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Abstract

The possibility of extracting wind power from unique configurations embedded in moving vehicles using microturbine devices has been investigated. In such environments with moving frames or platforms, powered either by humans like bicycles or by chemical reactions like automobiles, the specific power of the air motion is much greater and less intermittent than in stationary wind turbines anchored to the ground in open atmospheric conditions. In a translational frame of reference, the rate of work done by the drag force acting on the wind harnessing device due to the relative motion of air should be taken into account in the overall performance evaluation through an energy balance. A device with a venting tube has been tested that connects a high-pressure stagnating flow region in the front of the vehicle with a low-pressure region at its rear. Our analysis identified two key areas to focus on for potentially significant rewards: (1) vehicles with high energy conversion efficiency, which require a high mass flow rate through the venting duct, and (2) vehicles with low energy conversion efficiency with wakes, which will be globally affected by the introduction of the venting duct device in a manner that reduces their drag so that there is a net gain in power generation.

Keywords

Energy harvesting wind turbines car aerodynamics drag penalty computational fluid dynamics moving frames of reference

Introduction

As the global energy economy transitions away from traditional technologies to renewables, wind energy has become a promising alternative energy source over the years, especially with the design and construction of large wind farms in which each individual wind turbine is anchored to the ground. One major disadvantage of this setup is the downtime of power output when there is no wind blowing. In contrast, if one considers the flow environment around moving vehicles, there is always wind energy available, which could be extracted with appropriately designed energy converters/generators. The major advantage of such a system is the availability of high-velocity air almost all the time. Wind turbines are very rarely exposed to $26.7 m s^{- 1} (60 mph)$ wind, and when they are, most shut down to protect their structural integrity. The major challenge in conceiving and designing such a moving system is to harness this abundant wind energy with minimum possible energy loss due to the additional drag penalty caused by the generator’s exposure to wind.

The power density of this air motion appears to be proportional to $1 / 2 ρ U$ ³, which for a vehicle moving at $26.7 m s^{- 1} (60 mph)$ yields an energy flux of $11 kW m^{- 2}$ . If a device with an effective cross-sectional area of $0.1 - 0.2 m^{2}$ is used to convert some of this power into electricity, about 1.1–2.2 kW of power may be generated and become available. This amount of power accounts for up to 10% of the power provided by the engine to overcome the aerodynamic drag and friction forces between the wheels and the ground. Thus, the projected economic impact of such a device could be enormous. In the present work, a conceptual design of such a harnessing system is proposed to be considered, evaluated, and tested. This design has the potential to provide energy in a moving car or truck, which could be stored or directly used to power electronic devices and/or vehicle instrumentation. This embedded power generation is based on the development of microturbines that can be integrated into the vehicle, which utilize differential pressures that occur around the moving object. In the following paragraphs, the term vehicle encompasses both man- or fuel-powered moving systems.

Previous works and our current computational and experimental results have shown the existence of a large region of stagnating pressure in front of a typical car and a region of subatmospheric pressure behind the car. Our numerical simulations have shown that in the case of vehicle moving at a speed of $11 m s^{- 1}$ , higher pressure region is formed under stagnating conditions close to the front mask of the vehicle where up to $440 Pa$ is observed, whereas a back pressure of about $- 100 Pa$ is evident behind the car. This pressure difference over a typical car length of 5.4 m yields a pressure gradient of $100 Pa m^{- 1}$ , which is large enough to sustain a flow if a duct connects the two regions of extreme pressures. If this venting duct, which is open at both ends and has a micro-wind turbine installed in it, is introduced along the length of the car, a substantial amount of wind energy can be harnessed. This setup is shown in Figure 1.

Figure 1.

Venting duct-in-car and duct-in-truck embedded devices for wind energy harnessing.

As the car moves, air is expected to enter the duct after overcoming its flow resistance, since the pressure behind the car is below ambient pressure and the pressure up-front is close to stagnating conditions, that is, above ambient. If a pressure coefficient is defined as $c_{p} = 2 (p - p_{atm}) / ρ U_{0}^{2}$ where $U_{0}$ is the velocity of the vehicle, then $c_{p 0} = 1$ in the stagnation region in the front, while a pressure coefficient as low as $c_{pb} = - 0.25$ is possible behind the vehicle. Inviscid flow theory and Bernoulli’s equation lead to a velocity $U_{d}$ developing due to this pressure difference $c_{p 0} - c_{pb}$ , which can be expressed through

\frac{U_{d}}{U_{0}} = \sqrt{\frac{(c_{p 0} - c_{pb})}{c_{p 0}}} = k^{- 1} > 1

(1)

where k is the velocity ratio. On the other hand, if the flow was a fully developed laminar, viscous flow in which the pressure gradient is counterbalanced by the stress gradient, the average velocity sustained by a pressure difference $Δ p = (c_{p 0} - c_{pb}) 0.5 ρ U_{0}^{2}$ would be $\bar{U_{d}} = (R^{2} / 8 μ) Δ p / L$ , where R is the radius of the duct, $μ$ is the viscosity of air, and L is the length of the duct. Practically, however, the duct length is on the order of 10–30 duct diameters, $d_{p}$ , and the flow is certainly not fully developed. Thus, the mass flow rate captured by the duct, that is, the velocity inside the duct, will be determined by a balance between pressure and frictional forces not only inside the duct flow but also in the flow around the external surface of the vehicle, which initially sets the back pressure.

Generating such an opening in a car has a beneficial secondary effect since it is expected to reduce the overall drag coefficient due to the venting of the pressure difference between the front and the back of the car. It is known, for instance, that passive venting ducts along bluff bodies like spheres practically reduced the drag force by more than 60% in comparison with the case without ventilation.^1–4 This has been achieved by venting only 2% of the frontal area of the sphere to the base through a smooth internal duct.² In addition, a 20% velocity increase inside the duct has been measured over the approaching freestream velocity in this case. Unforced ventilation is a flow control technique which modifies the bluff body wake by bringing upstream flow to energize the wake and involves a feedback of downstream flow changes to the upstream flow parameters.² Similar global modification of the wake structure was achieved in Falchi et al.,¹ where a venting duct was introduced in the bluff body. Smoke visualization of the wake has shown a jet exhausting from the venting duct, which changes the base pressure and the overall drag. As a result, the drag coefficient is reduced by up to 20% compared with the nonvented case.

This idea has been tested by carrying out computations using computational fluid dynamics (CFD) model and experiments in a wind tunnel using an Ahmed body, a simplified geometry of a vehicle. Our CFD work and corresponding experimental evidence, which will be described later, indicated a remarkable 20%–48% reduction in drag coefficient by just introducing a circular venting duct. In the present case, however, the presence of a rotating turbine inside the venting duct is expected to increase the overall drag of the car slightly. Our time-dependent computations, in which the rotational motion of the turbine was also resolved by considering its dynamic equation of motion, indicated that this drag penalty is about 2.6% of the total drag in the case of generic trucks. The frictional drag typically generated on the internal surface of the duct has also been estimated by integrating the wall stress over this surface and found to be less than 1% of the overall drag for relatively small length-to-diameter ratios. Thus, these drag penalties are less than the original pressure drag reduction due to the venting effect, and therefore, a net effect of energy surplus into the system may be possible in principle.

Eventually, such an embedded wind power harnessing system has to be integrated with other vehicular systems, particularly with systems under the hood, where the air flow has to be optimized so that no additional drag penalty occurs. Similar systems can be installed in the cargo area of trucks without particular challenges in integration.

Theoretical framework: extending momentum theory to include a moving frame

If a horizontal axis microturbine is installed inside a duct, as is anticipated in the present work, some additional considerations should be provided since this setup constitutes a departure from classical wind turbines operating in the open under atmospheric pressure at the far field.

Control volume analysis for conservation of mass, axial and angular momentum balances, and energy conservation for an inviscid, incompressible axisymmetric flow yields

\oint_{A} ρ V \cdot d A = 0

(2)

\oint_{A} u_{z} ρ V \cdot d A = T - \oint_{A} p d A \cdot e_{z}

(3)

\oint_{A} r u_{θ} ρ V \cdot d A = Q

(4)

\oint_{A} [\frac{P}{ρ} + \frac{| V |^{2}}{2}] ρ V \cdot d A = P

(5)

where $V = (u_{r}, u_{θ}, u_{z})$ is the velocity vector resolved in the axial, radial, and azimuthal directions, respectively; r is the radius; $ρ$ is the density of air; $A$ denotes the outward-pointing area vector of the control surface; $e_{z}$ is the unit vector in the z direction; p is the pressure; T is the axial force (thrust) acting on the rotor; Q is the torque; and P is the power extracted from the rotor.

We now consider a one-dimensional model without friction in the configuration shown in Figure 2 and in a reference system of coordinates associated with a stationary vehicle and an upstream relative air velocity $U_{0}$ . This upstream velocity comprises two contributions: first, the free wind blowing velocity ${\vec{U}}_{w}$ and second, the opposite of the vehicular velocity ${\vec{U}}_{v}$ . Thus, in this case, the two velocity vectors are aligned in opposite directions

U_{0} = U_{w} + U_{v}

(6)

Figure 2.

One-dimensional flow model.

For a control volume encompassing the turbine, where the average velocity upstream of the turbine is $u_{1}$ , mass conservation along the constant diameter duct requires that the velocity remains unchanged. Therefore, $u_{1} = u_{2} = u_{3} = U_{d}$ . As a result of this, the kinetic energy per unit mass in the total enthalpy per unit mass $[(p / ρ) + (1 / 2) | | V^{2} | |]$ cancels out in the difference between influx and outflux quantities, and therefore, the harnessed power is

P = (p_{2} - p_{3}) U_{d} A

(7)

This relation indicates that the power is extracted from the potential energy per unit mass $p / ρ$ , not the kinetic energy, and that the fluid velocity $U_{d}$ enters as part of flow rate only.

Bernoulli’s equation yields $p_{1} = p_{2} > p_{3} = p_{4}$ , and momentum balance leads to the axial force $T_{z} = A (p_{2} - p_{3})$ . It is this axial force, $T_{z}$ , and the friction over the inner surface of the hollow duct, $T_{f}$ , which will constitute the additional drag force, $T = T_{z} + T_{f}$ , that acts on the frame of the vehicle moving with relative velocity, $U_{0}$ , which has to be overcome by consuming work done, $U_{0} T$ . After introducing equation (5), the drag work becomes

U_{0} T = U_{w} T + U_{v} T

(8)

If friction is ignored and the vehicle is not moving, that is, $U_{v} = 0$ , then $U_{w} T_{z}$ is the drag work by the free wind which is the same as in the case of stationary classical wind turbines, and therefore, it does not affect the overall energy balance. The moment, however, the vehicle starts to move, that is, its velocity is $U_{v} \neq 0$ , the term $U_{w} T$ is not free anymore and both terms on the right-hand side of equation (8) are activated in the overall energy balance. In addition, because of the overall efficiency of the moving vehicle $η_{c}$ , the powertrain of the vehicle is required to provide a power $W_{T} = U_{0} T / η_{c}$ . If the wind power generated by the turbine is P, then the net available power will be $P_{N} = P - W_{T}$ . Thus, the first requirement for the proposed configuration is that

P - W_{T} > 0

(9)

Under the one-dimensionality assumption and assuming negligible friction forces $T_{f} = 0$ , equation (9) leads to

P_{N} = (U_{d} - \frac{U_{0}}{η_{c}}) (p_{2} - p_{3}) A > 0

(10a)

which is equivalent to $U_{d} > U_{0} / η_{c}$

\frac{U_{d}}{U_{0}} > \frac{1}{η_{c}}

(10b)

η_{c} > k

(10c)

This simplified one-dimensional model shows that the harnessed energy flux is extracted at a rate defined by $U_{d}$ , while the drag penalty is consumed at a rate defined by the vehicle velocity $U_{0}$ .

In the ideal case of $η_{c} = 1$ and if a value of $k = 0.85$ can be achieved, for a circular duct with diameter $d_{d} = 0.3 m$ , a net power $P_{N} = 180 W$ could be expected. For a typical internal combustion engine (ICE), $η_{c} \approx 0.3$ , and for a typical electric car like the Tesla, $η_{c} \approx 0.75 - 0.90$ . Our preliminary experimental and computational work has indicated that the smallest value of k attained at the moment is $k = 0.63$ , a value which makes the concept under consideration more meaningful for electric car applications compared with gasoline fuel vehicles.

One additional factor which needs to be considered in the present analysis is the expected benefits of a potential drag reduction $Δ D_{car}$ , as a result of the introduction of the venting duct. Past work in the case of vented spheres² has shown 70% reduction in the drag coefficient. Our experimental results described later and CFD work have shown that the overall relative drag reduction $Δ D_{car} / D_{car}$ can be from 0.33 to 0.8, which is mostly due to a reduction in the drag coefficient $Δ C_{D_{0}} / C_{D_{0}}$ rather than the area reduction $Δ A / A$ . This drag reduction will reduce the work done by the moving vehicle by $Δ D_{car} U_{0}$ , which is a welcomed by-product of introducing the venting duct. This saving can be considered to be the upper limit of $W_{T}$ . Thus, a more relaxed requirement than equation (9) or equation (10b) will be

P_{N} = T U_{d} - \frac{T U_{0}}{η_{c}} + Δ D_{car} U_{0} > 0

(11)

If this relation is made dimensionless by the harnessed power, $T U_{d}$ , we can obtain the following requirement for the ratio as

\frac{P_{N}}{T U_{d}} = \frac{k Δ D_{car}}{T} + 1 - \frac{k}{η_{c}} \geq 0

(12)

It is obvious from this relation that the ratio $P_{N} / (T U_{d})$ can be maximized when $k Δ D / T$ is maximized and $k / η_{c}$ is minimized. The objective of this work is to determine the functional relations of these two nondimensional ratios to the geometric and flow parameters. Understanding these apparently nonlinear functional relations may lead to ways to maximize the nondimensional power ratio $P_{N} / (T U_{d})$ .

Experimental work

We designed, tested, and evaluated the performance of a laboratory prototype model of an Ahmed body in a wind tunnel. In the present context, the term Ahmed body is defined to include any simplified generic vehicle shape. This model is geometrically simple, yet representative of a typical bluff body, like an Ahmed body/generic truck while at the same time allowing for higher resolution measurements and computations of the flow inside the circular duct and around the body. This wind tunnel model was not a representative model of an actual size car or track. Since the focus of this study was the energy output of the wind turbine, it was decided to have a larger diameter turbine/duct so that a meaningful amount of energy can be harnessed with an acceptable efficiency. The wind turbine efficiency deteriorates rapidly with large downscaling of the model because the relative surface-area-to-volume ratio increases, and therefore, mechanical and fluidic friction starts to dominate entirely at small scales. On the other hand, the pressure gradient along the duct, which drives the flow through, is expected to be lower because the back pressure will decrease due to the decrease in the cross-sectional area. In that respect, the present wind tunnel results may be more conservative than those in the full-scale case.

The wind tunnel used is an open-section tunnel with a test cross section of $1.2 m \times 1.2 m$ and a length of $8.5 m$ . The air inside the tunnel is propelled by a 15-kW frequency-controlled motor which provides a volumetric flow rate of $10 m^{3} s^{- 1}$ and a maximum freestream air speed of about $11 m s^{- 1}$ . The inlet section of the wind tunnel is equipped with a flow straightener. The resultant flow inside the test section has 0.08% and 0.15% turbulence intensity at 11 and 3 m s⁻¹ air speed, respectively.⁵ A SolidWorks rendering of the model is shown in Figure 3(a). The design of this model was based on the optimized shape obtained through detailed CFD analysis, which is described later in the “Computational work” section. It consists of three parts: the intake, the wind turbine and its support, and the exit diffuser. The model was shaped like a rectangular box with dimensions $0.44 m \times 0.44 m \times 1.78 m$ and was attached to four low-friction wheels. The maximum Reynolds number attained in the present work based on the height of this model and maximum freestream velocity $U_{0}$ is $Re = 3 \times 10^{5}$ . A venting duct of 200 mm in diameter was inserted in the middle of this bluff body spanning its entire length. The intake was formed in a typical bellmouth shape, while the exhaust was shaped as a diffuser. The diffuser expanded the flow to a circular outlet of diameter 322 mm. In order to achieve optical access, the venting tube and side walls of the model were constructed using clear Plexiglas. The wind turbine was placed inside the duct. This prototype contained a three-blade turbine, as shown in Figure 3(b), which was connected to a DC motor that functioned as an electrical current generator. The three-blade and hub assembly was designed and fabricated through three-dimensional (3D) printing processes⁶ according to the guidelines listed in Wood⁷ and Burton et al.,⁸ which are based on the theories of Betz,⁹ Glauert,¹⁰ Joukowsky,¹¹ and Hansen et al.¹² The profiles of the wind turbine blades were based on NACA 6412 aerofoils. The turbine was located at a distance of 0.762 m from the entrance of the central tube and was attached to a 3D-printed structure which housed the generator and was held centrally in the tube by three plastic rods. The turbine hub was shaped into a teardrop-like to reduce its drag. The model was prevented from moving in the direction of the flow by a bracket attached to the bottom of the model that impinged on the force sensor fixed to the wind tunnel floor. A photograph of the fabricated physical model is shown in Figure 4(a). Figure 4(b) shows a view from the rear of the model with the turbine in place, and Figure 4(c) shows details of the diffuser cutaway section profile which was fabricated from foam layers.

Figure 3.

(a) SolidWorks rendering of wind tunnel model. Arrows indicate intake, wind turbine, and diverging nozzle/diffuser; (b) rendering of wind turbine and its support with hub.

Figure 4.

(a) Photograph of fabricated wind tunnel model, (b) view from the diffuser toward the wind turbine, (c) diffuser cutaway section showing the cross-sectional profile fabricated from layers of foam, and (d) designation and nomenclature of surfaces involved in drag force determination.

The performance evaluation of the model included measurements of the flow rate through the venting duct and at the exhaust, measurements of the voltage output of the turbine and its rotational speed, and measurements of the drag force acting on the model. Additional measurements of the velocity field within the venting pipe and in the wake of the body were carried out using hot-wire anemometers and particle image velocimetry (PIV) techniques, respectively. The force was measured using an ATI Nano17 six-degrees-of-freedom sensor capable of simultaneously measuring the three components of the net force and three components of the net moment acting on the model. The calibration of the force and moment sensor was performed by attaching a string to the sensor inside the working section of the wind tunnel and applying known weights at specific points and recording the corresponding signals. The output signals of the sensor and the output voltage of the wind turbine during the testing were recorded by a multichannel analog-to-digital converter controlled by a computer. In the present experimental work, the wind tunnel wall was not moving. This setup had no influence on the present measurements of drag because the local boundary layer thickness was much less than the clearance of the model and the wall. In addition, no changes in the measured aerodynamic forces were detected when the model was positioned at various distances from the wind tunnel wall. The mass flow rate and average velocity through the duct were determined by carrying out measurements of velocity profiles across two sections located upstream and downstream of the turbine using a pitot tube probe for total pressure measurements and wall static pressure information measured concurrently. These measurements were carried out while the turbine was rotating in the duct.

The tunnel walls interfere with the flow field around the bluff body model and cause a local flow acceleration, known as solid blockage, which changes the boundary layer around the model. An additional flow acceleration takes place in the viscous wake of the model, which is called wake blockage. Correction methods have been developed to take into account the solid and wake blockage effects. The basic empirical formula behind these corrections has been proposed by Maskell,¹³which has been adopted in the present consideration to evaluate the corrections of the C_D, U_d, k, and D measurements needed to compensate for blockage. If $C_{Dm}$ is the measured drag coefficient, then the corrected one $C_{D}$ is provided by the analytical expression

C_{D} = \frac{C_{Dm} + Δ C_{Pb}}{1 + 5 / 2 C_{Dm} \frac{A_{MC}}{A_{WT}}} ≅ (C_{Dm} + Δ c_{pw}) [1 - 5 / 2 C_{Dm} \frac{A_{C}}{A_{0}}]

(13)

where $A_{MC} / A_{WT}$ is the blockage ratio, which has values 0.112 and 0.134 for the two cases of wind tunnel testing, one with open intake and the other with closed intake, respectively. $A_{MC}$ is the cross section of the model for the two cases of testing, one with open intake, in which $A_{MC} = A_{C}$ , and the other with closed intake, that is, $A_{MC} = A_{0}$ . $A_{C}$ and $A_{0}$ are defined below, and $A_{WT}$ is the wind tunnel cross section. $Δ c_{pw}$ is the wake distortion term (due to pressure gradient in the wake) defined as $Δ c_{pw} = c_{pwc} - c_{pmb}$ , with $c_{pwc}$ being the pressure coefficient in empty wind tunnel at the location of the wake end and $c_{pmb}$ being the pressure coefficient in empty wind tunnel at the location of the base of the model. This term in the empty wind tunnel is quite low, of the order of 10⁻⁴, and it does not affect the present consideration. Under these conditions and for the maximum value of $C_{Dm}$ , the correction is only 2.2% of $C_{Dm}$ . The pressure coefficient $c_{pb}$ has been corrected according to the relation postulated by Maskell¹³

C_{D} = C (1 - \frac{c_{pb}}{c_{p 0}})

(14a)

in which C is a constant with value $C = 0.837$ , which has been also verified by Owen.¹⁴ Accordingly, the corresponding correction is only 0.23%. The correction on $U_{d}$ and k is based on equation (1), which, after considering equation (14a), leads to

U_{d} ~ \sqrt{C_{D}}

(14b)

The estimated correction on $U_{d}$ is only 1.1% at most. These minor corrections have been applied to the results discussed below.

Figure 5 shows values of the measured average velocity $U_{d}$ in the tube and the corresponding mass flow rate obtained at various external incoming velocities $U_{0}$ in the wind tunnel ranging from $3 to 11 m s^{- 1}$ . These results show that this device has a cut-in velocity of about $3 m s^{- 1}$ and that the velocity $U_{d}$ increases with the external velocity $U_{0}$ almost linearly. It is also evident that velocity ratios of about $U_{d} / U_{0} = 1.51$ or $k = 0.66$ are obtained inside the duct at all external velocities $U_{0}$ investigated. There results not only document the existence of flow within the venting duct, they also show that the pressure gradient which drives the flow is quite strong.

Figure 5.

Measured mass flow rate and average velocity inside the venting duct of the wind tunnel model.

Measurements of the drag force obtained at various incoming wind tunnel velocities are shown in Figure 6. Three different experiments were carried out: first, with the intake of the model covered so that no flow was entering the duct; second, with the intake open and without the wind turbine installed; and third, with the intake open and the turbine able to rotate in place. The drag forces appear to vary parabolically with the external velocity $U_{0}$ as is expected. It is also clear that the drag penalty in installing the wind turbine is rather small, at most 5% of the overall drag, and mostly evident at higher velocities. The data demonstrate that the presence of the duct reduces the overall drag considerably.

Figure 6.

Measured drag and relative drag reduction $Δ D / D_{0}$ .

Values of the relative drag decrease in reference to $D_{0}$ , $(Δ D / D_{0}) = ((D_{0} - D_{dTD}) / D_{0})$ , are also plotted in the same Figure 6. In the present notation, $D_{0}$ is the drag of the Ahmed body with its intake covered and $D_{dT}$ is its drag with the duct open and the turbine extracting power from the flow. The drag reduction increases with increasing velocity till it reaches a maximum value of 72.5% at $6 m s^{- 1}$ . Then, it decreases with velocity and is about 30% at the highest external velocity.

One obvious question is how much of this drag reduction is due to the opening of the duct which reduces the cross-sectional area $A_{0}$ and how much is due to the interference between its wake and exhaust flow as hypothesized earlier. In order to answer this question, the results were further analyzed and the nondimensional drag coefficients were computed. In the case of the body with the duct covered, which, as mentioned earlier, is considered as the base value of the drag, the drag force is provided by

D_{0} = C_{D 0} A_{0} \frac{1}{2} ρ U_{0}^{2}

(15)

where $A_{0}$ is the cross-sectional area of the body; $A_{0} = bh$ , which in the present case is rectangular with $b = h = 0.44 m$ , that is, $A_{0} = 0.193 m^{2}$ . The drag when the duct is open with the turbine extracting energy is defined as

D_{dT} = C_{DdT} A_{C} \frac{1}{2} ρ U_{0}^{2}

(16)

where $A_{C}$ is the new cross-sectional area given by

A_{C} = A_{0} - (\frac{π}{4} d_{d}^{2} - A_{t})

(17)

where $A_{t}$ is the projected area of the turbine blades and supports onto the cross section of the duct, which was estimated to be $7.5 \times 10^{- 3} m^{2}$ . The diameter of the duct is $d_{d}$ . It is trivial to show that the relative change in the drag force, $Δ D / D_{0}$ , can be decomposed, for a constant dynamic pressure $(1 / 2) ρ U_{0}^{2}$ , into the following simple relation

\frac{Δ D}{D_{0}} = \frac{Δ C_{D}}{C_{D_{0}}} + \frac{Δ A}{A_{0}} - \frac{Δ C_{D}}{C_{D_{0}}} \frac{Δ A}{A_{0}}

(18)

where the corresponding changes in drag coefficient and area are given by $Δ C_{D} = C_{D_{0}} - C_{DdT}$ and

Δ A = A_{0} - A_{C} = \frac{π}{4} d_{d}^{2} - A_{t} = 0.0239 m^{2}

(19)

and therefore $Δ A / A_{0} = 0.123$ . The coefficient of drag $C_{dT}$ has been estimated from the experimental data of drag $D_{dT}$ shown in Figure 6 and equation (16) and has been plotted in Figure 7. The drag $D_{dT}$ can also be decomposed into the drag of the turbine $D_{WT}$ and the drag of the remaining body $D_{d}$ so that $D_{dT} = D_{WT} + D_{d}$ with

D_{WT} = C_{WT} A_{T} \frac{1}{2} ρ U_{0}^{2} = C_{T} A_{T} \frac{1}{2} ρ U_{d}^{2} = C_{T} A_{T} \frac{1}{2} ρ \frac{1}{k^{2}} U_{0}^{2}

(20)

where $A_{T} = (π / 4) d_{d}^{2}$ , and $C_{WT}$ and $C_{T}$ are the drag coefficients with respect to the moving with the vehicle coordinate system or the local coordinate system associated with duct, respectively. The drag of the rest of the body with the duct open is given by

D_{d} = C_{Dd} A_{C} \frac{1}{2} ρ U_{0}^{2}

(21)

Figure 7.

Estimated drag coefficients and values of their relative change $(Δ C_{D}) / C_{D 0}$ .

The coefficients $C_{D 0}$ , $C_{Dd}$ , and $C_{DdT}$ are plotted in Figure 7. They all follow the same qualitative behavior as the drag forces. However, the reduction of the relative drag coefficient

\frac{Δ C_{D}}{C_{D_{0}}} = \frac{(C_{D_{0}} - C_{DdT})}{C_{D_{0}}}

(22)

shows the genuine effect of the interference between the external flow and the exhausting duct flow, which energizes the wake, since the effects of different cross-sectional areas have been taken out. In fact, while the relative reduction in cross section is a constant value, depending on geometry, $Δ A / A_{0} = 0.123$ , the relative drag coefficient reduction is about 18% at $11 m s^{- 1}$ and 72.5% at $6.5 m s^{- 1}$ . Thus, most of the contribution to the drag force reduction is due to the change in the drag coefficient and not the cross-sectional area reduction. This can be further corroborated by plotting the contributing terms of the drag force reduction described by equation (18). The results are plotted in Figure 8, where estimates of the ratio $Δ C_{D} / C_{D 0}$ , the constant value of $Δ A / A_{0}$ , and their cross product $(Δ C_{D} / C_{D 0}) (Δ A / A_{0})$ are plotted together with the quantity $(Δ A / A_{0}) - (Δ C_{D} / C_{D 0}) (Δ A / A_{0})$ which involves the two terms including the effects of area reduction. It can be seen from these data that at $6 m s^{- 1}$ , the maximum drag force reduction is $0.76$ , while the major contribution to this is provided by the reduction of the corresponding drag coefficient, which is $0.72$ . This contribution accounts for $94.7 %$ of the total value. At the maximum velocity tested here, the relative drag coefficient reduction is $0.18$ , which accounts for $62 %$ of the maximum force reduction of $0.291$ . This figure also contains the values of the reconstructed relative reduction of the drag force by simply adding the contributing terms according to equation (18). As expected, these reconstructed values coincide with the original data, which demonstrates some consistency in the decomposition procedure. The results shown in Figures 5 and 6 demonstrate clearly the existence of a pressure gradient–driven flow with a considerable throughput rate. This flow interferes with the external flow to reduce the drag coefficient considerably, which is combined with the area reduction to further reduce the drag force.

Figure 8.

Breakdown of directly measured relative drag force reduction, $Δ D / D_{0}$ , to contributing parts and comparison with its reconstructive values.

The voltage output from the turbine was measured by connecting the output leads from the DC motor to the data acquisition board and recording the output voltage time series. The measured voltages shown in Figure 9 are plotted at various external velocities. It should be noted that the measured voltage v is directly related to the output power through $v^{2} / R$ , where R is the external resistance in the circuit that dissipates the power into heat. In the first series of experiments, the voltage was measured with the turbine installed inside the duct following the same procedure with which the pressure/velocity measurements were obtained. In this setup, the calculated power is designated as $P_{w, p}$ . In the second series of experiments, the model was taken out of the wind tunnel; the turbine was removed from the duct and was subsequently attached on a tower and placed in the wind tunnel to obtain measurements simulating operation in the open atmosphere. This is called the stand-alone case of the turbine, and its power output is designated as $P_{w, 0}$ . The comparison between these two data sets shows that the extracted power from the turbine in the venting duct is consistently higher than that from the stand-alone turbine. It appears that the reason for this is the increased velocity inside the duct, while the upstream velocity remains the same in both cases and the increased efficiency associated with ducted turbines.^15–18 The data also suggest that their power ratio, which is proportional to ratio of the output voltages squared, is between 3 and 3.4. For instance, at $11 m s^{- 1}$ , the ratio is $P_{w, p} / P_{w, 0} = (1.32 / 0.73)^{2} = 3.26$ .

Figure 9.

Voltage output measurements at various external velocities with turbine installed inside the duct or in a stand-alone setup in the same wind tunnel.

To further evaluate the effect of the venting tube on the back pressure, a time-resolved PIV technique was used to obtain the velocity field data in the region of the model. The wake region of interest is shown schematically in Figure 10. PIV data were captured using a continuous laser and a high-speed CMOS (complementary metal oxide semiconductor) camera. The beam from a Millennia Vs Spectra-Physics CW laser source of $5.5 W$ continuous output power at 532 nm is reformed into a sheet using a cylindrical lens to illuminate a plane in the region of interest. A Vision Research v710 Phantom high-speed camera with a resolution of $1280 \times 800$ pixels is placed outside the wind tunnel. The sampling rate of the camera was set at 400 fps. The images from the captured movie were processed using open-source PIVLab software to obtain the velocity vector field.¹⁹ The interrogation window used is set to correspond to a real window in the flow domain of $12.6 \times 12.6 m^{2}$ .

Figure 10.

Region of interest for PIV data analysis in the back of the model.

Figure 11 shows a sample velocity field after subtracting the mean component. The image is slightly misaligned with respect to the centerline of exhaust jet, which is located at a y location of about $0.16 m$ . The freestream flow around the model is not captured. The bottom of the frame shows a nearly stagnant air downstream of the model’s solid back wall. Velocity components in nearly stagnant air appear in the reversed direction after the mean flow component is subtracted. No stagnant air region is evident on the top of the frame due to picture’s misalignment with jet’s centerline. Nearly uniform velocity region is evident at an x location of $0 m$ and a y location of about 0.1–0.22 m, corresponding to the location of the diffuser exit. The presence of uniform velocity indicates existence of a large potential core region leaving the venting duct. Further downstream, the potential core flow is mixed with the stagnant air directly downstream of the model’s back walls, resulting in the recirculating flow regions. One such region is clearly seen at an x location of $0.05 m$ and a y location of $0.06 m$ . The pressure obtained from PIV data by solving the Pressure Poisson Equation²⁰ is shown in Figure 11(b). The coefficient of pressure is reduced in the region corresponding to the jet exhaust. Integrating the pressure coefficient along the left frame boundary and normalizing by the boundary length yield an average pressure coefficient of $- 0.22$ . This value can be compared with an estimated pressure coefficient of about $- 0.43$ in the case of no venting tube. The increase in the back pressure associated with the potential core is responsible for net drag reduction.

Figure 11.

(a) PIV data in the back region of the car and (b) the associated coefficient of pressure calculated using velocity data.

Computational work

Time-dependent computations were carried out by numerically solving the incompressible unsteady Reynolds-averaged Navier–Stokes (URANS) equations and using the one-equation turbulence model of Spalart–Allmaras (S-A). The system of differential equations used in tensor notation is given as follows

\frac{\partial {\bar{U}}_{i}}{\partial x_{i}} = 0

(23)

ρ \frac{\partial \bar{U_{i}}}{\partial t} + ρ \bar{U_{j}} \frac{\partial \bar{U_{i}}}{\partial x_{j}} = - \frac{\partial}{\partial x_{i}} [- \bar{p} δ_{ij} + 2 μ {\bar{S}}_{ij} - ρ \bar{u_{i} u_{j}}]

(24)

where p is the pressure, $ρ$ is the density, $μ$ is the viscosity, ${\bar{U}}_{i}$ is the mean velocity component in the i direction and ${\bar{S}}_{ij} = (1 / 2) [(\partial {\bar{U}}_{i} / \partial x_{i}) + (\partial {\bar{U}}_{i} / \partial x_{i})]$ is the mean strain rate. The numerical discretization scheme was second order in accuracy in space.

As mentioned earlier, the geometry of the model was chosen after performing detailed analysis on the results of over 100 CFD simulations in ANSYS/Fluent to find the optimal geometry for the scale of the design. The optimization strategy was based on maximizing the flow rate through the venting duct while maintaining the pressure difference between the front and the rear of the vehicle. At the intake of the tube, a bellmouth with an elliptic profile for its shape was used.

The final design, as shown in Figure 12, measures $1.778 m$ in length and has an outer cross-sectional area measuring $0.202 m^{2}$ .

Figure 12.

(a) Computational model and (b) computational domain with mesh.

The model was made in three separate parts to avoid meshing issues at interfaces which are required to allow one body to rotate relative to another. The mesh was divided into three parts to reduce problems during mesh generation. These are (1) main body, (2) turbine (rotating), and (3) turbine support (nonrotating). Each part was modeled separately and then saved as a SolidWorks part file. The eventual flow domain had a size of $6 m \times 4 m \times 4 m$ . Figure 13 shows an isometric view of the computational flow domain with the mesh.

Figure 13.

Computational flow domain with mesh.

Grid size independent solutions were tested for three different mesh sizes. Table 1 gives information related to the mesh used in the three different subdomains for three different mesh sizes. The minimum grid size in simulation 1 which had the highest resolution with nearly $9, 600, 000$ grid points was $0.08 mm$ on the turbine blades domain and 0.2 mm on the body of the model.

Table 1.

Mesh size details for the three subdomains.

	Turbine	Turbine support	Body	Total
Simulation 1: high resolution
Nodes	925,698	166,339	714,187	1,806,224
Mesh size	5,004,704	833,369	3,780,666	9,618,739
Minimum size (m)	$8.542 \times 10^{- 5}$	$5 \times 10^{- 5}$	$2.6 \times 10^{- 4}$
Maximum size (m)	$5.4669 \times 10^{- 3}$	$6.4 \times 10^{- 3}$	$0.26624$
Minimum edge length (m)	$0.012753$	$9.9847 \times 10^{- 3}$	$0.18295$
Simulation 2: 10% mesh size reduction
Nodes	832,993	147,538	643,558	1,624,089
Mesh size	4,504,748	750,157	3,402,475	8,657,380
Minimum size (m)	$9.5715 \times 10^{- 5}$	$9.425 \times 10^{- 4}$	$2.6869 \times 10^{- 4}$
Maximum size (m)	$6.1258 \times 10^{- 3}$	$7.54 \times 10^{- 3}$	$0.27513$
Simulation 3: 20% mesh size reduction
Nodes	742,726	128,262	566,230	1,437,218
Mesh size	4,003,616	666,858	3,028,034	7,698,508
Minimum size (m)	$1.0618 \times 10^{- 4}$	$1.0699 \times 10^{- 3}$	$6.1779 \times 10^{- 4}$
Maximum size (m)	$6.7952 \times 10^{- 3}$	$8.5594 \times 10^{- 3}$	$0.63261$

To compute the motion of the wind turbine rotor due to an applied torque, one can apply the rigid-body conservation of angular momentum to the rotor assuming a single degree of freedom

J \frac{d^{2} δ}{d t^{2}} = M_{m} (t) - M_{b} (t) - M_{D} (t)

(25)

where J is the mass moment of inertia of the generator rotors, $δ$ is the angular position, $M_{m} (t)$ is the time-dependent mechanical torque that acts on the spindle of the generator, $M_{b} (t)$ is the back torque from the generator, and $M_{D} (t)$ is the damping torque. The damping torque can be approximated as

M_{D} (t) = D \frac{d δ}{d t}

(26)

where D is the generator damping coefficient, which has been determined experimentally. Substituting equation (26) into equation (25) and rewriting the expression in terms of the angular velocity $ω (t)$ give

\frac{d ω (t)}{d t} + \frac{D}{J} ω (t) = \frac{M_{m} (t) - M_{b} (t)}{J}

(27)

The first-order differential equation in equation (27) can be solved by utilizing an integrating factor

\frac{d}{d t} [ω (t) \exp (\frac{D}{J} t)] = [\frac{M_{m} (t) - M_{b} (t)}{J}] \exp (\frac{D}{J} t)

(28)

Considering an incremental period of time (from t to $t + Δ t$ ), the solution to equation (28) is found as

\begin{matrix} ω (t + Δ t) = ω (t) \exp (- \frac{D}{J} Δ t) \\ + \frac{1}{J} \int_{t}^{t + Δ t} [M_{m} (τ) - M_{b} (τ)] \exp (\frac{D}{J} (τ - (t + Δ t))) d τ \end{matrix}

(29)

The change in the angular position of the rotor is found from the definition of $ω (t)$ as

Δ δ (t) = ω (t) Δ t

(30)

The manner in which equations (26) and (27) were employed to determine the motion of the rotor is laid out in the following steps:

At time $t = 0$ , $δ (0)$ and $ω (0)$ are known. The torques acting on the rotor are determined by a CFD solver at time $t = 0$ . This was achieved by finding the force from the pressure acting on the infinitesimal grid size of the surface of the turbine and then computing its moments appropriately by multiplying with the corresponding arms before integrating over the total surface.

The new angular position $Δ δ (0)$ is determined by applying the known $ω (0)$ value in equation (27).

The torques acting on the rotor are determined by the CFD solver at time $t = Δ t$ using the same approach outlined in Step 1.

Using the known $ω (0)$ value in equation (29), the new angular velocity $ω (Δ t)$ is obtained.

The result is then substituted into equation (30) to obtain the new location $δ (Δ t)$ .

Repeat Steps 3 to 5 for subsequent timesteps.

The timestep was selected to satisfy the Courant–Friedrichs–Lewy (CFL) condition that the distance that any information travels during the timestep length within the mesh must be lower than the distance between mesh elements. The present calculations are carried out with a timestep value of $0.00025 ms$ .

It is also important to note that the present computations of the scaled-down Ahmed body were carried out under the same conditions the experimental wind tunnel data were obtained, that is, away from the wall and under the same incoming flow velocity of $11 m s^{- 1}$ .

The present flow is the result of a mutual interaction between the external flow which imposes a pressure gradient between the front and the rear of the vehicle and the internal flow through the duct. The internal flow through the duct exhausts into the wake and therefore affects the back pressure and tends to reduce the pressure gradient. A balanced distribution of meshing between the external and internal flow domains is critical in establishing the flow field. Coarse meshing of the flow domain inside the duct and fine mesh in the external flow will underestimate the captured flow rate through the duct, while a coarse mesh in the external flow domain will not set up the correct pressure gradient to drive the duct flow. As mentioned earlier, three different grids were used to test the convergence and mesh independence solution. The results are shown in Figure 14 where the area-weighted velocity through the duct is plotted as a function of flow time for the three different meshes whose bulk characteristics are listed in Table 1. It appears that the solutions obtained in simulations using the mesh of simulations 1 and 2 converged within 0.4% from each other. The minimum mesh size near the body of the vehicle used in simulation 1 was 0.26 mm which was considered to be adequate to resolve viscous boundary layers with a thickness of a few millimeters. As mentioned earlier, the mesh resolution close to the turbine blades was $0.08 mm$ , enough to resolve submillimeter size boundary layers.

Figure 14.

Solution convergence for three different mesh sizes: area-weighted velocity inside duct.

Computational results

Figure 15(a) shows velocity magnitude contours of the flow domain with the turbine inside the model for the case of the external velocity $U_{0} = 11 m s^{- 1}$ . The flow inside the duct is accelerated to $18 m s^{- 1}$ , which is about 63% higher than the upstream value of $U_{0}$ . This flow rotates the turbine and, after the energy extraction, enters the diffuser where it decelerates to substantially lower values. Details of the velocity field in the area around the turbine are shown in Figure 15(b) where the most notable characteristic is the wake of the hub which encloses the electrical generator.

Figure 15.

(a) Global view of computed velocity magnitude contours $U_{0} = 11 m s^{- 1}$ and (b) computed velocity contours in the turbine area $U_{0} = 11 m s^{- 1}$ .

The steady-state equilibrium value of the angular velocity of the rotating turbine was calculated to be $350 rad s^{- 1}$ , while the corresponding torque is $0.118 N m$ , which provides a net output power of about $41 W$ and a power coefficient of $C_{P} = 41 / 99 = 0.413$ .

Figure 16(a) and (b) shows vorticity magnitude contours distribution in the overall flow field and in the turbine area of the duct, respectively. The boundary layers developing over the external and internal surfaces are visible since the scale resolution is very satisfactory. In fact, the blade seems to cut through the boundary layer in the duct flow (Figure 16(b)). Figure 17(a) shows the vortex core regions in the turbine area found by thresholding the entrophy contours. In this figure, the three blades of the turbine are shown together with the three cylindrical supports of the turbine motor assembly. The helical tip vortices are evident even though they have interacted with the internal wall boundary layers. Finally, Figure 17(b) shows the transient development of the voltage output, which, in the beginning, is proportional to time and eventually reaches a steady-state value of about $1.42 V$ at $t = 0.06 s$ . It should be noted that the rotational velocity of the turbine follows a very similar behavior with a terminal velocity of $350 rad s^{- 1}$ . This suggests that it reaches its steady-state velocity within one to two rotations.

Figure 16.

(a) Global view of computed vorticity magnitude contours $U_{0} = 11 m s^{- 1}$ and (b) computed vorticity contours in the turbine area $U_{0} = 11 m s^{- 1}$ .

Figure 17.

(a) Computed vortex core region contours based on velocity $U_{0} = 11 m s^{- 1}$ and (b) transient output voltage development.

The computational data of average velocity within the venting duct, the drag force, and the output voltage of the wind turbine were compared directly with the available corresponding experimental results obtained in the wind tunnel testing. Table 2 lists this comparison between the computational results and the experimental data of bulk quantities. It should be noted here that both models used in the wind tunnel experiments and CFD simulations were identical and under the same flow conditions. The experimental results appear to be consistently lower than the CFD data by about 5% on voltage, 6% on velocity, and 13% on mass flow rate and drag.

Table 2.

Comparison of CFD and experimental results at $U_{0} = 11 m s^{- 1}$ .

	$U_{d} (m s^{- 1})$	$\overset{\cdot}{m} (kg s^{- 1})$	Drag (N)	Voltage (V)
CFD	18.12	0.680	1.1	1.42
Experiment	17.3	0.590	0.89	1.35

CFD: computational fluid dynamics.

Significance and concluding remarks

Our theoretical, computational, and experimental work indicated some significant trends and prospects in harnessing the kinetic energy of fluids in a moving frame as is the case for moving vehicles, passenger cars, or trucks to power some of their electrical systems. In such moving environments, the specific power of the air motion is much greater and less intermittent than in stationary wind turbines anchored to the ground and operating in open atmospheric conditions. The ratio of corresponding specific power outputs of a device moving at $97 kph (60 mph)$ and a classical stationary wind turbine operating at its most frequent wind speed of $24 kph (15 mph)$ will be $\approx (60 / 15)^{3} = 64$ . Thus, if the challenges associated with the development of such a device are resolved, significant benefits are expected in power generation although the expected net generated output will be between 0.1 and 1 kW. The reason is that wind energy will be harnessed by millions of vehicles, which will constitute a vast distributed decentralized system of power generation. If we assume that only $1 %$ of the 250 million cars and trucks in operation in the United States are moving and that an efficiency of $50 %$ is associated with the electrical conversion process, which has not been considered so far, then an amount of about $1 GW$ of power may be generated at a given time.

In the present research, we explored for the first time the prospects of harnessing wind energy from moving vehicles by analyzing the flow through and around a generic Ahmed body. This has been accomplished by carrying out several experimental, theoretical, and computational tasks that illuminated some of the challenges associated with the prospects of new technologies that extract energy from wind in a moving frame. The work has clearly shown the benefits discovered by adding the duct to the vehicle tested, which is associated with a drag reduction due, not only to the change in the cross-sectional area of the model but also to reenergizing the wake by the exhaust flow through the duct. The power ratio achieved in the present configuration is 3.26 in reference to a stand-alone similar wind turbine in the open atmosphere. The driving force of the flow through the device is clearly the pressure gradient imposed by the stagnating conditions up-front and the negative back pressure in the rear. Ideally, the greater the pressure difference between the front and back pressures, the higher the velocity inside the duct should be. Thus, vehicles with lower negative back pressure and therefore higher drag may provide better conditions in capturing flows with higher mass flow rate through the duct. Counteracting on this, however, are the frictional forces developing over the internal surface of the duct, which are proportional to $L / d_{p}$ , and the mutual interference between the flow through the duct and the pressure distribution around the vehicle, particularly the back pressure, which may inhibit the onset of increased flow rate through a feedback mechanism that reduces the initial pressure difference.

As mentioned earlier, most of the drag of bluff bodies and particularly of vehicles is due to pressure drag, which is generated at the rear end. The structure of the wake which affects the back pressure is very complex, with a separation zone and counter-rotating vortices coming off the side edges, whose strength is mainly determined by the base surface angle. Values of the coefficient of pressure at the rear end of bluff bodies $c_{pb}$ can be as low as $- 1.2$ in two-dimensional (2D) cylinders or $- 0.125 to - 0.65$ in 3D bluff bodies.^{9,12,16,17,21–31} These values can be used to obtain a preliminary range of the expected levels of power extraction. The present findings related to the intense vortical activity in the wake of the Ahmed body agree very well with the recent results³¹ which also have demonstrated how a large suction in the wake of such a vehicle can be manipulated to reduce the overall drag force.

Moving against the wind, as in the conventional application for a classical wind turbine shown in a previous work³² where the moving frame is a bicycle, is a special case of the present work. The theoretical framework developed here is more general since it covers man-powered or auto-powered vehicles. Particularly, in the present research, we identified some specific areas inside or outside moving vehicles with local velocities greater than the translation velocity of the vehicle where net energy extraction is possible. Further research is needed to locate additional positions inside or outside vehicles where energy extraction may be meaningful. Optimization of the size of the duct and Venturi section, which are restricted by the limited availability of space, along with the diffuser design, which controls the exit pressure of the venting flow, should be further studied. It is desirable to capture the maximum possible flow rate inside the venting duct. Therefore, we envision that the bottom part of the engine compartment will be sealed off so that air entering the area under the hood will be eventually flowing toward the venting duct where the wind turbine will be located.

Footnotes

Acknowledgements

The authors thank Jose Cortez, Ali Moussa, and Yussef Rickli for their contributions to the preliminary computations.

Handling Editor: James Baldwin

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The financial support provided by the Pope Fund is greatly acknowledged. Provisional patent # 61941633.

ORCID iD

Yiannis Andreopoulos

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