A Performance Study of a Cross-flow Air Turbine Utilizing an Orifice for OWC WEC

A direct method to calculate the general dimension and flow parameters for the runner and nozzle section was utilized referring to Mockmore et al.⁽⁹⁾ and Fukutomi et al.⁽¹⁰⁾ respectively. The designed crossflow air turbine is illustrated in Fig. 1 and the design parameters are described in Table 1. The cross-flow turbine in its simplest form consists of a nozzle and a runner section. The induced air flow due to increasing wave level moves through the rectangular crosssection nozzle and flows into the runner. When the wave level is decreased, the air flow from the atmosphere passes through the symmetric shape of nozzle and enters the runner again. Thus, the circulating air flow is continuously moving through the nozzles and runner section that rotate the blade in uni-direction.

Fig. 1

Configuration of the cross-flow air turbine

Table 1

Design parameters for the cross-flow air turbine

CFD simulations of the cross-flow turbine in 3D steady state and transient state were processed using the commercial CFD code ANSYS CFX 14.0. The single domain of the cross-flow air turbine excluding OWC chamber and wave elevation was determined for simplicity of analysis. The full scale of the turbine was adopted for steady state simulation to acquire real performance characteristics of the turbine under real air flow rate conditions. The transient simulation was conducted as 1/16 scale to verify the simulation result by comparing with the experiment result. The mesh comprising fine hexahedral grids, shown in Fig. 2, was generated by ANSYS ICEM CFD so that the high accuracy of analysis results are obtained. The simulations were processed with SST turbulence model. The boundary condition, shown in Fig. 3, for the steady state simulation was set with different rotational speed of 16, 32, 48, 64 rpm and uni-directional inlet air velocity from 2 m/s to 40 m/s, calculated using the design wave elevation and periods, for full scale conditions. In addition, the bi-directional flow having sinusoidal pattern, calculated using the linear wave theory with 0.125m wave height and 0.125~2 sec periods, allows the volume of air induced due to wave motion to pass through the turbine for the transient simulation. The single air phase in boundary condition was used which allows only air to move through the turbine. General Grid Interface (GGI) method was applied for the mesh connection between each parts with the interface.

Fig. 2

Mesh of the cross-flow air turbine by ICEM CFD

Fig. 3

Boundary condition setup of the turbine

Time-series data is cyclical and it is represented into one phase single time-series by a phase averaging method. The primary aim of the phase averaging is not only to obtain smooth result from unstable data from simulation and experiment but also to represent all data, which have different time steps, in one single phase so that all data can be compared in same time range. The time of the time-series data is converted to nondimensionalized by substituting the actual time with a non-dimensional phase (t/T). The time series is divided into segments of repeating cycles with zero-up-crossing. Then, the phase of the data points is allocated by subtracting the previous adjacent zero-up-crossing time and dividing by the cycle period⁽¹³⁾ as shown in Equation (1), where time of zero crossing of immediate cycle (Tzero), time of zero-crossing of end of immediate cycle (Tzero+1), measured time (T measured) and 0 ≤ t/T < 1.

The flow rate through an orifice was determined by calculation of the equations due to its difficulty of calibrating the oscillating flow rate, which contains the air compressibility. It is assumed that the air inside the chamber is isentropic for which a state equation for the open system can be represented in Equation (2), where absolute chamber pressure (pc), chamber density (ρc), and specific heat ratio of the air (γ=1.4).

Linearized expression for the density of air inside the chamber can be illustrated⁽¹⁴⁾ as following Equation (3),

and

A simplified expression of the air flow rate through the PTO system⁽¹⁵⁾ can be described as depicted in Equation (5), where initial chamber volume (V0). The second term in the RHS of the equation is expressed as a modification due to the air compressibility.⁽¹⁴⁾ This equation was adopted to calculate the flow rate through an orifice for both inflow and outflow due to its air compressibility and its simplicity, which can be easily applied in both inflow and outflow.

The dimensions of the orifice plates were designed according to EN ISO standard.⁽¹³⁾ The diameter ratio of the orifice, β=d/D, where d=orifice diameter and D=nozzle diameter, was calculated based on the cross-sectional area of the turbine nozzle.⁽¹²⁾ Various orifice plates with different orifice ratio were tested to obtain similar behavior of turbine damping effects, and the size of the orifice is 0.3D to 0.5D.

The entire domain of the orifice plate have same model scale as the 1/16 scaled turbine, and it was analyzed excluding the OWC chamber and wave motion as well as depicted in Fig. 5. The mesh comprising fine hexahedral grids with 1.51 x 10⁶ nodes was generated as shown in Fig. 4. The transient type of simulation was applied so that same bi-directional sinusoidal flow can pass through the orifice, which generate the damping effects. The same condition of sinusoidal air flow as the turbine was adopted in order to compare the result under same flow condition.

Fig. 4

Mesh of the orifice plate by ICEM CFD

Fig. 5

Boundary condition setup of the orifice

The experiment was designed and conducted at an experiment facility of Korea Maritime and Ocean University to validate the result of CFD analysis by the experimental result, which represents a real flow behavior. To generate the turbine damping effect through the nozzle, the 1/16 scaled OWC chamber was adopted into the wave tank. The orifice plate as the turbine substitute was then installed inside the nozzle of the OWC chamber. The boundary conditions (wave heights and periods) to generate the same condition of bi-directional flow into the orifice were designed equally.

The orifice plates were installed at the nozzle of the OWC chamber as shown in Fig. 6. The OWC chamber installed in the wave tank which faces the oncoming wave, generated by the piston type wave maker. The OWC chamber model is composed of Acrylic material with its thickness of 10 mm so that the wave behavior can be observed. The design wave was fixed as 0.125 m with 1.25 to 2.0 sec of periods. The diameter ratio of the orifice plates (0.3D, 0.33D, 0.35D, 0.37D, 0.4D) were tested. The two ultrasonic wave height meters were installed on 1 m front of and at the top of the OWC chamber to measure the height of oncoming wave and inside the chamber respectively. With the measured wave height inside the chamber and period, the flow rate passing through the orifice were calculated using the equation (5).

Fig. 6

3D schematic drawing of experimental setup in wave tank

Fig. 7

Configuration of experimental setup

The performance of the full-scaled cross-flow air turbine was acquired by CFD steady state simulation, and Fig. 8 depicts the performance curve by a dimensional analysis method.⁽¹⁷⁾ The turbine was investigated by varying the rotational speed of blades (16, 32, 48 and 64 rpm for full scale) and the inlet air velocity (from 2 m/s to 40 m/s). The peak performance of the turbine was 0.587 at the rotational speed of 48 rpm and the inlet velocity of 12 m/s. All performance for different rotational speed of the turbine have relatively same tendency. When it comes to noise issue in turbine operation, the low rotational speed (16 rpm) of the turbine could be more suitable although the performance of 16 rpm is slightly less than the others. After the stall region, the performance curves tend to significantly drop, and it means that the operating range of the turbine is relatively narrow. The operating range of this turbine is positioned mainly between 0.2 to 0.8 flow coefficient, whereas typical Wells turbine and impulse turbine have 0 to 0.2 and over 0.6 respectively. From this result, it can be said that this cross-flow air turbine is able to operate effectively between 0.2 to 0.8 flow range which is not suitable for other turbines.

Fig. 8

Performance of the cross-flow air turbine by dimensionless analysis

It is noted that the investigation of this turbine is the early stage of research, thus it needs to be improved by further modification of geometries or possible variables.

The analysis of 1/16 scaled turbine under bi-directional flow have been carried out by CFD transient simulation that both for investigation of flow behavior through the turbine and for validation of CFD result with an experimental data. Fig. 9 presents the bi-directional flow behavior through the turbine at 2/8 period of 1.25 sec, which the flow velocity through the blade is the highest. Fig. 10 indicates the power distribution on entire rotor domain. The divided power output was calculated by each torque of the runner blades during one cycle. Based on the center circle (zero), the outside lines represent the absorbed kinematic air energy by the rotor blades, and inner lines represent the energy loss due to turbulence and swirl of air at region 1 and 2 as shown in Fig. 9. It is shown that the power output was mainly captured at stage 1 for exhalation cycle and at stage 2 for inhalation cycle unlike power reduction and loss were observed in region 1 and 2. In addition, all different period have similar tendency of power distribution. The higher power output was acquired at shorter period as 1.25 sec, and the power amount was decreased as longer period.

Fig. 9

Velocity vectors in the turbine domain at 2/8 period of 1.25 sec

Fig. 10

Power distribution on entire rotor at 1.25 sec wave period

A relation between flow rate and pressure drop during one cycle can be obtained as a hysteresis loop with the phase averaging method as shown in Fig. 11. The hysteresis loop consists of exhalation and inhalation of the air flow. The right side of the graph represents an exhalation of an air and the left side depicts an air inhalation. The gap between an increasing and decreasing lines for both outflow and inflow occurred due to the change of air density by the different air acceleration. For short period, at 1.25 sec, an irregular behavior in the hysteresis loop was obtained due to its significant effect of air compressibility. In addition, the pressure drop between upstream and downstream of the turbine becomes smaller as an increase of period, decrease the flow rate.

Fig. 11

Relation between pressure and flow rate with phase averaging at 1000 rpm and 1.25 sec wave period

With the phase averaged data of pressure, flow rate and torque, an aerodynamic power and turbine’s shaft power were obtained as shown in Fig. 12. The air power represents the aerodynamic energy amount of incoming air, and the shaft power depicts the mechanical energy converted by the turbine. The feature of both air and shaft power graph have similar configuration as the torque graph. The averaged power output of air and shaft power was applied to calculate the averaged efficiency of the turbine performance during one cycle due to its varying data as time series. The summary of the turbine performance for different periods is illustrated in Table 2. All case have similar performance and the overall efficiency is around 23.6%. The maximum efficiency of the turbine was 25.7% at 2.0 period and 1000 rpm rotational speed. The producing power at 2.0 sec by the turbine was 3 times less than at 1.25 sec. Hence, from this result, this turbine is more suitable at the condition of shorter wave period to produce larger amount of energy even though the overall performance is slightly less than at long period. However, it must be noted that this performance result is close to theoretical result due to its linear wave theory, which produces linear motion of air flow with less turbulence into the turbine. This means that the turbine performance could be significantly decreased if this device is applied on real sea. Thus, further study for improvement of the device will be conducted.

Fig. 12

Phased averaged shaft power and air power at 1.25 sec period

Table 2

Summary of performance of the model scaled cross-flow air turbine

The numerical analysis of orifices having different dimension (0.3D to 0.5D) by CFD have been carried out under same bi-directional flow condition to find the orifice which can simulate similar damping effects of the turbine. The entire CFD result of the orifices and turbine at 1.5 sec wave period is depicted in Fig. 13. Varying the diameter ratio of the orifice at same bi-directional flow rate induced the different pressure drop across the upstream and downstream of the orifice in one cycle, and the smaller size of the orifice diameter caused the increase of the pressure drop across the orifice. It is indicated that the ratio 0.3D have a significantly closer fitting behavior to the turbine performance and a proper solidity as the turbine. With the 0.3D orifice, the turbine damping effects can be predicted, and it can be applied on further research of the turbine for both its verification and simplicity in study.

Fig. 13

Phased averaged pressure drop and flow rate diagram of the orifice plates with the turbine damping effects at 1.5 sec period

The experiment of orifice plate (0.3D to 0.4D) embedded in the OWC chamber was processed at the condition of 0.125 m wave height and 1.25 sec wave period (same condition as CFD simulation). The predicted performance of the orifice by CFD was compared with experimental result, and one of comparisons (0.3D orifice at 1.25 sec wave period and 0.125 m wave height) was shown in Fig. 14. With only the result, it was observed a relatively good agreement between CFD and experimental results that validates the methodology.

Fig. 14

Validations of a orifice between CFD and experimental result (0.3D orifice, 1.25 sec and 0.125 m wave height)

The remarkable hysteresis loop for the chamber pressure and the air flow rate through an orifice was observed from the experimental result rather than from the CFD result due to relatively nonlinear motion of the air flow by wave into the chamber. More irregular feature during exhalation process than inhalation process was captured. The reason for this is than the air flow through the orifice during the exhalation process is pressurized and pushed to atmosphere by nonlinear motion of wave piston, whereas the incoming air from atmosphere is supplied with relatively constant atmospheric pressure. In addition, the shorter wave period inducing higher pressure inside the chamber gets more effect of air compressibility. It means that power loss in the air chamber can be captured at shorter period.