Experimental Study of Dye Degradation in a Single-Jet Cavitation System

Abstract

Fluid mechanical conditions are crucial for cavitation formation, and significantly influence chemical reactivity. This study investigates process conditions such as pressure, degassing, cavitation and reaction volume, and the sound emission of oxidative dye degradation by cavitation. For ensuring comparability and scalability, dimensionless similarity numbers aligned to the process were introduced. A further focus of the paper is reproducibility with corresponding guidelines. Measurements of dye degradation were carried out without additional chemicals. The oxidation process was assessed by the chemiluminescence of luminol. For this purpose, configurations with three nozzle sizes at different pressure differences were investigated. The generated cavitating jet was captured by imaging techniques and correlated to degradation. The most energy-efficient configuration was obtained by the smallest nozzle diameter of 0.6 mm at a pressure difference of 40 bar. Significant degassing occurred during cavitation. It was more pronounced with smaller nozzle diameters, correlating with higher degradation. Furthermore, discontinuous treatment methods can improve efficiency. Scaling to higher flow rates through multiple reactors in parallel proved more effective, compared to increasing the nozzle diameter or the pressure difference. For the same treated volume, two parallel reactors increased degradation by a factor of 1.35. The insights provide perspectives for optimizing jet cavitation reactors for water treatment.

1. Introduction

Water is increasingly contaminated by various chemical substances, which poses a significant threat, as illustrated for the case of synthetic dye in [1,2]. The use of hydrodynamic cavitation (HC) presently is one of the most promising strategies for reducing undesirable substances that cannot be removed by classical wastewater treatments. The implosion of cavitation bubbles or clouds of such bubbles lead to locally extreme thermodynamic states termed “hot-spots” [3]. It can be used for the homolytic cleavage of water, generating highly reactive hydroxyl radicals. These radicals have a strong oxidative effect with a high oxidation potential of 2.8 V, and are categorized as an advanced oxidation process (AOP) for the degradation of chemical substances [4].

Numerous studies have been conducted on the degradation of organic substances using HC. In [5], a Venturi nozzle was used in an acidic medium at 5 bar with the addition of 2040 μM of H₂O₂ to achieve 100% decolourisation of the dye Reactive Red 120. Without H₂O₂, 60% decolourization was obtained. In contrast, for the degradation of pharmaceutical micropollutants through shear-induced cavitation, a 47–86% reduction in the concentration of diclofenac and carbamazepine within 15 min at 50 °C was observed with the addition of 340 mg/L H₂O₂ [6]. Askarniya et al. [7] investigated the degradation of Congo red (CR) at a concentration of 20 mg/L by HC using an orifice plate combined with Fenton’s reagent. The maximum decolorization achieved at pH 3 in 60 min was 70% for a solution with a FeSO₄ concentration of 25 mg/L and 1000 mg/L H₂O₂. The operation was performed at 6 bar and 40 °C. At pH 6.5, and HC only achieved 21% decolorization. In [8], HC was generated through a ball valve at a pressure difference of 0.14 bar and a 50% degradation of CR was obtained with an initial concentration of 15 mg/L. It is suggested that the degradation was solely due to thermal factors. In [9], CR was degraded by up to 38.8% using HC. A simulatively optimized Venturi nozzle was used, and the inlet pressure was set to 5 bar. Degradation of 11.6% was achieved, starting from an initial concentration of 20 mg/L, with an orifice using HC in the same setup, during a treatment time of 60 min at 33 °C. Investigating the nozzle geometry of the cavitating device, a Venturi nozzle with 4 mm diameter was optimized by experiment and simulation comparing it to different orifice plate configurations, e.g., one 4 mm hole orifice and a plate with 33 holes with a 0.69 mm hole diameter each [9]. The decolorization was found to be most effective at an inlet pressure of 6 bar, achieving 11.6% for one hole, 26.2% for 33 holes, and 38.8% for Venturi configuration over 60 min at 5 bar. Further research has been conducted on the degradation of dyes with HC at a relatively low inlet pressure [10,11,12,13]. Degradation was achieved at very low inlet pressures, below 10 bar, in all studies. However, in the configuration in the present study, cavitation started to occur for the nozzles used above a pressure difference of 7 bar which marks a difference compared to the mentioned configurations.

The studies in the literature typically differ from each other in several key parameters, such as temperature, treatment time, initial concentration, pH value, and the cavitation device used. Therefore, it is difficult to compare their results. With this background, the present experimental setup was designed to control and maintain several parameters at a constant level to warrant reproducibility. In the presented study the nozzle contour, temperature, initial concentration and pH, system volume, reactor size, water quality, pump, reactor, piping system and tank are constant. The pressure difference ${\Delta p}_{12}$, the nozzle diameter $d$, and the treatment time $t_T$ were varied systematically to investigate their respective influence. All the tests were conducted several times [14]. In [15], the requirements for experiments involving cavitation were proposed which are extended here, furthermore adding the influence of the treatment sequence, i.e., the procedure before, during and after the degradation tests.

The investigations in the present paper were conducted using CR as a reference substance. Although it is toxic, it is commonly utilized in the textile industry [16]. The qualification of the degradation experiment becomes pivotal for making reliable statements about the overall efficiency of HC. The aim was to identify characteristic parameters and promising configurations to gain insights into the efficacy of the HC process in purifying water optimization for the highest degradation within the parameters investigated. For this reason and to measure only the effect of HC, no additional chemical substance was added to the aqueous solution. This study focuses only on HC to investigate the influence on it as a single process, knowing that adaptation into a multi-process is of interest [17]. Avoiding chemicals also has benefits in terms of sustainability, since this prevents additional environmental pollution and damage to the ecosystem, with the formation of by-products that are counter-productive to the purification of the water.

The present study includes contributions on the influence of process conditions, carefully considered dimensionless numbers relevant to the process, the proof of oxidation by chemiluminescence, statements on scalability, and guidelines for the reproducibility of corresponding investigations.

2. Configuration

2.1. Experimental Setup

In the present work, HC was investigated in the special form of jet cavitation. The experiments were carried out in a reactor integrated in a closed hydraulic circuit, with the scheme shown in Figure 1. It consisted of a stainless-steel pipe system with an open tank (6) ($V$ = 2 L), containing process measuring instruments (7). The flow was driven by an in-line piston pump (8) (Oertzen 312 Profi, Germany, ${∆p}_{12, max}$ = 170 bar; ${\dot{V}}_{max}$ = 10 L/min). The reactor had a square cross-section (1) and a volume of $V_R$ = 0.135 L. Cavitation was generated in a jet emitted from a nozzle with dimensions reported in Figure 2. The reactor had transparent PMMA windows providing visual access to the cavitating flow for the different measurement methods employed, which is summarized as cavitation analysis unit (2). To determine the size spectra of the remaining bubbles, a bubble analysis unit (3) was installed downstream of the cavitation device.

Pressure measurements were located before (p₁) and after (p₂) the reactor. Pressure p₁ was regulated by the volume flow rate (4a) in the bypass. The flow rate through the reactor was measured by an oval gear flow meter (9) further discussed below. The outlet pressure p₂ was adjustable independently of the volume flow rate by means of a throttle and a pump (4b). A cooling system (5) was integrated in the circuit to keep the temperature constant.

The pressure difference ${∆p}_{12}=p_1-p_2$ was in the range of $0 \mathrm{b}\mathrm{a}\mathrm{r}\le {∆p}_{12}\le 60 \mathrm{b}\mathrm{a}\mathrm{r}$ and three different nozzles were employed, with diameter $d=\left\{0.6;1.0;1.7\right\} \mathrm{m}\mathrm{m}$. The goal was to investigate the influence of these two parameters on the degradation. The temperature was maintained in the range of ${\vartheta }_T=27 °\mathrm{C}\pm 2 °\mathrm{C}$. To designate the configuration under investigation, a 4-digit acronym was defined indicating nozzle diameter and pressure difference. For example, 0640—stands for $d=0.6 \mathrm{m}\mathrm{m}$ and ${∆p}_{12}=40 \mathrm{b}\mathrm{a}\mathrm{r}$.

Figure 2 provides information about the geometry of the reactor and the included nozzle. These were identical in all cases, if not stated otherwise. The cavitation device was located vertically in the test rig with the nozzle introduced by $l_e=25 \mathrm{m}\mathrm{m}$ into the reactor. Characteristic features of the nozzles are their diameter $d$, ratio $l/d$ of nozzle length to diameter, and constriction length $l_d$, as defined in Table 1. The jet created downstream of the nozzle cavities, to an extent, was determined by the parameters of the system. The amount of cavitation can be characterized by the length of the cavitation zone,${ l}_c$, which is smaller than the length of the reactor, $l_R$ (Figure 2).

Table 1. Numerical values of the geometry parameters in Figure 2.

Parameter	${\mathit{d}}_1$	${\mathit{d}}_{\mathit{N}}$	${\mathit{l}}_{\mathit{d}}$	$\mathit{l}/\mathit{d}$	${\mathit{d}}_2$	${\mathit{l}}_{\mathit{e}}$	${\mathit{l}}_{\mathit{R}}$	${\mathit{d}}_{\mathit{R}}$
numerical value	3 mm	12 mm	5.5 mm	2.5	9 mm	25 mm	150 mm	30 mm

Table 1. Numerical values of the geometry parameters in Figure 2.

Parameter	${\mathit{d}}_1$	${\mathit{d}}_{\mathit{N}}$	${\mathit{l}}_{\mathit{d}}$	$\mathit{l}/\mathit{d}$	${\mathit{d}}_2$	${\mathit{l}}_{\mathit{e}}$	${\mathit{l}}_{\mathit{R}}$	${\mathit{d}}_{\mathit{R}}$
numerical value	3 mm	12 mm	5.5 mm	2.5	9 mm	25 mm	150 mm	30 mm

The operational conditions for a given nozzle are mainly controlled by the pressure difference ${∆p}_{12}$, the flow rate $\dot{V}$, and the back pressure $p_2$, also named reactor pressure. The value of $p_2$ depends on the flow rate $\dot{V}$, the outlet pipe size $d_2$, and the pressure drop of the piping to the tank. The latter can be adjusted by the throttle and pump in unit 4b. The back pressure $p_2$ was measured 100 mm downstream of the reactor outlet which is sufficiently close. The measurement point for $p_1$ was located 400 mm upstream of the nozzle exit in the supply pipe with inner diameter $d_1$ and outer diameter $d_N$.

Another design parameter for piping is the constriction coefficient ${\beta }_c$. In the present case, it was used to characterize the relative size of the nozzle diameter $d$ to the hydraulic diameter of the reactor $d_R$ which is equal to the edge length of its square cross-section. In the present study, ${\beta }_c$ ranged from 0.02 to 0.06.

2.2. Measurement of Process Variables

When investigating the degradation by cavitation, particular attention was paid to the reproducibility and comparability of the results. For this reason, several relevant process parameters were monitored. The pressure upstream ($p_1$) and downstream ($p_2$) of the reactor were measured by pressure transmitters (ADZ Nagano TPSI, Ottendorf-Okrilla, Germany). Furthermore, the vapor pressure $p_v$ values were obtained from recognized tables and ambient pressure $p_a$ recorded from a barometer. The measurement of the volume flow $\dot{V}$ was performed with a positive displacement oval gear flow meter (Kobold DON-H, Hofheim, Germany) installed upstream of the reactor (9 in Figure 1). An estimated number of cycles $N_c$ per treatment can be derived for each configuration by

$$N_c=t_T {\displaystyle \frac{\dot{V}}{V}}$$

(1)

assuming an equal exchange of the tank volume over time.

The process temperature ${\vartheta }_T$ (Otom, PT1000, Germany), the pH value (Hamilton Polilyte Plus, Jülich, Germany), the dissolved oxygen ${sO}_2$ (Hamilton VisiFerm, Munich, Germany), and the redox potential $E^0$ (Hamilton EasyFerm Plus, Germany) were monitored continuously before and during the whole procedure of treatment (7 in Figure 1). Based on the process values, the hydraulic power

$$P={∆p}_{12}\dot{V}$$

(2)

and the hydraulic energy introduced over the time interval $t_T$

$$E={∆p}_{12} \dot{V} t_T$$

(3)

were determined. Furthermore, a microphone (PCB-130F20, PCB Piezotronics, Hückelhoven, Germany) was installed next to the reactor to measure the noise emission.

3. Process Characterization

3.1. Influencing Effects and Dimensionless Numbers

The experiments reported here show that the process of degrading pollutants by HC mainly depends on the following parameters: nozzle diameter $d$, difference between reactor and vapor pressure $∆p_{2v} (=p_2-p_v)$, volume flow rate $\dot{V }$, pressure difference between reactor and ambient atmosphere $∆p_{2a} (=p_2-p_a)$, pressure difference between upstream and downstream position of the reactor $∆p_{12} (=p_1-p_2)$, and the main dimensions of the reactor (the hydraulic diameter $d_R$ and the length $l_R$, the material properties of liquid such as density $\rho$, kinematic viscosity $\nu ,$ surface tension $\gamma$ and partial density ${\rho }_{O2}$ of initially dissolved oxygen). These values affect the cavitation volume $V_c$ formed in the reactor, which, in turn, significantly determines the effect of oxidation in the reactor. The list of variables accounts for effects, which are related to the process: intensity of cavitation, jet flow regime, and effect of degassing. For comparability and scalability, dimensionless similarity numbers were derived using Buckingham’s Π-theorem [19] for the present setting. In accordance with the theorem, the number of dimensionless groups ${\Pi }_I$ to frame a problem is equal to the number of variables $k_i$, which determine the process, minus the basic dimensions of the variables, such as mass, length and time. In the present case, 11 influencing variables were identified. As a result, eight dimensionless groups ${\Pi }_I$ can be formulated, with the present choice shown in

Table 2. Non-dimensional groups found by applying Buckingham’s Π-theorem.

i	1	2	3	4	5	6	7	8
${\mathit{\Pi }}_{\mathit{I}}$	$\frac{{∆\mathit{p}}_{2\mathit{a}}}{{∆\mathit{p}}_{2\mathit{v}}}$	$\frac{{∆\mathit{p}}_{12}}{{∆\mathit{p}}_{2\mathit{v}}}$	$\frac{{\dot{\mathit{V}}}^2\mathit{\rho }}{{∆\mathit{p}}_{2\mathit{v}} {\mathit{d}}^4}$	$\frac{\mathit{\nu } \mathit{d}}{\dot{\mathit{V}}}$	$\frac{\mathit{\gamma }}{{∆\mathit{p}}_{2\mathit{v}} \mathit{d}}$	$\frac{{\dot{\mathit{V}}}^2{\mathit{\rho }}_{\mathit{O}2}}{{∆\mathit{p}}_{2\mathit{v}} {\mathit{d}}^4}$	$\frac{{\mathit{d}}_{\mathit{R}}}{\mathit{d}}$	$\frac{{\mathit{l}}_{\mathit{R}}}{\mathit{d}}$

.

The dimensionless groups obtained in the first step can be combined in functional relationships. The combinations ${\Pi }_I^{*}$ shown in

Table 3. Dimensionless numbers and ratios by functional combinations of dimensionless groups in Table 2.

${\mathit{\Pi }}_{\mathit{i}}^{\mathit{*}}$	$\widetilde{{\mathit{\Pi }}_{\mathit{i}}^{\mathit{*}}}$	Physical Meaning
${\Pi }_3^{-1}$	${\displaystyle \frac{{\Delta p}_{2v} }{\rho }}{\displaystyle \frac{d^4}{{\dot{V}}^2}}={Ka}_d$	Cavitation number based on diameter. Indicates tendency of the flow to cavitate.
${\Pi }_2^{-1}$	${\displaystyle \frac{{∆p}_{2v}}{{∆p}_{12}}}={Ka}_p$	Cavitation number without geometrical influence, ratio of pressure difference reactor to phase change divided by the pressure drop of the nozzle inlet and reactor. Indicates tendency of the flow to cavitate.
${ \Pi }_4^{-1}$	${\displaystyle \frac{\dot{V}}{\nu d}}={Re}_d$	Reynolds number, ratio of inertial to viscous force. Indicates the flow regime.
${\Pi }_1$	${\displaystyle \frac{{∆p}_{2a}}{{∆p}_{2v}}}=GDP$	Gas dissolution potential. Indicates the potential for degassing due to cavitation.
${\Pi }_3·{\Pi }_5^{-1}$	${\displaystyle \frac{\rho }{\gamma }}{\displaystyle \frac{{\dot{V}}^2}{d^3}}={We}_d$	Weber number, ratio of inertial to surface tension forces. Indicates bubble deformation.
${\left[{\Pi }_3·{\Pi }_5^{-1}\right]}^{0.5}·{\Pi }_4$	${\displaystyle \frac{\sqrt{\rho }\nu }{\sqrt{\gamma d}}}={Oh}_d$	$\mathrm{Ohnesorge} \mathrm{number}, \mathrm{ratio} \mathrm{of} \mathrm{square} \mathrm{root} \mathrm{of} {We}_d$$\mathrm{and} {Re}_d$ number. Indicates interface stability.
${\Pi }_6·{\Pi }_3^{-1}$	${\displaystyle \frac{{\rho }_{O2}}{\rho }}=OX$	OX value, ratio of dissolved oxygen fraction at starting condition in water. A criterion for possible degassing.
${\Pi }_8·{\Pi }_7^{-1}$	${\displaystyle \frac{l_R}{d_R}}=RS$	RS value, ratio of reactor length to diameter. Indicates the local conditions in the reactor. A measure of recirculation and pressure gradient.

represent well-known similarity numbers. The overall temperature is ensured to be constant throughout the process, so that the influence of the temperature is global and accounted for by the material properties.

The dimensionless numbers in Table 3 are defined in terms of quantities that can be measured in the test rig. In particular, with regard to the challenge of defining cavitation numbers as referenced in the literature [20], this study proposes a more robust definition for the purpose of comparison of different investigations for experiment and simulation on the basis of measured variables. For all configurations investigated the values of $OX$ and $RS$ were identical with $OX=$2.3 × 10⁻⁵ and $RS=$ 4.4. In

Table 4. Investigated test cases and related dimensionless numbers.

Configuration	${\mathit{K}\mathit{a}}_{\mathit{d}}$	${\mathit{K}\mathit{a}}_{\mathit{p}}$	${\mathit{R}\mathit{e}}_{\mathit{d}}$	GDP	${\mathit{W}\mathit{e}}_{\mathit{d}}$	${\mathit{O}\mathit{h}}_{\mathit{d}}$
0602	0.51	0.49	9400	0.010	1600	0.180
0620	0.06	0.05	28,700	0.048	15,100	0.180
0640	0.03	0.03	40,800	0.067	30,600	0.180
0660	0.02	0.02	49,900	0.102	45,600	0.180
1002	0.46	0.49	16,500	0.020	3000	0.108
1020	0.09	0.06	39,500	0.142	17,100	0.108
1040	0.05	0.03	54,800	0.254	33,000	0.108
1060	0.04	0.02	66,600	0.341	48,800	0.108
1702	0.90	0.56	21,500	0.142	3000	0.064
1710	0.31	0.17	44,600	0.423	12,900	0.064
1720	0.22	0.12	62,300	0.593	25,100	0.064
1730	0.19	0.10	76,000	0.675	37,400	0.064

, the operational conditions for the investigated cases are displayed in terms of the remaining similarity numbers.

3.2. Materials and Methods for Process Evaluation

The process of water treatment by HC, as described before, is primarily characterized by the flow conditions, which then determine reactivity. For the assessment of the degradation efficiency, the dye Congo red (CR), dissolved in demineralized (DI) water, served as a reference substance for organic pollutants. The reactivity of the flow is driven by the bubble collapse and the resulting radicals [3], and must be quantified using suitable indicators. The investigation of dye degradation focused on the differences between the configurations studied to identify optimal conditions for degradation. An attempt was made to correlate the dye degradation observed with the size of the cavitation volume, the acoustic emission and the reactivity. The reactivity of the flow and the formation of hydroxyl radicals were analyzed using the chemiluminescence of luminol [21].

Table 5. Overview of the objectives, materials, and methods.

Investigation	Dye degradation	Cavitating jet length and acoustic sound emission	Flow reactivity by hydroxyl radicals
Material	DI water, Congo red	DI water	DI water, luminol, NaHCO3
Objective	Degradation level and rate	Cavitation length and acoustic sound emission	Detection of reactive areas
Method	Absorbance measurement using UV-Vis spectroscopy	Image acquisition and processing with laser light sheet illumination; sound level measurement	Long exposure image acquisition of chemiluminescence

provides a comprehensive overview of the employed methods, materials, objectives, and evaluation methods.

3.2.1. Investigation of Dye Degradation

The effectivity of degradation by HC was evaluated using the dye CR. This is an anionic diazo dye purchased from Thermo Fisher Scientific, Karlsruhe, Germany (CAS: 573-58-0) with a molar mass of $M=696.66 \mathrm{g}/\mathrm{m}\mathrm{o}\mathrm{l}$. The dye is nowadays used in diagnostics and research [22,23]. CR exhibits high solubility in water, is optically and biologically stable owing to its intricate aromatic structure [24], is not decreased by conventional water treatment, has high resistance against natural degradation, is considered carcinogenic and toxic [25,26], and is known to generate severe environmental problems [27]. It is readily available and storable, easy to measure by UV-Vis spectroscopy, and relatively easy to dispose of.

To quantify the degradation of CR due to cavitation treatment its concentration was determined using spectrophotometry measurement and the linear relation between absorbance (extinction $E_{\lambda }$) and concentration c, according the Lambert–Beer law. The degradation is defined as the ratio of the remaining concentration to the starting concentration, c/c₀. The success of the treatment process is expressed by the degradation $\xi$, with

$$\xi =1-{\displaystyle \frac{c}{c_0}}$$

(4)

The initial concentration of CR, solved in DI water, was set to $30 \mathrm{m}\mathrm{g}/\mathrm{L}$ for all cases.

3.2.2. Length of the Cavitating Jet and Sound Emission

Investigating the dependence of the degradation process on the flow conditions requires quantifying flow field and cavitation in one or the other way. During the experiments, the length of the cavitation region $l_c$, indicated in Figure 2, turned out to be a suitable parameter for this purpose. It was obtained from digital image processing from the cavitation analysis unit (2) in Figure 1 using a high-speed imaging camera (PCO 2000, PCO, Alzenau, Germany) in front of the reactor, with an exposure time of $t_e=10 \mathrm{\mu }\mathrm{s}$ and a frame rate of f = 15 Hz with side illumination from a light sheet (Nd:YAG laser). The values reported below result from averaging over 300 frames. All images were processed in the same way by thresholding, defined to minimize image noise, and generate binary images [28]. Furthermore, the jet structures and the surrounding gas bubbles were recorded using shadowgraphy with backlighting by laser pulse with the same setting as mentioned above. In addition, a digital single-lens reflex (DSLR) camera (Canon EOS 650D, Krefeld, Germany) with a temporal resolution of $t_e=20 \mathrm{m}\mathrm{s}$ and illumination by a powerful spotlight from the side were used for images of the cavitation region as perceived by the human eye.

As a second criterion, the cavitation intensity was measured by a microphone (PCB-130F20, PCB Piezotronics, Germany) determining the sound pressure level $L_p$ in dB, defined as $L_p=20 {\mathrm{l}\mathrm{o}\mathrm{g}}_{10}(p^{’}/p_{ref})$ with the pressure fluctuation $p^{’}$ and the reference pressure $p_{ref}=20 \mathrm{\mu }\mathrm{P}\mathrm{a}$ [29]. The microphone was positioned at a distance of $l_{mic}=500 \mathrm{m}\mathrm{m}$ pointing to the reactor and mounted mechanically decoupled from it. The signal of the microphone was measured with a temporal resolution of 20 kHz.

3.2.3. Investigation of Reactivity

Hydroxyl radicals are highly reactive, non-selective and short-living oxidants degrading on timescales of nanoseconds [30] which makes them difficult to detect directly [31]. Hence, oxidation and the formation of hydroxyl radicals were detected indirectly by chemiluminescence (CL) of luminol (CAS: 521-31-3; 98% purity, Thermo Fisher Scientific, Germany). Chemiluminescence is also known as cold light emission at room temperature [32]. The oxidative species result from cavitation during which the hydroxyl radicals form and react with luminol, a process emitting blue light [28]. For that purpose, $V=2\mathrm{L}$ of an alkaline luminol solution with $2 \mathrm{g}/\mathrm{L}$ luminol and $7.5 \mathrm{g}/\mathrm{L}$ NaHCO₃ was prepared in DI water resulting in a $pH$ value of 9.5. The images of chemiluminescence were acquired using a DSLR camera (Canon EOS 650D, Germany) and lens EF 50 (Canon, Germany) mm with 1:1.8 STM in a fully darkened room. The exposure time was $t_e=5 \mathrm{m}\mathrm{i}\mathrm{n}$ (ISO 800, F/1.8) and the distance of the camera sensor to the reactor was $l_s=380 \mathrm{m}\mathrm{m}$. The subsequent processing of the images was performed as defined in [27] and used in [33]. Images were binarized, but before this, a threshold value was defined to minimize image noise. The reactive volume was calculated from the two-dimensional area by assuming rotational symmetry [21].

4. Degradation Process

4.1. Procedure

The procedure of treatment, here for degrading CR by HC, was first qualified to ensure the reproducibility of the results using the guidelines for experiments with cavitation and degradation given in [34]. These comprise the specification of the location of measuring points, geometric dimensions to the full extent, measurement of dissolved oxygen, temperature, pH value, proof of oxidation (AOP), and characterizing the flow condition with cavitation. To ensure reproducibility of the experiments, the following three aspects were found to be of particular importance.

First, the configuration of the test rig. Materials were selected that are resistant against the dye as well as against corrosion caused by the cavitation due to oxidation. Furthermore, components were installed that allow the process to be adjustable in terms of temperature and pressure. In particular, constant temperature is important due to the temperature dependence of the reaction kinetics and temperature-dependent fluid properties, such as vapor pressure and viscosity. When configuring the test rig, the measuring points were defined in relation to the nozzle exit as this is the central reference point of the process. Numerous process variables were recorded, the most decisive being supply pressure $p_1$ and back pressure $p_2$, as they are key quantities for cavitation, as well as degassing. For optical accessibility of cavitation patterns, the reactor walls were made of transparent PMMA. With degradation experiments, it is important to bear in mind the entire system and to ensure that none of the components in the circuit causes degradation. Therefore, in order to isolate degradation caused by cavitation, it is essential to know the characteristics of other influencing parts, e.g., pumps or pipe system, and to use inert materials.

Table 6. Overview of the causes of concentration changes without cavitation in the reactor.

Device	Effect to Prevent	Countermeasure
pipe system, tank, pump	adhesion to surface	stainless steel
large tank	sedimentation	stirrer
pump	cavitation	installation of piston pumps

provides an overview of measures to prevent changes in concentration generated by components of the test rig. Solutions implemented for this purpose are listed.

The second important aspect was found to be the measurement procedure of the dye samples. The methodology for identifying degradation is described in Section 3.2 above. Sampling was carried out in the tank by pipette. Measurement by UV-Vis spectroscopy was performed in duplicate immediately after collection. The systematic uncertainty of the dye concentration measurement was within 3%.

Third, the procedure of running the degradation experiment is of importance to ensure comparability between different configurations and reproducibility of the results. The standard procedure employed here throughout, except if stated otherwise, consist of three phases. Phase I comprises the preparatory treatment. After the dye solution was filled into the system, it was circulated without cavitation to obtain constant dye concentration throughout the entire system, monitored by ensuring that the changes in concentration were below 1%. Phase II involves the treatment by HC and circulation after the process without HC. During this phase, process variables were continuously measured and samples were taken every 10 min. This interval was selected after extensive experience with the process. Phase III is the post-treatment phase during which the system was cleaned to restore the initial conditions. To this end, the system was flushed with DI water until the dye concentration was less than 5% of the initial concentration. This procedure was established and optimized in more than 100 degradation experiments.

4.2. Proof of Concept

The effectiveness of degradation of CR by HC was initially demonstrated with the configuration $d=1 \mathrm{m}\mathrm{m}$ and variable pressure difference $∆p_{12}$. The subsequent treatment by HC was limited to $t_T=60 \mathrm{m}\mathrm{i}\mathrm{n}$. Figure 3a displays the results for the degradation $\xi$ calculated by (4) over the treatment time $t_T$. The images in Figure 3b show the area of high bubble density in the reactor downstream of the nozzle outlet, containing vapor and air bubbles, which is associated with the extent of the cavitation volume.

As shown in Figure 3, at $∆p_{12}=2 \mathrm{b}\mathrm{a}\mathrm{r}$, no visible cavitation and no change in concentration could be detected. These conditions are the same as at the end of pre-treatment phase (Phase I), further named “circulation” (CIR).

Cavitation could be observed at $∆p_{12}=20 \mathrm{b}\mathrm{a}\mathrm{r}$ and the concentration of CR then changed over time. The increase in the pressure difference $∆p_{12}$ to 40 bar and 60 bar resulted in stronger degradation, but both values yielded nearly the same level of degradation $\xi$ of about ten percent, although the image in Figure 3 obtained with $∆p_{12}=60 \mathrm{b}\mathrm{a}\mathrm{r}$ shows a significant increase in bubble area compared to the case with $∆p_{12}=40 \mathrm{b}\mathrm{a}\mathrm{r}$.

The results demonstrate that the degradation of CR by HC strongly depends on the pressure difference. Only if cavitation occurs, oxidation takes place and affects the dye concentration. In the configuration studied here, the overall dye degradation appears to saturate at some level of pressure difference, beyond which a further increase in pressure difference does not increase the total reaction rate.

4.3. Effect of Non-Cavitating Circulation

Initial tests showed that results vary depending on the treatment procedure. The reasons are given in Section 4.1 above. Circulating the liquid without cavitation before and after the treatment was found to have a substantial influence on the degradation rate achieved. This is an important issue when results of different devices of different researchers are to be compared. Dilution and wetting effects at the beginning of each test lead to apparent changes in concentration, which is not a degradation process but a saturation of the system. The state of equilibrium regarding constant concentration for this reason is called “saturated” and needs to be obtained before the treatment. The time of circulation until a saturated system is achieved does not depend on the nozzle configuration but on the size of the piping system. This was verified in preliminary tests by sampling in the tank every 5 min over a period of 30 min until the concentration changed by less than 1% for at least 10 min. This resulted in a pre-circulation time of $t_{pre}=15 \mathrm{m}\mathrm{i}\mathrm{n}$ at $∆p_{12}=2 \mathrm{b}\mathrm{a}\mathrm{r}$, which was used for all subsequent tests.

In Figure 4, the degradation results of three different treatment procedures with $d=1 \mathrm{m}\mathrm{m}$ are shown using different combinations of cavitating circulation. To this end, three phases are defined: Phase I designated circulation, without cavitation. For this nozzle with $d=1 \mathrm{m}\mathrm{m}$ this requires $∆p_{12}>7\mathrm{b}\mathrm{a}\mathrm{r}$. The data in Figure 4 were obtained with $∆p_{12}=2\mathrm{b}\mathrm{a}\mathrm{r}$ during this phase. Phase II designated regular cavitation with the nominal pressure difference at $∆p_{12}$. Phase III designates posterior circulation without cavitation. Phase III in Figure 4 was, again, conducted at $∆p_{12}=2 \mathrm{b}\mathrm{a}\mathrm{r}$.

In Figure 4, Case 1 presents the result when applying the procedure with prior circulation (Phase I) followed by a treatment at $∆p_{12}=40 \mathrm{b}\mathrm{a}\mathrm{r}$ over $t_T=120 \mathrm{m}\mathrm{i}\mathrm{n}$. In this case, Phase III is absent and Phase II extends beyond the duration of the other cases which is marked as II*.

Case 2 was run without prior circulation starting directly in Phase II with a treatment time of $t_T=60 \mathrm{m}\mathrm{i}\mathrm{n}$. The initial change of the concentration was significantly stronger compared to Case 1 with prior circulation. The interpolated curve of $\xi$ over $t_T$ is clearly non-linear for Case 2, while the trend for Case 1 has a more linear behavior. The changes in degradation by oxidation, dilution, and wetting overall, which are independent of the cavitation overlap with the cavitation-generated degradation and cannot be clearly separated in this case. At $t=20 \mathrm{m}\mathrm{i}\mathrm{n}$, the amount of degradation in Case 2 is almost twice the one of Case 1. It is obvious that interference with the impact of the system can lead to the wrong interpretation of measured data and erroneous conclusions. Hence, it is important to establish a well-defined state of the entire system that is reproducible and comparable to other cases before any dedicated treatment is performed.

Case 3 corresponds to Case 2 but replaces cavitation in Phase II* by a posterior circulation. This case yields degradation identical to Case 1 until the end of Phase II. The change in concentration after the treatment phase was about 2% for this configuration. This is much less than with cavitation in Case 1 but still amounts to about 13% at $t=120 \mathrm{m}\mathrm{i}\mathrm{n}$ and still exhibiting a gradient. The reason for this behavior is that oxidative species generated by cavitation are still present in the system, circulating and reacting. Regarding energy consumption, circulation after cavitation treatment is an attractive effect to increase efficiency by reducing the cost of treatment. This aspect is further addressed in Figure 8 below and discussed in Section 4.4. Case 2 is now used as the standard procedure.

4.4. Efficiency and Degassing

In addition to the pressure difference, the influence of the nozzle diameter on efficiency was examined. Besides the nozzle with $d=1 \mathrm{m}\mathrm{m}$, a smaller nozzle of $d=0.6 \mathrm{m}\mathrm{m}$ and a larger nozzle with $d=1.7 \mathrm{m}\mathrm{m}$ were employed still using the standard procedure described in Section 4.1. Figure 5a shows the degradation $\xi$ obtained with different configurations normalized by the used cycles. In Figure 5b, degradation is plotted over the input of hydraulic energy E as calculated by (3). All other parameters were kept constant.

For each nozzle diameter, degradation increases with pressure difference $∆p_{12}=40 \mathrm{b}\mathrm{a}\mathrm{r}$. The highest $\xi$ values were obtained at the highest pressure difference that could be realized with the setup. With the smallest nozzle, the best degradation of $\xi =14.5$% was achieved at 60 bar (0660). For $d=1.7 \mathrm{m}\mathrm{m}$ at 30 bar, i.e., configuration 1730, the degradation of $\xi =7.6$% was significantly lower than for 0660, although investing a markedly higher energy input.

Relating the degradation $\xi$ for the different cases, Figure 5a shows that the highest value was obtained for 0640 with $\xi /N_c=$ 0.36%. Using $d=1 \mathrm{m}\mathrm{m}$ and $d=1.7\mathrm{m}\mathrm{m}$, the highest degradation per cycle was obtained by 1040 with 0.11% and 1730 with 0.03%, which is significantly lower than with the 0.6 mm nozzle.

Figure 5b reveals that the degradation value saturates beyond a certain energy input and seems to asymptotically approach a limit value. There is evidence that degradation shows only minor changes above a critical pressure difference of 40 bar for 0640 and 1040 in the configuration investigated. Beyond this point, the required input of additional energy to achieve a marginal increase in degradation is high.

The energetically best operating condition is not at the largest pressure difference for $d=0.6\mathrm{m}\mathrm{m}$ and $d=1.0 \mathrm{m}\mathrm{m}$ nozzle. In the configuration with $d=1.7 \mathrm{m}\mathrm{m}$, the highest pressure difference employed was 30 bar, while temperature was held constant in the setup. The maximum degradation may not be reached in the range investigated, but it is obvious that a degradation level comparable to 0.6 mm requires a greater energy input, which, in turn, would not yield in any greater efficiency.

Figure 6 shows the results for the most efficient cases of each nozzle: 0640, 1040 (see Figure 4, Case 1), and 1730. To better compare the configurations, hydraulic energy $E$ was normalized by $E_{ref}$, the energy of case 0640 after 60 min.

Table 7. Numerical comparison of the degradation obtained in the cases shown in Figure 6 for $t_T=120 \mathrm{m}\mathrm{i}\mathrm{n}$.

Configuration	0640	1040	1730
$\xi$ in %	23.5	17.0	13.3
$k$ in 1/s	3.7 × 10−5	2.6 × 10−5	2.0 × 10−5
$E$ in MJ	0.6	1.4	2.5
$E/E_{ref}$	2	4.5	7.9

reports the corresponding numerical values. All data were obtained by averaging over seven repetitions of the experiment.

Figure 6 shows for all three curves that degradation over hydraulic energy for a treatment time of $t_T=120 \mathrm{m}\mathrm{i}\mathrm{n}$ is approximately linear. This is mainly due to the moderate degradation rate within this time. Comparing all the cases for the same energy consumption (vertical dashed line) shows that the degradation in case 0640 is roughly three times higher than for case 1040 and seven times higher than for case 1730. At the end of the treatment with configuration 0640 after $t_T=120 \mathrm{m}\mathrm{i}\mathrm{n}$, a degradation of $\xi =24\%$ was achieved, while with configuration 1040 a degradation of $\xi =17\%$ was obtained at 2.2 times higher energy, and with configuration 1730 a degradation of $\xi =13\%$ at 4 times the energy $E_{ref}$.

The degradation rate $k$ for these cases was calculated from

$$k=-{\displaystyle \frac{1}{t_T}} ln\left({\displaystyle \frac{c}{c_0}}\right),$$

(5)

a pseudo-first-order approach for the degradation and is reported in Table 7. The configuration with $d=0.6 \mathrm{m}\mathrm{m}$ yielded the highest degradation $\xi$ and the highest degradation rate $k$ were at the lowest energy consumption $E$.

Comparing the time to reach a degradation of 14% (horizontal dashed line in Figure 6), the required treatment time increases strongly with increasing nozzle diameter. For 0640, a treatment time of $t_T=60 \mathrm{m}\mathrm{i}\mathrm{n}$ was required, while $t_T=90\mathrm{m}\mathrm{i}\mathrm{n}$ with 1040 were needed for the same degradation. Case 1730 did not reach 14% within $t_T=120 \mathrm{m}\mathrm{i}\mathrm{n}$.

In all experiments, the process temperature was kept constant at ${\vartheta }_T=27 °\mathrm{C}\pm 2 °\mathrm{C}$, and the $pH$ value and the redox potential $E^0$ also did not change. Only the dissolved oxygen $s{\mathrm{O}}_2$ changed significantly over time for the different configurations during treatment. The change in dissolved oxygen $∆s{\mathrm{O}}_2$ is defined as the difference between the initial dissolved oxygen of fully saturated liquid and the equilibrium state of dissolved oxygen during treatment. The treatment started at $s{\mathrm{O}}_2=100\%$ with a saturated condition at temperature ${\vartheta }_T=25 °\mathrm{C}$. An equilibrium state of dissolved oxygen was reached after a maximum of $t_T=15 \mathrm{m}\mathrm{i}\mathrm{n}$ for all cases [15]. Figure 7 shows the degradation $\xi$ over the change in dissolved oxygen $∆s{\mathrm{O}}_2$ for different nozzle diameters.

Figure 7 shows a strong correlation between the degradation of CR and the change in dissolved oxygen $∆s{\mathrm{O}}_2$. The values of $∆s{\mathrm{O}}_2$ reported correspond to an equilibrium saturation state during treatment, reached after operating $t_T=15\mathrm{m}\mathrm{i}\mathrm{n}$ after the start of the experiment with its initial oxygen concentration in the water [15]. This quantity was measured in the tank and reflects the amount of degassing during the experiment. The degradation increases with decrease in dissolved oxygen. This relation depends only weakly on the nozzle size, which is emphasized by the broken lines in Figure 7. The decreasing dissolved oxygen is attributed to the effect of degassing. Changes in the content of dissolved oxygen in water are due to cavitation and the flow conditions in the reactor on one hand and the conditions in the open tank, where bubbles are separated, on the other hand. When conducting the experiment, this eventually yields a new equilibrium state for the treatment. Figure 7 and Figure 5 show that the smaller the nozzle diameter, the stronger the degassing and the degradation for same pressure difference ${∆p}_{12}$ or same energy consumption $E$. The relative increase in $∆s{\mathrm{O}}_2$ in Figure 7 is stronger for small pressure differences, as seen for ${∆p}_{12}=20 \mathrm{b}\mathrm{a}\mathrm{r}$, and weaker for large differences, as seen for ${∆p}_{12}=40 \mathrm{b}\mathrm{a}\mathrm{r}$ and $60\mathrm{b}\mathrm{a}\mathrm{r}$. With a decreasing nozzle size, as well as with a decreasing pressure difference, the volume flow rate decreases. This results in a longer residence time of bubbles in the reactor, leading to more frequent bubble interaction and, as a result, to larger bubbles. These larger bubbles can be separated better in the tank. The relations of $∆s{\mathrm{O}}_2$ to the flow conditions and dimensionless numbers are further discussed in Section 5.1 below.

The above results demonstrate that, among the cases investigated, configuration 0640 performed best. In the following, this configuration will be used to determine the influence of circulation posterior to the cavitation process with respect to additional degradation effects. This has the potential to increase the efficiency of a process application. It is conjectured that some of the degradation results reported in the literature [34] not only result from cavitation itself, but also from a post-treatment phase, where dissolved oxidative species generate further degradation. This is to be kept in mind when comparing results and procedures. Sometime after the start of treatment, the process reaches chemical equilibrium. According to Yasui [35], a number of 67 chemical reactions have to be considered for the system of water and air. It can be assumed that after the treatment by cavitation back reactions occur until a new equilibrium is reached. In the present study, the concentration of CR is relatively low, so that remaining radicals react with the substance leading to a measurable lower concentration. In addition to the back reactions, the open tank causes a slow increase in the oxygen concentration in the water up to the initial saturation state. With the scope of an energy-efficient treatment procedure, it is important to study the effect of these back reactions on the degradation of CR and to evaluate it. For this purpose, after the cavitation treatment, the dye solution was circulated in the system without cavitation at ${∆p}_{12}=2 \mathrm{b}\mathrm{a}\mathrm{r}$ until the fluid was again in a saturated state. For example, circulating after treatment at ${∆p}_{12}=40 \mathrm{b}\mathrm{a}\mathrm{r}$ for 60 min the level of dissolved oxygen rises back to $s{\mathrm{O}}_2=90\%$ within 30 min.

In Figure 4, case 3, a further increase in degradation after treatment was observed. To determine which treatment procedure results in the lowest energy consumption, Figure 8 shows the results of different treatment procedures investigated for the nozzle with diameter $d=0.6 \mathrm{m}\mathrm{m}$.

Figure 8. Degradation $\xi$ over specific energy $e=E/\xi$ in kJ/% for different procedures composed of treatment by cavitation (CAV) at ${∆p}_{12}=40\mathrm{b}\mathrm{a}\mathrm{r}$ and circulation without cavitation (CIR) at ${∆p}_{12}=2 \mathrm{b}\mathrm{a}\mathrm{r}$ using the nozzle $d=0.6 \mathrm{m}\mathrm{m}$. The results are the averages of seven measurements. Numbers are related to cases in

Table 8. Overview of five procedures and performance values shown in Figure 8.

Case	Procedure Phase	Degradation ξ per Phase in %	Energy E in kJ	Specific Energy e in kJ/%
1	CAV 30 min; CIR 30 min	6.8 + 1.5 = 8.2	159	19.4
2	CAV 60 min; CIR 30 min	13.9 + 1.6 = 15.5	316	20.4
3	2 times Case 1	6.8 + 1.5 + 7.1 + 1.7 = 17.1	318	18.6
4	CAV 60 min	13.9	314	22.6
5	CAV 120 min	23.5	629	26.8

.

Figure 8. Degradation $\xi$ over specific energy $e=E/\xi$ in kJ/% for different procedures composed of treatment by cavitation (CAV) at ${∆p}_{12}=40\mathrm{b}\mathrm{a}\mathrm{r}$ and circulation without cavitation (CIR) at ${∆p}_{12}=2 \mathrm{b}\mathrm{a}\mathrm{r}$ using the nozzle $d=0.6 \mathrm{m}\mathrm{m}$. The results are the averages of seven measurements. Numbers are related to cases in Table 8.

The treatment by cavitation (CAV) was performed at ${∆p}_{12}=40 \mathrm{b}\mathrm{a}\mathrm{r}$ and circulation (CIR) at ${∆p}_{12}=2 \mathrm{b}\mathrm{a}\mathrm{r}$. The overview in Table 8 provides the conditions and energy consumption for the different cases.

The additional degradation by CIR averaged from $\xi =1.6\%$ after $t_T=30 \mathrm{m}\mathrm{i}\mathrm{n}$ or $t_T=60 \mathrm{m}\mathrm{i}\mathrm{n}$ of cavitation. CIR yields similar amounts of degradation, even after several sequential treatments. The effect of degradation during CIR posterior treatment, however, decreases strongly after 30 min. The effect decreases in time and does not lead to the same degradation of CAV by just increasing the duration of CIR. In terms of energy efficiency, the best result was obtained for Case 3, with about 18.6 kJ for 1% degradation, compared to Case 5 requiring 26.8 kJ/%, which gives the worst efficiency. The degradation by circulation causes minor differences in efficiency but has energetically positive aspects regarding the application of the cavitation process over a longer period.

5. Conditions and Reactivity of the Flow

5.1. Flow Conditions

To understand the effectiveness of the degradation process, it is essential to analyze the fluid–mechanical conditions in the cavitation reactor. Visual observations showed distinct differences in the cavitating jet flow among the various configurations, manifesting, e.g., by jet length and undissolved gas bubbles. Audible variations in sound emission by cavitation reflecting variations in pressure difference and nozzle diameter could also be noticed. The relationship between the length of the cavitation region, the volume for potential reactions, and the resulting degradation is an important issue and discussed now.

Figure 9 displays images of the three configurations: 0640, 1040, and 1730. These configurations are the most efficient or have the highest degradation of the nozzles examined. In all three configurations, the formation of hydrodynamic jet cavitation is evident in the water-filled reactor because of inflow through the nozzle from below. The collapse of bubbles occurs at the center of the reactor chamber, away from the wall, after a certain distance from the nozzle outlet. Figure 9 further illustrates the cavitating jet flow and the different conditions of degassed bubbles near the jet, capturing exposure times ranging from milliseconds to microseconds.

Figure 9 displays high-speed photography images, revealing turbulent jet flow after the nozzle exit in all cases. The photos of exposure time $t_e=11 \mathrm{\mu }\mathrm{s}$ display transient flow conditions in the reactor chamber indicating black pixels as gas bubbles. In the images of the DSLR camera white represents gas. The jet forms downstream of the nozzle exit vortex cavitation due to shearing, which is also called shear layer cavitation. The shear layer vortices cause localized pressure minima that lead to cavitation. The core of the jet after the nozzle is liquid until the surrounding unstable and fluctuating shear layer merges from all sides [36]. The characterization of the nozzle by volume flow over pressure difference revealed no cavitational choking. In the reactor after the nozzle, gas bubbles filled with vapor and air are formed by the evaporating air saturated water and implode in distance $l_c$ from the nozzle outlet. The length $l_c$ rises with an increasing nozzle diameter. The decay of the normalized axial velocity is similar for the configurations [37].

The images indicate that cavitation is most intense and occurs the earliest after nozzle exit using the smallest nozzle. The DSLR image in Figure 9 for 0640 displays the highest brightness of the DSLR images after the nozzle exit, suggesting a high density of bubbles in the jet. In contrast, for 1730, the cavitation region is less densely concentrated, which strongly depends on the back pressure $p_2$.

The release of air is especially noticeable in images with a high temporal resolution for 0640 and to a lesser extent for 1040, as evidenced by the bubbles visible next to the jet. In [38], more and larger bubbles were detected in the reactor outlet for 0640 than for 1040, and in 1730, only marginal degassed bubbles appeared. The back pressure $p_2$ at the reactor outlet, which depends on the flow rate and the piping, determines the different degassing conditions. The smallest nozzle $d=0.6 \mathrm{m}\mathrm{m}$ has the lowest flow rate at comparable pressure difference resulting in the lowest value of $p_2$ and the largest residence time, which promotes degassing. Size and volume fraction of the degassed bubbles increase with decreasing $p_2$ according to the saturation depending on pressure according to Henry’s law [39].

Based on the values of the dimensionless numbers introduced in Table 3, the cases displayed in Figure 9 can be assessed further.

Table 9. Values of parameters and dimensionless numbers for the three different nozzles and the cases with the highest degradation.

Parameters and Similarity Numbers	0640	1040	1730
$\xi$$\mathrm{in} \% (t_T$ = 2 h)	23.5	17.0	13.3
$∆p_{12}$ in bar	40	40	30
$\dot{V}$ in L/min	1.3	2.9	6.9
$p_2$ in bar	1.0	1.3	3.0
$∆s{\mathrm{O}}_2$ in %	37	35	19
${Ka}_p$	0.03	0.05	0.19
${Ka}_d$	0.03	0.03	0.10
${Re}_d$	39,700	53,300	73,900
${We}_d$	30,600	33,000	37,400
${Oh}_d$	0.180	0.108	0.064
$GDP$	0.07	0.25	0.67

lists the measured conditions for setups with the highest degradation obtained for each nozzle. The configurations are similar in terms of pressure difference ${∆p}_{12}$ but differ in volume flow rate, hence pressure $p_2$, impacting the change of dissolved oxygen $∆s{\mathrm{O}}_2$. For 0640, the lowest pressure $p_2$ is related to the highest value of $∆s{\mathrm{O}}_2$ due to relatively strong degassing in the reactor.

The assessment in terms of dimensionless numbers clarifies the differences in the flow conditions during the degradation process. The two defined cavitation numbers are both affected by back pressure $p_2$; however, ${Ka}_p$ is more sensitive to variations in pressure conditions and displays clearer changes between configurations, thus making it a favored measure in comparison to degradation in the following. The second important parameter for cavitation is the pressure difference which is provided by labeling in the figures to each data point.

From Table 9, it can be observed that ${Ka}_p$ is the smallest for 0640, indicating most intense cavitation with the lowest back pressure. The Reynolds number increases with nozzle diameter confirming the image impression of Figure 9, that all three cases are turbulent jet flows. At a comparable velocity but increasing nozzle diameter, a longer jet length but a larger core area without cavitation can also be observed, which both influences the reaction volume. The Weber number differs relatively little between the configurations. ${We}_d$ and ${Oh}_d$ numbers are both clearly in the range of atomizing jets for all cases [40]. Furthermore, the $GDP$ number increases with nozzle diameter for comparable pressure differences, obtaining the lowest value for 0640 and the highest for 1730.

The process depends on cavitation, which is characterized by pressure conditions. These pressure conditions play a crucial role in degassing and degradation. Figure 10 illustrates the impact of pressure difference variation on degradation and degassing for the nozzle diameters. Cavitation occurs in all operating states.

In Figure 10a, the degradation for the three nozzles analyzed is observed to increase with rising pressure difference. Moreover, the discrepancy between the nozzles $0.6 \mathrm{m}\mathrm{m}$ and $1.0 \mathrm{m}\mathrm{m}$ rises from ${∆p}_{12}=40$ bar on and also leaving linearity of degradation increase between 40 to 60 bar. However, the image recordings in Figure 9 show visual changes in the gas fractions around the jet for this range of differential pressures, indicating an influence of outgassing. Figure 10b therefore shows the relationship between degassing and the cavitation number ${Ka}_p$. The influence of the back pressure on the value of the cavitation number is shown by the curve of the $d=1.7 \mathrm{m}\mathrm{m}$ nozzle, which was operated at a significantly higher value. The definition of the cavitation number ${Ka}_p$ highlights the different back pressure conditions. A cavitation number defined by pressure difference and nozzle velocity would also not provide the same values for the different nozzles but would disregard the back pressure as an essential criterion. Figure 10b shows that for $0.6 \mathrm{m}\mathrm{m}$ and $1.0 \mathrm{m}\mathrm{m}$ with the same pressure difference, a stronger outgassing occurs at $d=0.6 \mathrm{m}\mathrm{m}$, which can have an intensifying effect on the degradation process. The cavitation number also indicates this. Comparing similar ${Ka}_p$ values in the range above ${∆p}_{12}=40$ bar, the $d=1.0 \mathrm{m}\mathrm{m}$ exhibits lower levels of degradation but stronger degassing.

Comparing changes in dissolved oxygen $∆s{\mathrm{O}}_2$ reveals that the highest changes occur for $d=0.6 \mathrm{m}\mathrm{m}$ and lowest for $d=1.7 \mathrm{m}\mathrm{m}$. The reasons are twofold. First, degassing at $d=0.6\mathrm{m}\mathrm{m}$ is stronger due to the lower back pressure $p_2$. This also indicates that nozzle with $d=0.6 \mathrm{m}\mathrm{m}$ more liquid evaporates by cavitation leading to a higher degradation. If the volume flow is increased by using a larger nozzle without changing the reactor outlet area, the back pressure $p_2$ increases according to a square root. The rise of degassing is therefore more noticeable with an increase of pressure difference ${∆p}_{12}$ compared to using a larger nozzle diameter. The results show that a low ${Ka}_p$ number and therefore low back pressure $p_2$ combined with a small nozzle are beneficial for effective degradation.

5.2. Cavitation Jet Length and Acoustic Sound Emission

The extent of the cavitation area and its acoustic emission characteristics may be used to characterize the operational state in a cavitation experiment. As the visibility of the cavitation area is not given in many cases, the acoustic emission can be used as a relatively cost-effective monitoring parameter. In present study, the visibility is explicitly provided, enabling the determination of the cavitation region and thus approximately also the volume of reactions.

The length of the cavitation area and the cavitation volume are visually different between the configurations. Audible differences can also be recorded with varying pressure differences and nozzles. The axial expansion of the cavitation area is related to the cavitation volume, which impacts the resulting degradation. Figure 11a shows the length $l_c$ of the cavitation area, normalized by the nozzle diameter, (a) plotted over cavitation number ${Ka}_p$ and (b) over sound pressure level $L_p$ in dB.

In Figure 11a, it is evident that the axial length of the cavitation area increases with the pressure difference, resulted by the decrease in cavitation number ${Ka}_p$. The normalized cavitation length for 0640 is $l_{\mathrm{c}}/d$ = 33 at ${Ka}_p$ = 0.03, while for 1040 it is $l_{\mathrm{c}}/d$ = 28 at ${Ka}_p$ = 0.07. The shape of curve in Figure 11a is concave for all nozzles which is usually the case for cavitation. The increase in cavitation length is a result of the pressure-velocity relationship according to the Bernoulli equation and the non-linear effects such as exponential bubble growth, leading to even lower pressure minima in the flow. The offset of the nozzle $d=1.7 \mathrm{m}\mathrm{m}$ results from the higher back pressure $p_2$.

Figure 11b displays the correlation between sound pressure emission and the normalized cavitation length. The sound pressure level $L_p$ is used to represent the cavitation intensity as it is related to the collapse of vapor-air bubbles and propagation of pressure waves. The sound emission was the highest for the case 1060, with $L_p$ = 87 dB. At a pressure difference of ${∆p}_{12}$ = 10 bar, the sound level of $L_p$ = 63–66 dB was relatively low, as there wasalmost no cavitation visible and audible for all nozzle configurations. At ${∆p}_{12}$ = 20 bar, cavitation was clearly visual and acoustic evident for all nozzles, and the sound pressure level increased up to $L_p$ = 75–80 dB. With increasing pressure difference and thus increasing the length of the cavitation volume, sound pressure level increases as well. Importantly, the sound pressure level is not proportional to degradation. The case 0640 achieves $L_p$ = 81 dB at best degradation, and case 1040 at $L_p$ = 86 dB, while case 1730 has the lowest value of $L_p$ = 78 dB. The nozzle of 0.6 mm generally has reduced noise emissions due to the lower flow rate. This aspect contributes significantly to the offset between the nozzles.

The sound pressure level mainly depends on the source of the sound, which is primarily the flow leaving the nozzle and the collapsing bubbles. Additionally, degassing can dampen the sound emission, resulting in a lower gradient in noise emission for higher pressure differences. The emphasis was placed on the emission of sound in this context, as it is an easily quantifiable and accessible parameter that is not reliant upon the visibility of cavitation.

The acoustic sound emission as well as dissolved oxygen and degradation are employed as target process variables and are found to be effective as process monitoring parameters. The results displayed in Figure 12 show a monotone increase of sound emission and dissolved oxygen when increasing the pressure difference ${∆p}_{12}$. Here, degassing is equated with change in dissolved oxygen $∆s{\mathrm{O}}_2$, as oxygen is representative of most gases contained in the air. The highest amount of degassing was measured for case 0660. It is seen that the amount of degassing increases with increasing pressure difference. When comparing the nozzles with each other, e.g., at ${∆p}_{12}$ = 60 bar, it becomes apparent that the smaller the nozzle the stronger the degassing and the lower the sound emission. Overall, degassing and sound emission rises with increasing pressure difference. That displays the effect of damping due to a high volume of gas bubbles in the reactor.

In Figure 12b, sound emission is related to degradation. Similar to $∆s{\mathrm{O}}_2$, the correlation between sound emission and degradation is nonlinear for the investigated range of pressure difference ${∆p}_{12}$. If the process is to be characterized in a preliminary, approximate way, the sound emission can be used as a monitoring value for the operational state of the process. However, a particularly loud process is not necessarily associated with high degradation and the same degradation cannot necessarily be inferred from the same value of the sound pressure level with different nozzles.

5.3. Reactivity

The flow conditions determine the reactivity of the flow and influence degradation results. Cavitation-induced reactivity is highly dependent on the free radicals formed by homolytic cleavage of water, particularly hydroxyl radicals (HO∙). Different methods to detect OH radicals are discussed in [21]. Reactivity can be determined by chemiluminescence of luminol (CL), which detects the oxidative effect of OH radicals. The reaction between luminol and hydroxyl radicals causes chemiluminescence, which results in a visible blue light emission. The presence of blue light confirms the oxidation process and thus the reactivity of the flow. Importantly, the generated amount of hydroxyl radicals by cavitation is not measured directly.

The area of emitted light recorded from the chemiluminescence of luminol can be used to correlate with the degradation of oxidative substances such as Bisphenol A [33]. Figure 13a displays the extension of the recorded emission area and Figure 13b the degradation over the approximated relative reaction volume. The reaction volume is calculated from the emission area using rotational symmetry; the volume of the cavitation reactor has been used for its normalization.

The area by collected light emission on the image, due to chemiluminescence, increases with pressure difference. The reaction volume is the smallest for the $d$ = 0.6 mm nozzle, behaving similarly to the extent of the cavitation region. The evaluation by CL does not reflect the intensity of the reaction, but it proves the reactivity of the flow. For the best degradation results, the ratio of reaction volume to reactor volume was 0.7‰ for 0640 and 4.1‰ for 1040. This shows that the reaction volume increased for the larger nozzle with higher volume flow at the same pressure difference. However, degassing increases for all nozzle cases as well with increasing pressure difference ${∆p}_{12}$. Chemiluminescence strongly increases with increasing bubble density in the jet and the reactor, proved by increased scattering of light. The higher the flow rate the larger the volume of unsolved air and vapor bubbles.

The CL method offers several advantages, including the use of simple measurement technology in the form of a DSLR camera with a 5 min exposure time, and the requirement of only NaHCO₃ and luminol, which must be dissolved in water. The absorption of light by the camera depends on the optical measurement technology (sensor, lens) used and the room darkening; the room must be completely darkened. The emission of light from the inside to the outside of the jet means that the resulting area on the image depends on the bubble density of the jet and the environment, and thus on the scattering of the light. Larger nozzles will lead to an overestimation of the reaction volume because the bubble-free core area is not considered. Furthermore, temperature range is important, influencing the reaction and CL, which was therefore set constant in the present study.

The results of this method depend on the geometrical configuration of the measuring volume, the combination of process values such as ${∆p}_{12}$ and $d$ with the resulting bubble density, but also the image processing with the threshold setting, which affects the volume size of all but not the trend of CL due to the process configuration.

6. Aspects of Scalability

In process engineering, scalability is the ability of a process or technology to operate efficiently at different scales. It must be adaptable to both smaller and larger scales without losing quality or efficiency. The scale-up of the cavitation process for the degradation of micropollutants on a laboratory scale describes the transition from proof of functionality and effectivity with smaller volumes, to optimizing the process on a pilot scale with increased performance, and achieving industrial efficiencies in terms of energy, treated volume and processing time. To achieve the goal of higher flow rates at the same level of efficiency, it is necessary to understand the key influencing factors and how to control them. The economic importance of scalability is illustrated by the relationship between the efficiency of the degradation and the cost efficiency (energy used) compared to industrial scales. On a laboratory scale, case 0640 was the most energy-efficient of the cases investigated.

To study scale-up of the treatment “flow rate”, three cases were defined based on case 0640 as a reference. The scaling was accomplished in the circuit by (i) increasing the nozzle diameter $d$, case 1040, (ii) increasing the pressure difference ${∆p}_{12}$, case 6060, and (iii) increasing the number of reactors $N_R$ used in parallel. The respective scale-up was then assessed in terms of degradation and energy consumption.

Table 10. Overview of scale-up configurations investigated and their resulting impact on the process.

Case	Ratio to 0640	Case	$\dot{\mathit{V}}$ in L/min	$\mathit{k}$ in 1/s	$\mathit{E}$/VT in kWh/m3	${\mathit{p}}_2$ in bar	${\mathit{\Delta }\mathit{s}\mathit{O}}_2$ in %	${\mathit{K}\mathit{a}}_{\mathit{p}}$	${\mathit{R}\mathit{e}}_{\mathit{d}}$
Base	-	0640	1.3	4.2 × 10−5	1.11	1.07	37	0.025	39,700
$\mathrm{Scale} S_d$	$d/d_0$ = 1.67	1040	2.9	2.9 × 10−5	1.11	1.31	35	0.032	53,300
$\mathrm{Scale} S_{∆p}$	${∆p}_{12}/{∆p}_{\mathrm{12,0}}$ = 1.5	0660	1.6	4.4 × 10−5	1.67	1.11	48	0.018	48,500
$\mathrm{Scale} S_N$	$N_{\mathrm{R}}/N_{\mathrm{R},0 }$= 2	2 × 0640	2.6	5.8 × 10−5	1.11	1.09	31	0.026	39,700

reports the process parameters obtained with the same treatment time, $t_T$ = 60 min, and the values related to the reference case 0640 identified by the index ‘0’.

The results are visualized in Figure 14. Important parameters were monitored: the back pressure $p_2$, total volume flow $\dot{V}$ and degassing ${\Delta sO}_2$, which affect the oxidation and therefore degradation behavior. It is important to note that the total volume to be treated remains the same for all cases.

When the nozzle diameter is increased while the pressure difference remains the same, case (i), the back pressure $p_2$ increases significantly and degassing decreases. This leads to an increase in the Reynolds number but also cavitation number, resulting in lower cavitation intensity but higher turbulence. For all variants of scaling, the maximum degradation of case 0640 was not reached for this case, as shown in Figure 14a. Increasing the volume flow rate by nozzle diameter does not yield a simple linear scaling of the degradation but changes a complex coupled process influenced by degassing, pressure level, and fluid mechanical characteristics. In Figure 14b, the energy-to-degradation value E/ξ is highest of all scaling cases indicating the worst scenario.

When scaling the pressure difference, case (ii), back pressure increases slightly, and several effects become stronger, such as degassing, turbulent fluctuations, and cavitation intensity. Figure 14 shows a slight increase in degradation but a lower ${\xi /N}_c$ value in comparison to case 0640, but a higher to scaling the diameter.

Doubling the configuration 0640 to $N_R$ = 2, case (iii), increased degradation by 35% in comparison to 0640 but doubled the energy input. Although doubling the volume of cavitation, the value of degradation is significantly lower in comparison to the expected value. The main cause of this discrepancy is that not two independent circuits with a doubled total volume flow from one tank were set up. The degradation rate that can be achieved in the case of “Scale $S_N$” with nonlinear kinetics by a pseudo first-order approach for the concentration change according to Equation (5) is only 67% comparing to the configuration of 0640 installed twice in full. An indicator for the difference is the lower degassing compared to the reference.

The configuration 0640 resulted in the highest degradation per loop, while increasing the nozzle diameter resulted in the lowest. Increasing pressure difference only resulted in an increase in energy of 78%. When using two reactors of 0640 in one circuit, the degradation per loop decreased by 33% in total to the reference 0640. This resulted by a similar flow rate in the two reactors as configuration 0640 but doubling the flow rate in the system. The increase in flow rate resulted in a rise in back pressure $p_2$ which in turn led to a reduction in degassing within the system.

Laboratory scale results using Congo red as reference substance resulted in an energy consumption per volume treated $V_T$ of 1.11 $\mathrm{k}\mathrm{W}\mathrm{h}/{\mathrm{m}}^3$ for 0640, Scale $S_d$ and doubling the reactor $S_N$. For the case scaling the pressure difference, it resulted in 1.67 $\mathrm{k}\mathrm{W}\mathrm{h}/{\mathrm{m}}^3$.

After acquisition costs, the primary factor to consider is the energy-to-degradation ration of operation. Based on further optimization of 0640, focus should be on increasing degradation by investigating the impact of degassing. On the other hand, alternating operation between CIR and HC can be used to reduce the energy required.

To optimize the ratio of degradation per energy in kWh, Case 3 discussed in Figure 8 is noteworthy. The change between treatment with CAV and circulation without CAV (CIR) resulted in a 20% improvement in degradation per energy consumption. This is an advantage especially for non-continuous treatment procedures and suitable for applications without time restrictions and the possibility of using load profiles from renewable energy sources.

The scalability tests conducted in the present study have shown that degradation does not scale simply by increasing the nozzle diameter or pressure difference to achieve a higher flow rate leading to a decrease in the energy-to-degradation ratio. For single nozzle configurations, the best approach is to maintain the same conditions in the reactor (0640) and scale the treatment volume by using a system of multiple independent reactors. It is important to obtain similarity for ${Ka}_p$ with comparable $p_2$ since these numbers significantly differ between nozzle sizes and have huge impact on cavitation, degassing and degradation.

7. Conclusions

The paper reports on the influence of different nozzle diameters and pressure differences on degradation and fluid conditions related in a jet cavitation system without addition of supplementary chemicals. Oxidation was confirmed by the method of chemiluminescence of luminol.

Dimensionless numbers were introduced to compare configurations regarding similarity. The study demonstrates that fluid conditions, such as cavitation extent, degassing, pressure difference, back pressure and diameter of the nozzle significantly influence degradation. Experimental reproducibility in cavitation experiments was ensured in this study through defined process procedures. For example, the circulation of the fluid in the system before starting was shown to be crucial for achieving reproducible concentration changes, respectively, degradation. Three different single-nozzle diameters were examined, varying the pressure differences between 2 and 60 bar.

Comparing the configurations, the highest degradation within continuous treatment was achieved by the smallest nozzle 0.6 mm at 40 bar. Increasing the nozzle diameter increased the flow rate but not degradation, while increasing pressure difference increased degradation until a turning point, possibly due to damping effects and geometrical limitations of the reactor volume.

The best energetic operating condition for degradation 0640 did not align with the largest pressure difference. Discontinuous treatment methods by changing between cavitation and non-cavitation circulation controlled by pressure difference showed improved efficiency.

Fluid mechanical similarity between different nozzle diameters was not fully assured, especially for cavitation number and hence back pressure. Significant degassing, particularly pronounced with smaller nozzle diameters, correlated with higher degradation rates. Scaling the process for higher flow rates was found most effective through multiple parallel reactor-nozzle configurations rather than increasing nozzle diameter or pressure difference alone.

Further investigation of scaling the processed volume in time while maintaining similarity with respect to cavitation number and Reynolds number is necessary. In order to ensure comparability, the potential degassing should also be considered in addition to the occurrence of cavitation when analyzing the dimensionless numbers, as its strong influence on the degradation and reactivity of the flow has been demonstrated. All in all, the present cavitation process demonstrated its usefulness for stimulating degradation of unwanted chemicals by hydrodynamic cavitation.