dissolved solids (TDS) was estimated as a function of N. Figure 2 presents the results of these simulations. Regarding specific energy consumption, it appears that each recovery rate is adapted to a certain number of stages. A single stage system is more energy efficient when a conversion rate of 50% is applied. Two stages are more energy efficient to reach Y=80% and three stages to reach Y=90%.

Indeed, at low conversion rate, the concentrate flow rate is high thus when using only one stage pressure drop along the unit is limited. On the contrary, for higher conversion rate (lower concentrate flow rate), the decrease of hydraulic pressure due to the increase of stages is more interesting from an energetic point of view. In the next part of the article, a conversion rate of 50%, 80% and 90% was thus reached with respectively one, two and three stages. On figure 2, it appears that specific energy consumption decreases with increasing number of pressure vessels in the first stage. For example, feed pressure decreases from 4.6 to 2.1 bars when N increases from 10 to 30. Nonetheless, an increasing number of pressure vessels will have a direct consequence on capital and maintenance cost. Moreover, the decrease of inlet pressure leads to a decrease in TDS rejection because of high diffusive transfer.

Number of pressure vessels influences both TDS rejection and energy consumption. Thus, it has to be optimized so as to minimize operating costs. Annual power cost ($ year -1 ) was obtained by multiplying specific energy consumption (kWh m -3 ) by the price per kilowatt hour ($ kWh -1 ) and by annual permeate flow (m 3 year -1 ). Maintenance costs were obtained by multiplying total number of elements (M) by replacement rate of 10 % and by the price of one element. These maintenance costs were calculated for each conversion rate (50, 80 and 90 %) by varying the number of pressure vessels in the first stage, N, thus varying the total number of pressure vessels. For each case, annual operating costs show a minimum for an optimum number of pressure vessel which is equal to 13 for Y=50% and Y=80% and 12 for Y=90%. In the rest of the study, N was taken equal to 12 so has to have 6 and 3 pressure vessels respectively in the second and third stage.

Concerning the number of elements per pressure vessel (M), van der Meer et al. (1998) showed that even though the classical system configuration of pressure vessels in RO and NF systems is a multistage design with a number of membrane modules per pressure vessel of 6 up to 8, this design trend results in high pressure losses because of high feed velocities and long feed/brine channel lengths (van der [START_REF] Van Der Meer | Only two membrane modules per pressure vessel? Hydraulic optimization of spiral-wound membrane filtration plants[END_REF]. The authors showed that an increase in permeate productivity of 20% can be achieved by lowering the number of membrane modules per pressure vessel. In contrast to the hydraulic optimum, they found an economic optimum between 3 to 4 elements per pressure vessel.

Research of optimal number of elements M was conducted using same approach as for N. The , 1998). At low number of membrane modules, the permeate flow rate decreases as a result of the increasing concentration polarization in this region. This effect becomes more pronounced at higher recoveries, caused by increasing osmotic pressure differences across the membrane surface, as a result of the increasing salt concentrations at the feed/brine side of the membranes at high recoveries. In the rest of the paper, number of elements (M) was taken equal to 6 for one stage and to 5 for two or three stages. The economic analysis of the process shows that an optimum conversion rate of 80% leads to a membrane capital cost of 0.016 $/m 3 . The increase in recovery rate enables a decrease in operating cost per cubic meter of treated water. Nonetheless, this increase in conversion rate would result in an increase in polarization concentration at membrane surface resulting in severe risk of scaling and a lower salt rejection. Indeed, TDS rejection decreases from 94.2% to 89.0% when increasing Y from 50 to 90%. However, this strategy avoids a too high demineralization of permeate water. In addition, nitrate concentration in permeate for Y=90% is still inferior to the recommendation for groundwater recharge [START_REF] Bellona | The pros and cons of using nanofiltration in lieu of reverse osmosis for indirect potable reuse applications[END_REF].

Economic analysis of filtration

As mean value of LSI of feed water was 1.3 which is superior to the recommended value of 1, use of acid was included in the economic evaluation of the process. ROSA proposes two agents (HCl, H2SO4) which enable the LSI to be lowered close to zero value by modifying pH. In this study, H2SO4

was chosen as sulfate ions are retained by more than 90% by NF-90 membrane and thus did not impact the permeate quality. The targeted LSI was 0.2 which required 140.5 mg of H2SO4 per liter of inlet effluent. This represented about 84 m 3 of H2SO4 (96%) per year. As the cost of a cubic meter of H2SO4 is about 730 $ thus annual expense for scaling control by acidification was about 61 000 $ (Table 3). Finally, acid cost was about four times operation and maintenance expenses. Proportion of electrical cost slightly increases when increasing conversion rate (figure 5).

Table 3. Economic analysis of operating and maintenance cost for nanofiltration operation with NF90-400 elements at several conversion rates.

Targeted conversion rate

Comparison with loose-nanofiltration and reverse osmosis process

To highlight the interest of using nanofiltration instead of reverse osmosis, same simulations were performed with NF-270, a loose NF membrane, and BW-30 a RO membrane (Dow Filmtec). Price of NF-270 and BW-30 elements were respectively 900 $ and 680 $ [START_REF] Yangali-Quintanilla | Proposing nanofiltration as acceptable barrier for organic contaminants in water reuse[END_REF].

Table 4 presents the comparison of these processes for Y=80%. As expected, use of RO enables capital cost saving of about 2-3 k$ per year because of lower prices of RO equipment. Table 5 presents the comparison of operating and maintenance cost of nanofiltration and reverse osmosis processes. For high conversion rates, booster pumping may be required between stages.

Operating and maintenance cost varies between 0.09 and 0.19 $/m 3 depending on the conversion rate and membrane type. These costs determined by ROSA are in accordance with literature concerning NF/RO systems (Cote et al., 2005;[START_REF] Englehardt | Urban net-zero water treatment and mineralization: experiments, modeling and design[END_REF]. Globally the cost decreases when increasing membrane permeability (Lp) which is as follow in l/h/m²/bar (LMHB): Lp BW30-400 = 3.2 LMHB < NF90-400 = 10.8 LMHB < NF270-400 = 13.6 LMHB. For Y=80% and an inlet flow rate of 125 m 3 /h, 29.6 k$/year and 35.2 k$/year could be saved using respectively NF90-400 and NF270-400 instead of BW30-400. This is in accordance with other authors (Yangali-Quintanilla et al., 2011;[START_REF] Bellona | The pros and cons of using nanofiltration in lieu of reverse osmosis for indirect potable reuse applications[END_REF]. Indeed, even if RO elements are less expensive than NF elements, energy requirement of the pumps was twice or third the one needed with NF processes which make operating and maintenance costs of RO process higher. Finally, type of NF (loose or tight NF) does not seem to influence considerably the process cost. Nonetheless, this influences performances and rejection rates of the process as it can be seen in table 6. Inlet pressure required to ensure the permeate flux strongly increases when using RO elements. BW30 elements enable near-total rejection of ionic species except nitrate ion whose rejection is 91%. These high rejection rates imply high hydraulic pressure almost twice the hydraulic pressure in NF. Thus, excepted for direct potable reuse, this type of membrane is not recommended for water reuse for groundwater recharge of other use that direct consumption. Rejection of monovalent ionic species with NF-270 does not exceed 70 % which makes it unsuitable for water reuse projects. In fact, as demonstrated in a previous paper (Azais et al. 2014), the NF-270 membrane could produce a good water quality according to the FAO irrigation standards for all of the analyzed parameters except for the potassium. Concerning the aquifer recharge, the CDPH specifies that for replenishing a groundwater basin, the effluent must not exceed 5 mg.L -1 of total nitrogen and 0.5 mg.L -1 of TOC for projects where no dilution in the subsurface is occurring (reclaimed water contribution of 100%). As presented in the Table 6, the major limitation of the NF-270 for water reuse is the poor rejection of nitrogenous species for groundwater recharge. The nitrate concentration in the NF-270 permeate is too close of the accepted limit to preconize this membrane for indirect potable water production. Besides, from previous laboratory tests, the NF-270 TOC permeate concentration marginally lower than the standard of the CDPH could limit its application for water reclamation.

NF-90 permits high TDS rejection which is not impacted per recovery rates. Moreover, it was shown that nitrate concentration in the NF-90 permeate would enable its reuse in direct consumption or ground recharge. Thus, tight NF membranes seem to be well-suited for reuse water projects with strict usages which could be an alternative to the current RO schemes.

Sensivity analysis of the cost of nanofiltration

A sensibility analysis was performed in order to evaluate the impact on the total cost of slight cost variations of membrane equipment. Basic case was defined as the one previously presented with NF-90 and Y=80%. Several cases were tested: a 10% decrease of both elements and pressure vessels, a 10% increase of both elements and pressure vessels, a membrane replacement rate of 5% instead of 10%, a membrane replacement rate of 15% instead of 10%, and a mix of these conditions (table 7). As it can be seen in table 7, variations of membrane equipment and/or membrane replacement rate can result in a modification of annual cost from -5 682 to 6 446 $/year in comparison with the basic case.

Thus, considering the project lifetime of ten years, total amount of the project can be modified by around 60 000 $ depending of current costs which is not negligible.

Economic evaluation of ozonation of NF retentates

Economic evaluation of ozonation step is necessary so as to define the optimal conversion rate which ensures a compromise between permeate flux and treatability of the NF retentate. Cost of retentate ozonation was estimated for the three conversion rates of the study and compared to direct ozonation of the effluent. Results are presented in table 8.

Table 8. Economic evaluation of ozonation step on secondary effluent for several conversion rates.

Cost of ozonation of secondary effluent in this study is in accordance with literature [START_REF] Margot | Treatment of micropollutants in municipal wastewater: Ozone or powdered activated carbon?[END_REF]Ni et al., 2013). Ozonation treatment would result in an increase of 30 % of the WWTP cost if considering that mean cost of WWTP with MBR is 0.49 $/ m 3 [START_REF] Guo | Review of cost versus scale: water and wastewater treatment and reuse processes[END_REF]. Increase in conversion rate lead to a decrease in operating and maintenance cost because of the reduction of treated volume and thus of the power of ozone generator. Finally, Table 9 presents a cost analysis of the coupling between ozonation and nanofiltration (NF90-400) for several conversion rates and considering a reuse of both permeate and retentate. [START_REF] Plumlee | Costs of Advanced Treatment in Water Reclamation[END_REF].

Nonetheless, quality of the treated water is much more satisfying than for ozonation alone and enables its reuse (Azais et al., 2016 b)). Indeed, ozonation alone does not enable elimination of ionic species and a complete mineralization and thus does not satisfy actual water reuse standards.

In comparison with NF alone, coupling of NF and ozonation results in approximately same CAPEX (table 3). If considering the optimum conversion rate of 80%, which is usually encountered at industrial scale [START_REF] Van Der Bruggen | Reuse, Treatment, and Discharge of the Concentrate of Pressure-Driven Membrane Processes[END_REF], in comparison with NF alone the coupling results in an increase capital costs of 0.005 $/m 3 /year and a decrease of operating cost of 0.019 $/m 3 /year. The cost saving due to the coupling between NF and ozonation is thus 0.014 $/m 3 /year which means 15 330 $/year for a flow rate of 125 m 3 /h.

If considering annual treated volumes with possible retentate recovery (thus increase of the annual treated volume), NF/O3 process would thus be more economical than nanofiltration alone. It has indeed the potential to be cost-competitive in some situations, especially when the recovery of otherwise wasted water is considered. This is in accordance with other authors who concluded that costs associated with zero liquid discharge (concentrate treatment) may be partially offset by the recovery [START_REF] Khan | Management of Concentrated Waste Streams from High-Pressure Membrane Water Treatment Systems[END_REF][START_REF] Umar | Recent Advancements in the Treatment of Municipal Wastewater Reverse Osmosis Concentrate-An Overview[END_REF]. Finally, by taking into account economy of scale, which is found for both capital, operating and maintenance costs [START_REF] Guo | Review of cost versus scale: water and wastewater treatment and reuse processes[END_REF], cost predicted in the present study could be considerably decreased which contributed to make this process attractive for wastewater reuse.

Conclusion

This study has put in evidence that ozonation of nanofiltration retentates would be an acceptable alternative solution from an economic point of view for wastewater reuse. It was shown that NF could be used in lieu of RO as advanced treatment. NF is an effective barrier for organic contaminants which is less expensive than RO because of lower O&M costs. Cost saving for a flow rate of 125 and Y=8 % could be 35 k£/year when using nanofiltration instead of reverse osmosis. This may be enhanced in the future if more demand of NF develops the market, meaning less capital cost when selecting NF membranes instead of RO. Concerning the filtration step of the proposed advanced process, a three stages configuration with a decreasing number of pressure vessels (N) in parallel -12, 6 and 3 pressures vessels with 6 elements (M) on first stage and 5 elements on second and third stages -is well-adapted. An optimum conversion rate of 80 % was found. Ozonation of nanofiltration retentates enable a possible reuse of both permeate and retentate and thus can result in lower production costs.

For instance, an economy of 15.4 k$/year of operating costs was obtained for a flow rate of 125 m 3 /h.

One can expect considerable cost saving for higher flow rates as usually encountered. Considering such a process will result in a reduction of greenhouse gas emission compared to conventional highenergy reuse processes based on the use of reverse osmosis.

(

  figure1). First stage is composed of N pressure vessels each including M elements in series. Next stage has N/2 pressure vessels and last stage N/4 pressure vessels. In the experimental study, three Volume Reduction Factor (VRF) were tested: 2, 5 and 10 which correspond to recovery rate (Y, defined as the ratio of permeate flow by feed flow) of about 50, 80 and 90 % respectively(Azais et al., 2016 a). To reach these recovery rates, number of stage has to be adapted. Y of 50 % was applied to the first stage and Y of 60% was applied to second stage thus resulting in global Y of 80 % for two stages. Y of 50% was applied on last stage resulting in final Y of 90 % close to VRF 10 which was obtained at pilot scale(Azais et al., 2016b). To reach these conversion rates, ROSA adjusted pressure at the entrance of each stage according to the number of stage and pressure vessels and type of membrane.

Figure 1 .

 1 Figure 1. Configuration of the nanofiltration unit (number of pressure vessels: first stage N=4, second stage N/2, third stage N/4).

Figure 2 .

 2 Figure 2. Influence of pressure vessel number in the first stage (N) (number of elements M=7).

  Figure 3 presents operating costs as a function of N and number of stages. Number of elements (M) in a pressure vessel was fixed to 7.

Figure 3 .

 3 Figure 3. Influence of number of pressure vessel in the first stage (N) and number of stages on annual operating costs (number of elements M=7).

  pressure vessel number was 12 in the first stage, 6 in the second stage and 3 in the last stage. M was varied between 2 and 8 (maximum authorized by ROSA). Then, operating costs were evaluated for each configuration. Results are presented in figure4.

Figure 4 .

 4 Figure 4. Influence of number of elements (M) and stages on annual operating costs (total number of pressure vessels N=12).

Figure 5 .

 5 Figure 5. Part of operating and maintenance costs for several conversion rates.

Table 1 .

 1 Water quality of the WWTP effluent.

	Parameters	Units	WWTP effluent
	pH	-	7.69 ± 0.31
	Conductivity	mS cm -1	1.30 ± 0.22
	Alkalinity	mg eq CaCO3 L -1	430 ± 80

  as estimated byYangali-Quintanila et al. (2010) (Yangali-Quintanila et al., 2010). To calculate the annual capital costs, project lifetime was taken equal to 10 years (life time of membranes) with an interest rate of 7%. Finally, two uses of the treated water (permeate) were considered: irrigation according to the FAO recommendations and the aquifer recharge in agreement with the Groundwater Recharge Requirements proposed by the California Department of Public Health (CDPH). The standard values are presented in a previous study (Azais et al. 2014).

Price

of kilowatt-hour was based on current rate in France which is about 0.09$.kWh -1 in accordance with

[START_REF] Plumlee | Costs of Advanced Treatment in Water Reclamation[END_REF]

[START_REF] Plumlee | Costs of Advanced Treatment in Water Reclamation[END_REF]

. Moreover, annual membrane replacement rate was taken equal to 10%

Table 2 .

 2 Table2presents the economic analysis of the process in term of final membrane capital cost (pressure vessel and membrane module) with one, two or three stages as shown on figure1. Economic analysis of membrane capital cost for nanofiltration operation with NF90-400 elements.

	Targeted conversion rate	Y = 50 %	Y = 80 %			Y = 90 %
	Stage	1	1	2	1	2	3
	System details
	Feed flow (m 3 .h -1 )	125	125	62.5	125	62.5	25
	Permeate flow (m 3 .h -1 )	62.5	62.5	37.5	62.5	37.5	12.5
	Retentate flow (m 3 .h -1 )	62.5	62.5	25	62.5	25	12.5
	Recovery rate (%)	50	50	60	50	60	50
	Total membrane area (m²)	2 676	3 344			3 902
	Average permeate flux (L.h -1 .m -2 )	23.4	29.9			28.8
	Feed pressure (bar)	5.04	5.55	7.52	5.55	7.52	6.75
	Economic analysis
	Pressure vessel (quantity)	12	12	6	12	6	3
	Pressure vessel cost ($)	18 000	27 000			31 500
	Membrane module (quantity)	72	60	30	60	30	15
	Membrane module cost ($)	61 200	76 500			89 250
	Membrane capital cost ($)	79 200	103 500			120 750
	Annual membrane capital cost ($/year)	11 276	14 736			17 192
	Annual membrane capital cost ($/m 3 )	0.020	0.016			0.017

Table 4 .

 4 Comparison of the membrane capital cost of nanofiltration and reverse osmosis for Y=80%.

			Annual membrane capital	Annual membrane capital
	Membrane	Membrane capital cost ($)
			cost ($/year)	cost ($/m 3 )
	NF90 -400	103 500	14 736	0.016
	NF 270 -400	108 000	15 377	0.017
	BW30 -400	88 200	12 558	0.014

Table 5 .

 5 Comparison of operating and maintenance cost of nanofiltration and reverse osmosis processes.

	Targeted conversion rate	Y = 50 %	Y = 80 %		Y = 90 %
		NF270-400
	Feed pressure (bar)	3.57	3.91	4.77	3.91	4.77	3.89
	Pumping power (kW)	16.97	23.87		24.41
	Specific consumption (kWh.m -3 )	0.27		0.24		0.22
	Electric cost ($.year -1 )	13 379	18 819		19 245
	Membrane replacement ($.year -1 )	6 480	8 100		9 450
	Acid ($.year -1 )	61 000	61 000		61 000
	O&M cost ($/year)	80 859	87 919		89 695
	O&M cost ($.m -3 )	0.12		0.10		0.09
		NF90-400
	Feed pressure (bar)	5.04	5.55	7.52	5.55	7.52	6.75
	Specific consumption (kWh.m -3 )	0.35		0.32		0.29
	Electric cost ($.year -1 )	17 246	24 913		26 165
	Membrane replacement ($.year -1 )	6 120	7 650		8 925
	Acid ($.year -1 )	61 000	61 000		61 000
	O&M cost ($/year)	84 366	93 563		96 090
	O&M cost ($.m -3 )	0.15		0.11		0.10
		BW30-400
	Feed pressure (bar)	11.18	13.2	17.22	13.2	17.22	15.68
	Specific consumption (kWh.m -3 )	0.80		0.71		0.63
	Electric cost ($.year -1 )	39 428	56 071		56 071
	Membrane replacement ($.year -1)	4 896	6 120		7 140
	Acid ($.year -1 )	61 000	61 000		61 000
	O&M cost ($/year)	105 324	123 191		124 211
	O&M cost ($.m -3 )	0.19		0.14		0.13

Table 6 .

 6 Comparison of performances and rejection rates of nanofiltration and reverse osmosis process.

	Targeted conversion rate	Y = 50 %	Y =80 %			Y = 90 %
	Stage	1	1	2	1	2	3
			NF-270
	Feed pressure (bar)	3.57	3.91	4.77	3.91	4.77	3.89
	Osmotic pressure (bar)	0.66	0.95			1.27
	Average permeate flux (L.h -1 .m -2 )	23.4	29.92			28.84
	TDS rejection (%)	62.5 ± 2.0	64.0 ± 1.5	70.0 ± 1.2 64.0 ± 1.5 70.0 ± 1.2 70.2 ± 0.1
	Average permeate conductivity (µS.cm -1 )	868.48	927.77			1037.4
	Permeate nitrate concentration (mg.L -1 )	4.93	4.78	5.2	4.78	5.2	6.36
	pH of permeate	6.15	6.2			6.28
			NF-90
	Feed pressure (bar)	5.04	5.55	7.52	5.55	7.52	6.75
	Osmotic pressure (bar)	0.78	1.51			2.52
	Average permeate flux (L.h -1 .m -2 )	23.4	29.9			22.44
	TDS rejection (%)	91.8 ± 1.9	95.5 ± 0.4	96.3 ± 0.1 91.8 ± 1.8 92.0 ± 2.3 90.3 ± 6.6
	Average permeate conductivity (µS.cm -1 )	98.2	113			152.5
	Permeate nitrate concentration (mg.L -1 )	3.40	3.23	3.52	3.13	3.52	4.01
	pH of permeate	5.22	5.28			5.41
			BW30
	Feed pressure (bar)	11.18	13.2	17.22	13.2	17.22	15.68
	Osmotic pressure (bar)	0.8	1.53			3.02
	Average permeate flux (L.h -1 .m -2 )	23.37	29.9			29.21
	TDS rejection (%)	> 99	> 99			> 99
	Average permeate conductivity (µS.cm -1 )	12.94	15.97			22.93
	Permeate nitrate concentration (mg.L -1 )	0.76	0.66	1.38	0.66	1.38	3.94
	pH of permeate	4.71	4.77			4.8

Table 7 .

 7 Effect of slight variations of membrane cost and replacement rates on the total cost of membrane operation.

	Membrane capital cost ($)	Annual membrane	Annual	∆$/year
		capital cost ($/year)	membrane
			replacement
			($/year)
	Basic case NF-90 Y=80%	14 736	7 650	0
	Pressure vessels and elements -10%	13 262	6 885	-2 239
	Pressure vessels and elements + 10%	16 210	8 415	2 239
	Annual membrane replacement rate 5%	14 736	3 825	-3 825
	Annual membrane replacement rate 15%	14 736	11 475	3 825
	Pressure vessels and elements + 10% and Annual membrane replacement rate 15%	16 210	12 622	6 446
	Pressure vessels and elements -10% and Annual membrane replacement rate 5%	13 262	3 443	-5 682

Table 9 .

 9 Cost analysis of coupling between ozonation and nanofiltration using NF90 -400 with reuse of permeate and retentate. NF/O3 treatment of the effluent (without considering the benefit of the reuse) resulted in an increase of almost 80% of the ozone process cost as demonstrated by[START_REF] Plumlee | Costs of Advanced Treatment in Water Reclamation[END_REF]

		0.09 -0.13	0.09 -0.24	0.16 -0.32	0.32 -0.42
	O&M cost ($.year -1 )	8 558 -12 967	4 273 -11 670 3 112 -9 336	3 112 -4 150
	Average O&M cost ($.m -3 )	0.010	0.014	0.028	0.033
	Average capital cost ($)	115 000	95 000	55 000	40 000
	Average capital cost ($.year -1 )	19 600	16 200	9 400	6 800
	Average capital cost ($.m -3 )	0.018	0.029	0.043	0.062

Acknowledgements

We would like to express our gratitude to Filmtec/Dow Chemical Company for the availability of their software ROSA on the internet. The authors acknowledge the French National Agency for Research (ANR) for supporting this study through the convention ANR JCJC 2016 project SAWARE (ANR-16-CE04-0002-01).