Flow and Combustion Characteristics of Wave Rotor–Trapped Vortex Combustor System

Abstract

Breaking through the limit of conventional compression and combustion, wave rotor and trapped vortex combustors are able to improve the thermal efficiency of gas turbines. Detailed two-dimensional numerical simulations based on Ansys Fluent were performed to study the flow and combustion characteristics of the wave rotor–trapped vortex combustor system. The calculated pressure characteristics agree with the experimental results giving a relative error for average pressure of 0.189% at Port 2 and of 0.672% at Port 4. The flow stratification characteristics and the periodic fluctuations were found to benefit the zonal organized combustion in the trapped vortex combustor. For the six cases of different rotor speeds, as the rotor speed increased, the oxygen mass fraction at the combustor inlet rose and then fell. The proportion of exhaust gas recirculation fell at first and then rose, and the combustion mode became unstable with the dominant frequencies of the fluctuations increasing.

1. Introduction

Gas turbines, as an important power equipment in aviation, electric power and other fields, play a significant role in national defense and economy. For the improvement of overall thermal efficiency, structure, and thrust-to-weight ratio, many advanced gas turbines were designed and studied, for example the trapped vortex combustor.

A trapped vortex combustor (TVC) is a new concept combustor with wide working range, light weight, stable combustion, and other advantages. It has been upgraded four times since its first proposal by Hsu [1]. In TVC, a suitable flow rate distribution, staging combustion, and perfect match of air and gas were realized, which finally led to the efficient combustion and the low NO_X emission. In addition, the changes of combustion in TVC over factors, such as flow distribution [2,3], fuel injection method [4], and cooling and intake condition [5] were studied by General Electric Company and Air Force Research Laboratory [6]. Furthermore, Briones et al. [7] compared the different combustion behavior with standard, RNG, and realizable k-epsilon RANS turbulence models. If a higher inlet pressure can be provided by wave rotor, there is going to be a great thermal efficiency promotion in TVC.

A wave rotor is able to accomplish the process of compression, expansion, and even combustion in a little volume by unsteady pressure wave. By the unsteady pressure wave, energy is transferred directly and efficiently from parts of working medium to other parts in each channel of wave rotor without mechanical components’ working. Compared to a traditional gas turbine, a wave rotor has four advantages. First of all, there is a short response time of the same scale with the pressure wave transfer time. Secondly, there is a low rotor speed and a low rotor centrifugal load. Thirdly, there is the low flow velocity and strong corrosion resistance. Last but not least, there is a high tolerable gas temperature due to the self-cooling by alternative flow of air and gas [8]. The application of wave rotor in aviation originated in the 1980s. The wave rotor was found to be capable of improving the cycle thermal efficiency significantly by increasing the cycle pressure ratio and the maximum cycle temperature. Berchtold, Tausing, and Pearson et al. [9] conducted a preliminary discussion on the combination feasibility of wave rotor and aviation gas turbine and analyzed the performance improvement of different gas turbines connected to wave rotor. Moritz [9], Snyder [10], and Welch et al. [11] successively combined the wave rotor and Allison Model 250 turboshaft engine and assessed the working condition and overall benefits from aspects of performance, compatibility and operability. Welch et al. [12] researched the performance gains of Allison Model 250-C30 turboshaft engine assembled with wave rotor, which are an increase of slight power and a decrease of substantial fuel consumption. It was also demonstrated that gas turbines could be improved through minor structural changes of wave rotor in early research. After that, NASA [13], Purdue University [14], Beihang University [15], Xiamen University [16], Dalian University of Technology [17], and Nanjing University of Aeronautics and Astronautics [18] developed groups of numerical simulations, designs, and experimental methods. Recently, pressure and temperature of working medium compressed in wave rotor were able to design quantitatively [19], which provided a requirement for further research on the combination of wave rotor and trapped vortex combustor.

When a wave rotor and a trapped vortex combustor are connected, there comes a new problem that the interaction of the wave rotor and the trapped vortex combustor as well as the combination of their advantages. There is no solution among studies on separate fields of them, except for a comprehensive analysis on entire flow field from the level of the core engine. However, little attention has been paid to the comprehensive analysis on systemic flow field.

In this research, the flow and combustion characteristics of a wave rotor–trapped vortex combustor system (named as system for short in this paper) were studied by numerical simulation. Focusing on the connecting positions of the wave rotor and TVC and the typical unsteady flow phenomena, different flow and combustion characteristics between the system and the single component were explored. Furthermore, the influence of the rotor speed on flow and combustion, which is caused by the rotatory machine, was investigated.

2. Model, Method, and Verification

2.1. Numerical Model

The system structure is represented in Figure 1a. Considering the symmetry of the wave rotor and TVC, a two-dimension (2D) simulation of the system is set up. Port 2 of the wave rotor is connected with the inlet of TVC, and Port 3 is connected with the outlet of TVC. Given that there is the coupling of lots of influencing factors on the flow field, it is important to control the parameters accurately and analyze the changes of the flow field over a single factor. Therefore, Port 3 of the wave rotor and the combustor outlet are made separately controlled boundaries in the simulation but are connected by a single port in the physical structure.

The principle and the 2D structure are represented in Figure 1. The quadrangular structured mesh, as shown in Figure 2, was set up in fluid domain by Ansys ICEM 19.2 with a total number of about 480,000 and the quality mostly above 0.59. The combustor outlet should have been connected with High Pressure Gas (HPG) inlet (Port 3), as shown in Figure 1a, but there is no structural connection between them in this research for the model simplification. Instead, an identity of total temperature and oxygen proportion at these two boundaries was ensured during iterations. Moreover, due to the flow loss, the total pressure at the combustor outlet is set higher than that at Port 3.

A transient numerical simulation was implemented into Ansys Fluent 19.2. The periodic boundaries and sliding meshes were used to simulate the rotation of wave rotor by two-dimensional translational motion. Moreover, the following settings were utilized to complete the simulation.

• Ideal gas model was applied to the gas phase;
• SIMPLE method was used to solve the Pressure–Velocity Coupling Equation;
• Second Order Upwind was made Spatial Discretization Schemes;
• Standard k-epsilon and Standard Wall Functions were chosen for the viscosity items [20];

The turbulent kinetic energy equation is shown following.

$$\frac{\partial }{\partial t}(\rho k)+\frac{\partial }{\partial x_i}\left(\rho k{u}_i\right)=\frac{\partial }{\partial x_j}\left[\left({\mu }_1+\frac{{\mu }_t}{{\sigma }_k}\right)\frac{\partial k}{\partial x_j}\right]+{\mu }_1\frac{\partial u_j}{\partial x_i}\left(\frac{\partial u_j}{\partial x_i}+\frac{\partial u_i}{\partial x_j}\right)-\rho \epsilon$$

(1)

The turbulent dissipation rate equation is shown following.

$$\frac{\partial }{\partial t}(\rho \epsilon )+\frac{\partial }{\partial x_i}\left(\rho \epsilon u_i\right)=\frac{\partial }{\partial x_j}\left[\left({\mu }_1+\frac{{\mu }_1}{{\sigma }_{\epsilon }}\right)\frac{\partial k}{\partial x_j}\right]+C_1{\mu }_1\frac{\partial u_j}{\partial x_i}\left(\frac{\partial u_j}{\partial x_i}+\frac{\partial u_i}{\partial x_j}\right)-C_2\rho \frac{{\epsilon }^2}{k}$$

(2)

With μ₁ as eddy viscosity and C₁, C₂, σ_k, σ_ε as empirical parameters.

• Eddy Dissipation Model (EDM) was used to simulate the combustion;

The source item of species i in the chemical reaction r is defined by one of the following equations, whose value is smaller.

$$R_{i,r}=v_{i,r}^{\prime }{M}_{w,i}A\rho \frac{\epsilon }{k}\underset{ℛ}{\min }\left(\frac{Y_{ℛ}}{v_{ℛ,r}^{\prime }{M}_{w,ℛ}}\right)$$

(3)

$$R_{i,r}=v_{i,r}^{\prime }{M}_{w,i}AB\rho \frac{\epsilon }{k}\frac{{{\displaystyle \sum }}_P^{Y_P}}{{{\displaystyle \sum }}_j^N{v}_{j,r}^{″}{M}_{w,j}}$$

(4)

with:

• A and B being the Magnuson constant of reactants and products,
• R and P being the reactants and products,
• v being the stoichiometric coefficients,
• M being the molar mass of species, and
• Y being the mass fraction of species.

Aviation kerosene was regarded as fuel, which is denoted by C₁₂H₂₃ in chemistry, and the chemical reaction equation is shown in the following;

$$4C_{12}{H}_{23}+71O_2\iff 48C{O}_2+46H_{2}O$$

(5)

• The Discrete Phase Model (DPM) was switched on for the injection and phase change of fuel. The parcels were injected at 80 m/s along the negative direction of x-axis and distributed by Rosin–Rammler Diameter Distribution Method with the diameter range from 30 μm to 80 μm and the average diameter as 50 μm. The discrete phase was iterated with continuous phase every 20 steps.

2.2. Boundary Condition

The wave rotor–trapped vortex combustor system was modeled upon the design point of wave rotor. The high-pressure outlet of the wave rotor (Port 2) is connected to the combustor inlet by an interface. Port 1 and Port 3 are made pressure inlets, and Port 4 and the combustor outlet are made pressure outlets, which is shown in

Table 1. Boundary condition.

Boundary	Type	Total Pressure (MPa)	Static Pressure (MPa)	Total Temperature (K)
Port 1	Pressure inlet	0.479308	/	458
Port 3	Pressure inlet	1.073684	/	1773
Port 4	Pressure outlet	/	0.397651	/
Combustor Outlet	Pressure outlet	/	1.072673	1773

.

The oxygen proportion is the key factor that affects the combustion state. Therefore, the identity of average oxygen proportions at the combustor outlet and Port 3 must be ensured. To make the simulation closed to the actual operation, the oxygen proportion at Port 3 will be iterated for two or three times until the difference between the oxygen proportions at Port 3 and the combustor outlet is within ±1%, which is shown in Figure 3.

2.3. Verification

The model of TVC references [21]. As for the wave rotor, the same simulation setting as in [19] was adopted to compare the results of the simulation and the experiment.

The pressure in different positions of Port 2 and Port 4 was monitored for verification. The monitored pressure values were made dimensionless into ratios to average pressure at Port 1 and then were averaged over ten timesteps, which was shown in Figure 4.

There are two reasons for the error. First, the averaged pressure may be unable to represent the unsteady state of the wave rotor accurately. Second, the gap leakage leads to the retention of gases in wave rotor which is represented as higher pressure in low pressure zones and lower pressure in high pressure zones, and this unsteady flow is hard to predict in simulation.

Comparing the average pressure ratio of the simulation and the experiment, a relative error for average pressure at Port 2 is 0.189% and that at Port 4 is 0.672%. A good agreement on simulation and experiment could be found obviously. The agreement proves the reliability of the simulation on the system in this research. In addition, the mesh has been verified to be grid-independent and time step-independent [19].

3. System Characteristics Analysis

3.1. Characteristics of Flow Stratification

When the wave rotor and the combustor work as two separated components, they have their own flow characteristics on which many studies have been carried out by scholars. When they compose a system, there is a flow interaction of these two components. Connecting to TVC by Port 2, the wave rotor can change the temperature distribution and the oxygen proportion distribution at its outlet through exhaust gas recirculation effect, which affects the intake condition of the combustor apart from increasing pressure and promoting combustion in TVC.

The exhaust gas recirculation effect in the wave rotor consists of following processes. Low Pressure Air (LPA) gets into the channel from compressor and partially changes into High Pressure Air (HPA) after a mix with High Pressure Gas (HPG) from the combustor outlet. Then HPA is sent to the combustor through Port 2. As the wave rotor rotates, Port 2 closes. The other detained part of HPA together with gas fails in entering the combustor. Both two gases exit through Port 4 without burning, which is called Fresh Air Exhaustion (FAE). Part of HPG turns into Low Pressure Gas (LPG) after expansion and also enters work components through Port 4 to do work. The detained part of HPG makes up Exhaust Gas Recirculation (EGR) with air and returns to combustor. From the temperature distribution and the oxygen proportion distribution in Figure 5, it could be found that the entry of fresh air and gas is in the open order of Port 1 and Port 3, which is similar to the exit of EGR and air. Most importantly, the oxygen proportion distribution and the temperature distribution were stratified at Port 2. The top stream includes more air and possesses lower temperature and higher oxygen proportion. The bottom stream includes more EGR and possesses contrary properties to those of the top stream. This is because the pressure waves and the mixing processes of air and gas are different among channels. HPA is designed to compose the top steam and EGR to compose the bottom stream by wave rotor. Compared to the traditional intake condition of TVC in total, there are higher temperature and lower oxygen proportion as new characteristics of TVC in the system.

With the flow developing in the combustor, the intake flow is separated by the splitter baffle. Most of the top stream gets in the primary combustion zone for burning. The bottom stream mixes with the flow outside the primary combustion zone and participates in a small amount of combustion with divorced flame. In other words, the stratified distributions of the oxygen proportion and the temperature remain along the flow to TVC. Tailored for the zonal organized combustion in TVC, the customized intake condition with the flow stratification is provided for each combustion zone in the combustor, which makes great progress in the TVC design.

3.2. Periodic Characteristics of Flow and Combustion

3.2.1. Periodicity and Time Domain Phenomena Inside components

The physical structure and working of wave rotor determine its distinct periodicity of operation parameters by nature. In each channel exists the pressure wave, and various pressure waves in channels constitute the periodic pressure wave system in the whole wave rotor. Despite the mechanical motion of wave rotor strictly determines the channel rotation related period, the oscillation of combustion will lead to the fluctuation of the pressure and temperature fields in wave rotor as well. The typical periods are as follows.

• Channel sweep period, which is the time for wave rotor to rotate for a single channel and equals to 6.38 × 10⁻⁵ s at design point.
• Half rotation period, which is the time for wave rotor to rotate for a half revolution (8.5 channels) and equals to 5.420 × 10⁻⁴ s at the design point.
• Full rotation period, which is the time for wave rotor to rotate for a full revolution (17 channels) and equals to 1.084 × 10⁻³ s at the design point.
• Combustion period, which is the time between the generation and the divorce of the flame in the combustor cavity.

During a combustion period, there are four processes.

At first, the flame transmission starts at the moment of the last flame divorcing. The fresh air and the fuel enter the cavity of TVC and make up an air mass of high temperature. Then, the air mass begins mixing with gas. When the air mass is of a proper oil–gas ratio, it is lighted by the gas of high temperature and high pressure. The oxygen proportion is highest and the temperature is lowest in this stage.

Then, it comes to the stable combustion stage during which the air mass becomes a part of the main stream in the cavity and takes part in the combustion. In this stage, fuel and air are consumed steady with the accumulation of heat.

With the development of combustion processes, there is not enough fuel or oxygen to maintain combustion. The air mass turns into the gas mass, and the gas mass is divorced from the cavity under the drive of the main stream, which is represented as the flame divorcing in Figure 5. The oxygen proportion is lowest and the temperature is highest in this stage.

Lastly, the new fresh air and fuel enter the cavity, which marks the beginning of new combustion period. The combustion products flow to the combustor outlet in the form of the gas mass. So, the combustion stage can be known by the gas at the combustor outlet.

Despite the parameter variation delay at the combustor outlet as a result of the distance between the combustion center and the combustor outlet, the time of a full combustion period will never change. From the variation of pressure and temperature over time at the combustor outlet in Figure 6, a nearly same period of pressure and temperature is found with the variation lag of temperature behind pressure by about 7.65 × 10⁻⁵ s. The identity is caused by the coupling of pressure and temperature in flow field, and the lag is triggered by the different transmitting of pressure and temperature. The average temperature period of ten adjacent fluctuation is (4.53 ± 0.3) × 10⁻⁴ s, which indicates the combustion period.

3.2.2. Analysis of Periodic Frequency Domain under Component Interaction

To confirm the existence of four typical periods, fast Fourier transform (FFT) was carried out on the quality weighted averages of pressure and temperature at the combustor outlet and Port 2, which creates the frequency spectra in Figure 7. The maximum amplitudes in the spectra are processed and represented in

Table 2. Period and frequency of temperature oscillation.

	Results of CFD-FFT		Prediction Based on Theory		Relative Error (%)
	Period (s)	Frequency (Hz)	Period (s)	Frequency (Hz)
Half Rotation Period	5.40 × 10−4	1838	5.420 × 10−4	1845	−0.38
Full Rotation Period	1.09 × 10−3	919	1.084 × 10−3	923	−0.43
Single Channel Period	6.40 × 10−5	15,620	6.380 × 10−5	15,674	−0.34
Combustion Period	4.66 × 10−4	2144	4.530 × 10−4	2208	−2.90

. Owing to errors within 3%, the frequency of CFD results is thought to tally with theory prediction. Therefore, the temperature fluctuation of CFD results is considered to correspond to the four combustion processes described above. The reason is that the variation of pressure is mainly caused by wave rotor and the variation of temperature is by combustor.

From the FFT frequency spectrum of pressure at the combustor outlet in Figure 7, it can be seen that the amplitude of 2144 Hz is large and shows a strong correlation and identity with the combustion period. It infers that the four periods can be monitored in the flow field, and both the period of wave rotor and the combustion period are going to be found in combustor. The typical fluctuation frequencies of temperature are 2144 Hz, 15,620 Hz, 919 Hz, and 1838 Hz in the order of the amplitude from large to small in the FFT frequency spectra of temperature and pressure at Port 2. The corresponding period of 2144 Hz is 6.4 × 10⁻⁵ s and has a difference from the channel sweep period of 0.395%. the four typical frequencies correspond to the combustion period, the channel sweep period, the half rotation period, and the full rotation period. It can be concluded that the fluctuations of temperature and pressure at Port 2 reflect the periods of combustion and wave rotor at the same time.

In summary, two components of the system are connected by Port 2 and their periods are found to reflect each other. This implies the interaction of periodic fluctuations inside two components, which has never been studied among studies on a single component.

4. Influence of Rotor Speed on System Flow Combustion Characteristics

4.1. Setting of Rotor Speed

The rotor speed is an important controllable variable to change the working state of wave rotor. The rotor speeds of 75%, 80%, 85%, 90%, 100%, and 110% at the design point were selected to investigate the influence of the rotor speed on the system working characteristics. The boundary conditions of the six working states are listed in

Table 3. Boundary conditions at inlet of combustor with different rotational speed.

Case	Rotor Speed Relative to Design Point	Rotor Speed (m/s)	Oil–Gas Ratio	Mach Number
V-1	75%	57.96	0.033	0.145
V-2	80%	61.82	0.025	0.177
V-3	85%	65.69	0.021	0.203
V-4	90%	69.55	0.020	0.205
V-5	100%	77.28	0.022	0.191
V-6	110%	85.01	0.022	0.195

. The reliable working speeds of wave rotor range from the rotor speeds of 80% to 120% at the design point. For this reason, the rotor speed of 75% is beyond the stable working speed range, whose result is for reference only.

4.2. Influence on Combustor Intake Conditions

EGR determines the intake condition of the combustor, and especially increases the temperature at the combustor inlet. Additionally, as a gas containing the combustion products with low oxygen proportion [22], EGR has a complex impact on the combustion. Thus, the mass fraction of EGR is taken as one of the most important indices to measure the system working state in this research.

Although a good index, the mass fraction of EGR is hard to measure directly. Oxygen, as shown in Figure 8, is capable of reflecting the mixing of air and gas as the tracer material. In channels, there is the mass transfer and the energy conversion between LPA of low temperature, low pressure, and high oxygen mass fraction from Port 1 and HPG of high temperature, high pressure, and low oxygen mass fraction. The fluid properties at Port 2, especially the oxygen mass fraction and temperature, are close to those of the gas (LPA or HPG) whose mass fraction is more in mixed gas. When the energy conversion is taken into account only, it can be assumed that the entire HPA comes from part of the LPA and entire EGR comes from part of the HPG. Under the assumption, their mass fractions can be calculated by the oxygen mass fraction.

The influence of the rotor speed on the mixing process can be found in Figure 9. As the rotor speed increased, the EGR proportion in total flow rate at Port 3 rose and then decreased, reaching the maximum at the rotor speed of 85%, but the HPA proportion in total flow rate at Port 1 showed an opposite trend to EGR proportion without synchronism, and reached the minimum at the rotor speed of 100%.

4.3. Influence on Periodicity

The period of wave rotor is caused by its rotation, which affects the period directly. The higher the rotor speed, the shorter the period.

The variation of the rotor speed changes the flow at the combustor inlet and affects the combustion and the combustion period. The streamline and the temperature distribution in Figure 10 show that the combustion mode and the combustion period will change with the rotor speed. There are hardly any changes of vortex location or any obvious fusion and divorce of the flame over time in V-1, V-2 and V-3. The laminar flow characteristics are easily found in these cases, which is attributed to the stable combustion state. Conversely, the combustion state is unstable in V-4 and V-5 where vortex locates in different position at different time. Developed from a little vortex behind the splitter baffle, the air mass grew further by the continuous fusion with the main stream in cavity and took part in the combustion. The air mass then was divorced from the main stream in the form of the gas mass after burning and moved to the combustor outlet. Represented as the divorce–growth–divorce of the flame, a fixed combustion period was formed and kept consistent with the flame transmitting period in Section 3.2.

Due to the stable flow characteristic in the stable combustion state, none of combustion period can be observed in V-1, 2, and 3. From the variation of the average temperature at the combustor outlet over time of V-5 and V-6 in Figure 11, the combustion period is easy to find in the unstable combustion state, and the period of V-5 is longer than that of V-6, which proves the change of the period over the rotor speed.

To confirm the change of the period over the rotor speed further, FFT was performed on the temperature and the pressure at Port 2 of the three unstable combustion cases which include V-4, 5, and 6, whose results are represented in Figure 7c,d, Figure 12 and Figure 13, respectively. Both the combustion period and the channel sweep period were monitored to find that they share a great correlation. The higher the rotor speed, the lower the periods. In

Table 4. Comparison of the theoretical values and the FFT results.

Case	Rotation Frequency of Single Channel (Hz)	FFTFrequencyof ChannelSweepPeriod (Hz)	Error ofChannelSweep Period Frequency (%)
V-4	14,113	14,090	0.163
V-5	15,682	15,620	0.395
V-6	17,250	17,150	0.580
Case	AverageFrequencyof CombustionPeriod (Hz)	FFT Frequency of CombustionPeriod (Hz)	Error ofCombustion Period Frequency (%)
V-4	2049.18	1991	2.91
V-5	2207.5	2144	2.96
V-6	2298.9	2450	6.17

, the monitored frequencies and the FFT frequencies were compared. It led to a result that the error of frequencies from these two methods is small. The error of the channel sweep period frequency is within 0.6%, and the error of the combustion period frequency is within 6.2%. Moreover, the periods obtained from the two methods decrease with the increase of the rotor speed, which confirms the conclusion.

5. Conclusions

The operation of the wave rotor–trapped vortex combustor system was studied using Ansys Fluent 19.2 with a special emphasis on the flow and combustion characteristics. The simulation of the compression process and the combustion process was established, and the corresponding verification was organized. The results showed the feasibility and a great potentiality of the system. In addition, the numerical simulations of the system under six rotor speeds were considered. Some of the main conclusions of the study can be summarized as follows:

• From the spatial distribution characteristics of the flow field, the flow stratification characteristics in the system were found. Formed by the exhaust–gas recirculation in wave rotor, the flow stratification benefits the zonal organized combustion in TVC.
• From the time variation characteristics of flow field, the flow and combustion periodicity in the system was discovered. The periodic characteristics of flow and combustion reflect the upstream turbulence caused by the rotation of wave rotor and the downstream turbulence caused by the divorce–growth–divorce of the flame in TVC.
• The influence of the rotor speed on those two key characteristics was investigated, and three points were found. Firstly, the proportion of exhaust–gas recirculation increases and then decreases with the increase of the rotor speed. Secondly, the combustion modes in the combustor are divided into the stable combustion state under low rotor speeds and the unstable combustion state under high rotor speeds with the rotor speed of 85% at the design point. Thirdly, the unstable combustion period becomes shorter when the rotor speed rises.