Aerodynamic design optimization of locally built FSR Isuzu bus through numerical simulation

Reducing the fuel consumption of commercial vehicles—especially those used for public transportation—has become increasingly important due to advancements in the automotive industry. On the other hand, the main disadvantages of buses and other commercial vehicles are their fuel consumption, exhaust pollutants, and crosswind stability. Most buses built in Ethiopia have aerodynamic rectangular shapes and strong drag resistance forces, which lead to higher fuel consumption. One of the most accessible buses in Ethiopia is the FSR Isuzu Bus; its external body is locally constructed and has a poor aerodynamic shape. The primary goal of this study is to reduce aerodynamic drag force by improving the outer body shape of the current FSR Isuzu Bus. It also aims to examine the impact of roughness (strip) on the overall aerodynamic characteristics of the bus when it encounters crosswinds, thereby reducing fuel consumption, roll moment, and side force. For computational fluid dynamics (CFD) analysis, ANSYS Fluent is used, and Solidwork is used to model the bus body. A comparison is made between the current CFD analysis of the bus body and the modified design at varying speeds. Three separate models are used in the analysis. At an average speed of 100 kmph, 29.58% (4 to 5 liters) of fuel can be saved, and the drag force is reduced by roughly 49.7% when comparing the new concept to the current bus. By utilizing a strip on the bus’s roof, the side force coefficient and the roll moment coefficient are subsequently reduced from model two to model three by 8.76% and 9.01%, respectively. The study’s conclusions indicate that the external body shape changes have reduced drag; and, adding roof strips has decreased drag to acceptable level and enhanced crosswind stability.


Introduction
The use of volatile fuels in automobiles is now a major concern for the environment and the sustainability of the economy.Many options have been investigated, such as increasing efficiency and using different fuels for the vehicle.Many attainable outcomes have been achieved through improvements in a few critical areas, such as aerodynamics, weight reduction, and power generation; nevertheless, reducing aerodynamic components like drag and lift is more efficient than increasing or decreasing vehicle weight or power generation [1][2][3].Since moving objects are surrounded by complex turbulent air flow, smooth, low-resistance vehicles are critical from an aerodynamics perspective.To improve engine cooling, engine rooms should also be arranged efficiently.By carefully positioning the intake and exhaust holes in relation to the pressure distribution throughout the car's surfaces, it is also possible to improve interior ventilation.Because aerodynamic features reduce air resistance during operation, they save fuel and improve driving stability against lift force and crosswind, which is important from an economic perspective [4].Aerodynamic drag reduction can be achieved at a cheap cost to boost fuel economy, and shape optimization for low drag has become an essential component of the whole vehicle design process [3,5,6].
In the world, the bus is the most important kind of transportation.Considering their high fuel use, buses would be more valuable if they had more aerodynamic shapes [7].To improve aerodynamics and reduce fuel consumption, the current design's surface or form can be changed.It will reduce the drag forces acting on the car, increasing fuel efficiency.Reducing aerodynamic drag is a top focus and endeavor for auto designers.If the resistance in a moving vehicle is decreased, higher speeds can be achieved with the same amount of power.When a vehicle moves forward, its aerodynamics can reduce opposing forces and enhance down forces and negative lifts acting on it.This leads to an increase in both fuel efficiency and load carrying capacity.Many drag forces can affect a vehicle, including lift, wave drag, and induced drag [8].Diesel engines with a displacement volume of 12 to 16 litres and a braking power of 800 to 1200 kW are typically used in high-speed express vehicles.Its fuel consumption rate is extremely high.At highway cruising speed (100 km h −1 ), nearly 2.5 to 3.5 km l −1 are reached.Research indicates that a minimum of 70% of a vehicle's braking force is lost as it reaches 100 km/h while trying to combat aerodynamic drag [9].
In order to find strategies for reducing the aerodynamic drag that a vehicle experiences on a surface with non-smooth dimples, Yiping Wang et al [10] conducted mathematical modeling.Using numerical simulations, the impact of applying a non-smooth, dimpled surface to the rear slope of a generic vehicle body on the reduction of aerodynamic drag was examined.Yang et al [6] suggested incorporating non-smooth features into a minivan's roof panel design to reduce the vehicle's aerodynamic drag.The aerodynamic drag properties are investigated by a stable computational fluid dynamics (CFD) method.A test conducted in a wind tunnel verifies the accuracy of the numerical approach.Final results show that maximal benefits of drag reduction up to 7.71% can be obtained using a rectangular circular concave arrangement.Pressure differences between the front and rear of the car create drag, which is reduced by the minivan's circular concave roof.The study conducted by Palanivendhan et al [8], surface dimples were added to a computer model of a bus, a commercial vehicle, to reduce aerodynamic drag and increase fuel economy.An intercity bus is redesigned by Roy et al [7] with better external aesthetics, less aerodynamic drag, and more passenger comfort.The principles of product design were applied to analyze the comfort and aesthetics.The results of the revised exterior body showed a reduction in coefficient of drag of about 45% and a reduction in overall aerodynamic drag of 60% as a result of the combined effects of the lower frontal area and drag.Abinesh and Arunkumar [11] Designed aerodynamic changes, such as exterior bodywork, for big vehicles like buses in order to reduce fuel consumption.They have concentrated on the front face, AC position, and rear view mirror of the VOLVO intercity bus and observed a 10% decrease in aerodynamic drag force.
Mathematically, the coefficient of drag is calculated by using the CFD ANSYS software to determine the drag force.The impact of changing the angle between the front windshield and engine hood for reducing air resistance in a car was examined by Bo [12].The flow structure around a passenger car with different add-on devices was determined by Mukut and Abedin [13] using an efficient numerical model based on Computational Fluid Dynamics (CFD).Drag coefficients for passenger cars are determined through examining the aerodynamics of the best-fitting vortex generator, spoiler, tail plates, and spoiler with VGs.Including these addon devices lowers the lift and drag coefficients in head-on wind.Kristina et al [14] examined a square-backed, reduced form.The wake nature is altered when tapers are built on the square back of a reference model from both the top and bottom.Tapering the top and bottom of the square back by 4% of the reference model length improves the drag reduction gained.According to Grandemange et al [15], chamfering a square back's top and bottom decreased an Ahmed body's drag coefficient.Despite a 5.8% reduction in drag, the square back shape of the Ahmed exceeded the modified Ahmed body at the ideal chamfer angle.Researchers additionally examined at how yaw angle affected drag and determined that the drag coefficient didn't change at intervals of 0.5% yaw angle.Muthuvel et al [16] aerodynamically modified the bus's outer surface and structure to reduce the drag force acting on the car, which reduced fuel consumption.
Rear view mirror removal can reduce the vehicle's drag by 4.5%, according to research by Mccallen et al [17].Separation and circulation of flow will occur from any opening in the vehicle's body.The effects of adding cab roof fairing to a scaled truck model without cab roof fairing on drag were studied by Kim et al [18].The findings were examined through wind tunnel testing and numerical simulations.When compared to a track without a cab roof fairing, the first test's drag reduction was 15.05% when a 2D cab roof fairing was used.The second test's drag reduction was 15.97%, which is marginally higher than the first investigation, when the 2D cab roof fairing was rounded on its sides.Complete modification of a 2D cab roof fairing yields a 19% reduction in drag, which is a significant improvement over a 2D modification.There was significant jet mass dispersion as a result of high turbulence intensities and small turbulence macro time and length frames.Consequently, vortex shedding and coherent vortical structures caused by add-on devices have a significant impact on the drag coefficient [19][20][21].
This study's primary goal is to reduce aerodynamic drag force by optimizing the exterior body design of the current FSR Isuzu Bus.It also aims to reduce side force, roll moment, and fuel consumption by examining how roughness (strip) impacts the bus's overall aerodynamic qualities in crosswinds.The bus body is modelled in Solidwork, and the CFD analysis is performed with ANSYS Fluent.The current CFD analysis of the bus body is compared with the improved design at different speeds.

Methodology
At higher speeds, the current FSR Isuzu bus's blunt, flat front surface generates more drag force and more air resistance to forward motion.Using the current vehicle as a foundation and proposing a fresh outer body shape design, this work aims to remedy the current issue.SolidWorks was utilized to produce the basic model of an Isuzu midi bus 1/15 that has been scaled down, as illustrated in figure 1.The model's underbody was chosen to be smooth, and side view mirrors, cooling airflow openings, and closed wheel wells were all excluded from the investigation.Numerical simulations have been performed on several FSR Isuzu bus designs.Every shape had been subjected to a CFD investigation.The appropriate level of drag reduction was taken into account from a design perspective, according to the study on [22].When designing and developing bus aerodynamic models, the geometric scaling method is frequently used to reduce expenses.The Prototype and Model ISZU bus are less comparable than they could be because of factors like Reynolds number, surface roughness, and tip clearance, which are sometimes hard to meet all the requirements for similarity.However, the current study's deviance is within an acceptable range-less than 5%.

Benchmarking the baseline model
FSR Isuzu bus shapes are represented by this baseline type in figure 1. Utilizing the FSR Isuzu bus as a reference, the study's aerodynamic analysis-which focuses mostly on body dimensions-was carried out.Ethiopians are currently leaning toward the newest version.The study of the bus is prompted by the current scenario because it is utilized by many public and private organizations for service and public transportation.However, because of aerodynamics and cross-wind stability, the design is ineffective in terms of total performance.
Three bus body models with the external body styling and appearance were prepared for this analysis.The original bus model, known as 'Model 1,' had a curved front end and smooth, rounded corners on the front and back of the roof, as presented in figures 1 and 3(a).Model #1 has a 25°inclination angle and a fillet of 6 mm on each edge, while the baseline model had an 8°inclination angle.The bus's front has a fully tapered aerodynamic shape.
Similar parts from the 'Model 1' bus were used to create the 'Model 2' bus, which is distinct in diffuser angle as shown in figure 2. The diffuser angle for both the baseline model and model one is 22.6°.However, the diffuser angle of model two has been increased to 25°and 30°and was decided to be optimal.Diffusers are flow control devices that are installed at the back bottom of cars to slow or diffuse airflow from the underside of the car, which helps the car's pressure return.The flow is intended to be swept upward from the bottom by the  diffuser's angle [23].A vehicle's rear diffuser, which has a major influence on the wake structure, can be angled at a favorable angle to maximize wake structure and to reduce drag [24][25][26][27].
The second bus model's design principles were applied in the development of the third bus model presented in figure 3(b).The models are simply distinguished by their stripes.The third bus model incorporates roof stripes (streamlines), a better diffuser angle on the back, smoother front and back borders, and a curved front surface.

Effect of strip on the aerodynamics of a bus subjected to crosswinds
The effects of roughness on the overall aerodynamic properties of a high-speed train in crosswinds are studied by Wang et al [28].Surface roughness can change a train's aerodynamic performance by influencing the flow characteristics in the boundary layer near to the wall.The roof of the train surface is provided with roughness in the shape of longitudinal strips.The results show that adding roughness can reduce the side force coefficient, roll moment coefficient, and surface pressure on the bus's roof and side when compared to the smooth model.It can be pushed away from the wall by rectangular strips, which also reduce turbulence in the boundary layer.In addition, the strips' blocking action has the potential to significantly reduce the amplitude of vorticity by lowering the instantaneous cross flow caused by turbulent motion and facilitating the splitting of large vortex formations into smaller vortex structures.Rough surfaces are strips that are adhered to the bus roof in a pleated pattern along the length of the bus, as presented in figures 4(a) and (b).The strips have height and width measurements of 1 mm and 3 mm, respectively.In all, ten strips that were uniformly spread across the car's roof were employed for this study.There was a 10 mm fillet on the back strip and a 15 mm fillet on the front.The FSR Isuzu passenger bus specification, which is utilized to compare important factors in the design assessments of the three models, is shown in table 1.

Turbulence modeling
The analysis was performed using FLUENT 2020, which solves the governing equations numerically through the application of the control-volume approach.The solver that was chosen was the implicit pressure-based solver.This shape is obtained by solving the continuity and momentum equations in succession.The flow is assumed to be incompressible and steady, and the equations are solved using the second order upwind approach.The k-ε model was chosen because of its high accuracy and rapid convergence.The spreading rate of both round and flat structures is more accurately predicted by the realizable k-ε model.

Geometry generation
Figure 1 shows a simplified version of a baseline SolidWorks model of an FSR Isuzu bus.The FSR bus type has the following measurements: 200 mm for height, 156.67 mm for width, 613.33 mm for length, and 318 mm for wheelbase.Upon uploading the car model into the ANSYS environment, an enclosure was generated around it.

Design of virtual wind tunnel
A fluent suggestion was followed in creating the enclosure to ensure proper results.An actual wind tunnel's construction is simulated by a virtual air box figure 5(a) based on the 3D CAD model.A bus's size corresponds to the tunnel's dimensions.The wind tunnel consists of an inlet, an outlet, walls, and a ground surface.Three car lengths separated the flow inlet plane from the bus body's front.The exit of the tunnel is five car lengths from the rear of the vehicle.A fairly wide simulation area was created by positioning the side plane roughly two car lengths away from the side surface of the car body.Two times the length of the car body is the domain's height.Like all other vehicles, commercial buses are generally geometrically symmetric about their longitudinal axis; this symmetry is achieved by inserting a plane along the bus's XY plane.As a result, the bus model was longitudinally divided in half [29].Using a Boolean operator, the volume was subtracted from the control volume in order to prevent the removed volume from meshing.Since the software fluent takes into account the no-slip condition on surfaces where the volume is removed, it has no effect on the solution.By decreasing the mesh's size, it significantly shortens the computation time.

Computational domain and boundary conditions for crosswind (side wind) stability
Except for the inlet and outlet limits, all boundaries are defined as non-slip walls according to the boundary criteria.The inlet boundary is assigned a uniform velocity, as shown in figure 5(b), and the exit is set up as a zeropressure outlet.The bus model is subjected to a 90°yaw angle of relative wind.There is a crosswind moving at 12 m s −1 that is adversely affecting the x-axis.

Boundary conditions
The analysis was carried out while the road was moving and its wheels were rotating.Only straight wind conditions at three distinct vehicle speeds-80, 100, and 120 kmph-were taken into consideration in the simulation.In order to simulate the conditions of constant wind velocity, a constant velocity inlet condition was applied at the inlet.At the outlet, operating pressure was set to atmospheric pressure, with zero-gauge pressure applied.Table 2 contains a list of all the boundary conditions that were used in the analysis.

Mesh generation
The surface mesh, shown in figure 6, was generated using ANSYS fluent.Both in the bus design and at the domain's surface is where the mesh is produced.A tetrahedron was the type of mesh used to discretize the computational domain.The triangle mesh served as the foundation for the fine mesh that developed for the surface bodies.

Fluent setup and simulation procedures
Fluent software used the realizable k-ε model to simulate each bus model.The realizable k-ε turbulence model is applied to the tetrahedron mesh.In the simulations, boundary conditions that hindered the bus's speed at 80 kmph, 100 kmph, or 120 kmph were applied.Turbulence at the velocity inlet was reduced by 1%.An integrated method was selected to address the pressure-velocity coupling.This linked approach has greater effectiveness and reliability.Explicit relaxation parameters for momentum and pressure were tested up to 0.25.
Reducing the explicit relaxation factors triggered a skewed mesh to converge approximately 0.85 times faster.Set at 0.95 is the turbulent viscosity relaxation factor.For ten consecutive iterations, the drag coefficient residual must remain constant at 1 × 10−5, indicating convergence.After convergence was reached, the solution was analyzed to determine how effective the newly proposed designs were.The zero-gauge pressure at the outlet is  applied with operating pressure equal to atmospheric pressure, and the constant velocity inlet condition is applied at the inlet.

Grid independence test
As geometries get more complicated, structured meshes become extremely skewed, which can lead to unphysical and erroneous solutions as well as longer calculation times [30].In numerical computations, CFD ought to yield the answers regardless of the grid or mesh that is employed.Accordingly, the grid independent test is displayed in figure 7.
For drag and lift coefficients, the baseline bus's grid independence study was done for computational grids made up of 850,982, 913,691,973,800, 1,068,780, 1,253,350, and 1,506,069 elements, as illustrated in figure 7.For the 1,068,780, 1,253,350, and 1,506,069 grids, there was no noticeable variation in drag.There is minimal fluctuation in the drag and lift coefficients when the number of elements varies.As a result, the mesh size of 10 mm and element count of 1,506,069 selected are precise enough to capture the flow phenomenon.

Result and discussions
The drag coefficient and flow field of the baseline model were initially examined in order to determine the drag coefficient reduction from various bus models with modifications.The changed models were simulated after the baseline model.Following the simulation, the flow field and drag coefficient of every model were compared.vehicle's body at an accelerated rate, with pressure dropping to negative values.When the body surface abruptly deviates, flow separates and a wake forms in the immediate area of the rear of the vehicle.Pressure drag can be decreased by shrinking the area of the low-pressure wake zone around the rear end.According to the literature, less pressure drag is tested for concepts like lowering the roof end, adding strips to the roof, improving the radius, tapering the roof, and diffusing the angle.The pressure distributions of the three models are depicted in figures 8(b)-(d).In comparison to the baseline model figure 8(a), the high pressure area decreased significantly for all three models.

Pressure and velocity distribution of different models
The baseline model and the three models' respective velocity distributions are displayed in figures 9(a)-(d).Velocity close to the inlet are represented by green colors, and high-velocity zones are represented by red colors.The low-velocity region includes, among other places, the bus's underbody, back, and front stagnation points.The bus experiences an increase in drag as turbulence develops in low-velocity zones.The velocity distribution in figure 9(a) can be used to show flow separation.The rear and roof of the car exhibit vertices and recirculation.The flow speeds up on the bus's roof and converges to reduce pressure.Induced pressure drag results from the separation of high-speed flow close to the rear.

Flow visualization with velocity vector at different rear diffuser angle at 100 kmph
Figure 10 illustrates how the recirculation flow behind the bus models could be disrupted by increasing diffuser angles.Regaining its velocity in the wake area helps reduce drag.At 30°, 25°, and 22.5°, respectively, the recirculation flow behind the bus is lower.Increased ground clearance at all rear diffuser angles results in an increase in drag [31].The fluid flow from the left and right sides of the body enters the diffuser region more easily when the mass flow beneath body flow is increased, which is achieved by raising the rear diffuser angle.The wake region's acceleration and recovery velocity from the flow past the diffuser may enhance the wake structure behind the bus models.Two objects, called 'separation bubbles' because they were two reversed vortices, were visible in the wake's recirculation region.Reducing the recirculation region and drag is achieved by moving the junction position of the upper and lower flows upward and closer to the trunk deck when the rear diffuser angle is increased up to 30°.
The vortices that formed at 22.5°behind the buses spread out over a wide area.Figure 10(c) at 30°shows the flow attached, preventing the formation of vortices at the rear, which were later observed traveling towards the ground.This change in aerodynamic properties is due to the influence of the rear diffuser angle.Because of this, the wake zone of 22.5°diffuser angle covers a wider region than the wake zones of 25°and 30°.In the same manner, the wake region area at 25°diffuser angle is higher than the wake region area at 30°diffuser angle.Consequently, it revealed that a considerable and reasonable reduction in drag occurs when using a 30°diffuser angle.Above 30°, the flow separates but stays connected to the diffusers.

Comparison of smooth and rough models (strip) subjected to crosswind (side wind)
Figures 11(a)-(b) illustrates how the vortex structures above the roof of the smooth (without strip) and rough (with strip) models vary significantly from one another.Large-scale, often higher-energy vortices appear on the roof of the smooth model and have high turbulence (marked by black).On the other hand, the model's roughness delays the turbulent transition by preventing the growth of observable vortex formations until the end of the roof.The strips provide extra energy to the flow in the sub-layer so that the energy exchange inside the boundary layer becomes more severe [28].Therefore, the large-scale vortex structures have been dissipated.The intensity of the vortex structure for the rough model tends to be weaker than that of the smooth model (marked by red color), so the corresponding suction effect has been decreased, which can help reduce the lateral force and overturning moment.
The larger vortex core sizes and stronger forces in the vortex structures that surround the smooth model are the primary reasons for the poor aerodynamic performance.The low speed airflow can be developed more steadily by the rectangular strips since they reduce the flow velocity and turbulence disturbance near the wall.For this main reason, the rough model provides higher crosswind stability.

Surface pressure coefficients (Cp)
The Surface Pressure Coefficients (Cp) distribution for 'smooth surface' and 'rough surface' is illustrated in figures 12(a)-(b).In both cases, the distribution of Cp around the bus body is similar.Still, there are minuscule variations in the measured Cp's magnitude.On the windward side (wws), positive results are observed; however, in areas where the flow is accelerating, negative results are observed.The Cp values typically decrease as the flow accelerates from the windward side to the roof.
The Cp findings for the two scenarios show noticeable variations as the flow moves closer to the roof.The effect of roughness is evident despite the fact the Cp values in both scenarios decrease as the flow travels from the windward side (wws) to the roof.When compared to Cp findings obtained with a smooth roof surface, the influence of roughness on the bus roof resulted in significantly lower Cp values, suggesting strong suctions.When comparing the flow on the roof to the results obtained with a smooth surface, it is evident that the rough surface leads to an overall lower Cp distribution (i.e., larger negative values are obtained).This aerodynamic streamlining is intended to prevent vortices from being released by the concave roof grooves.These strips, together with the pressure shielding above the rear hatch, reduce the negative pressure at the back of the vehicle.This significantly increased the traction force needed to keep the vehicle stable.

Characteristics of aerodynamic loads
The safety of a bus in a crosswind is significantly influenced by side force and roll moment.To simplify analysis, it was defined side force coefficient C S and roll moment coefficient C mz as follows: Where A = 0.1226 m 2 (height * length) is the projected area of the bus in the x direction, Fs is the side force, M z is the roll moment, and the moment center is at point (0, 0.116, 0), H is height of bus 0.2 m,V wind speed 12 m s −1 .
According to the simulation result, side force and roll moment values for smooth surfaces are 11.565N and −0.1015 N, respectively, while side force and roll moment values for rough surfaces are 10.557N and −0.092336 N, respectively.And the side force coefficient C S and roll moment coefficient C mz are presented in table 3.
Time-averaged results are provided for both rough and smooth models in table 3. The side force coefficient and roll moment coefficient of the rough surface model are observed to be 8.76% and 9.01% lower, respectively, than those of the smooth model.This suggests that a bus with a particular level of roughness can operate more steadily and safely, which is in line with the findings from the flow field analysis.

Comparing drag force and lift force
The drag force is derived from the drag coefficient whereas the lift force is derived from the lift coefficient.
( )  In table 5, all of the lift values are negative.Enhancing the vehicle's ability to maintain its position on the road and reducing the steering instability of the bus is highly advantageous when the values of the lift forces are negative, indicating downward lift.When using modified models, the power, drag coefficient, and drag forces have all been sufficiently reduced; however, the downward lift force is significantly less than that of the baseline model.A negative rear spoiler and an underbody dam are two more methods to increase the downward force that must be added in addition to altering the underbody pshape.The lift force that the new designs experience when driving at different speeds is compared with the baseline model.Therefore, the modified models require an additional underbody design.At 80 kmph, Model 3 reduces the lift force from −270.86 N to −82.85 N by 69%, as presented in table 5 [9].According to table 6, the Model 3 can save up to 29.65% on fuel consumption at 80 kmph when compared to the base model traveling at the same speed.Model 2 demonstrated the second-highest reduction in fuel consumption, with figures of 29.36%, 29.37%, and 29.31% at speeds of 80, 100, and 120 kmph, respectively.Similarly, at 80, 100, and 120 kmph, respectively, Model 1 uses less fuel than a baseline model by 28.06%, 27.98%, and 27.9%.

Power and fuel savings
The following formula is used to determine the power savings of the streamlined bus model over the original bus model.

( )
Where ṁ fuel = Mass flow rate (m 3 /s) P sav = Power saved (W) Q LHV = Lower heating value (lower heating value of diesel fuel is 42.5 MJ/kg) r fuel = Density of fuel at ambient temperature (860 kg/m 3 ) h engine = Thermal efficiency of the engine (thermal efficiency of the engine is 35%) The unit of fuel consumption is m 3 /s to convert to litter per hour L/hr, the conversion is carried out using the relation given below.
1 m 3 /s = 3.6 × 10 6 L/hr Table 7 illustrates how the modified bus lowered the power requirement of the original bus.When comparing model 3 to the baseline bus, the power demand is reduced by 7184.84W, 14045.57W, and 24300.57W at 80 km/ h, 10 0 km h −1 , and 120 km h −1 , respectively.When comparing the model 3 with the baseline bus, the fuel savings at 80 km h −1 , 100 km h −1 , and 120 km h −1 are 2.23 l h −1 , 4.12 l h −1 , and 6.92 l h −1 , respectively.

Validation of the present computational algorithm
The current investigation's numerical result for the total drag coefficient, C d = 0.61678 for the 'baseline model,' closely matches the 0.6-0.8range that was previously reported in [33,34].The present value of C d lies exactly in the middle of the range.This gives confidence in the present computational scheme.The speed variation with the drag coefficient is depicted in figure 13.
According to research on the relationship between vehicle speed and drag resistance [35,36], higher vehicle velocities necessitate a higher power output to overcome aerodynamic drag.The results of the current simulation are nearly identical to them.

Conclusions
The goal of the paper is to improve the aerodynamics of the FSR Isuzu bus and remodel the exterior design of an existing FSR Isuzu bus for use on Ethiopian roadways.As per the computational analysis, the external design modifications made improved the aerodynamic performance of the bus body.The drag coefficient, which has an impact on fuel economy, is significantly improved.As a result, the following conclusions are drawn from results and discussion part.
o The finding shows that improving the diffuser angle from 22.5 degrees to 30 degrees and changing the external bus body design increased buses' aerodynamic efficiency.Therefore, as the rear diffuser angle rises, drag force is reduced and a negative lift is dropped.
o A vehicle's aerodynamic performance was enhanced by a strip on the roof, which reduced the lift and drag coefficients to a reasonable level.By lowering the coefficient of lift, these improvements promote the car's better stability at higher speeds.o Model three has improved crosswind stability.By applying a strip to the roof surface, the roll moment coefficient and side force coefficient were reduced by 9.01% and 8.76%, respectively.
o At an average speed of 80, 100, and 120 kmph, the drag coefficients of Model 1 (shape modification) and Model 2 (raising diffuser angle) improved by 46.7% and 48.7%, respectively, while the lift coefficient significantly dropped.
o When compared to the baseline bus, the model three (fit strip on the roof of the model 2) improved the drag coefficient by 49.45% and had a significant increase in lift coefficient from model 2 (27% lift coefficient lowered from model 2).
o There is a fuel savings of about 29.65% when comparing the base model at 80 kmph to the Model 3 at the same speed.This increase in fuel efficiency will have a major effect on the reduction of annual fuel consumption.

Figure 3 .
Figure 3. Geometrical modeling of bus models (a) model one (b) model three.

Figure 4 .
Figure 4. Model three (a) coordinate system with reference to wind (b) Orientation of angle θ with respect to wind.

Figure 5 .
Figure 5. (a) Virtual wind tunnel targeted for CFD simulation (b) boundary condition for side wind.

Figure 7 .
Figure 7. Grid independence test result for Cd.

Figure 8 (
a) illustrates how stagnant incoming air causes a build-up of pressure on the vehicle's front surface.Stagnation is the part of the car that initially comes into touch with the air as it is driving, air flows over the

3. 7 .
Calculation of fuel consumption = Percentage fuel reduction 3 5 percentage total drag reduction 5 Where P sav = Power saved (W) -F D Base = Drag force of the baseline bus (N) -F D Modified = Drag force of the Modified bus (N) v bus = Speed of the bus (m/s)• Fuel saved by the reduction of the drag force is calculated using the equation given below[32]

Figure 13 .
Figure 13.Drag coefficient for baseline model at various speed.

Table 3 .
Results of C S and C mz for smooth and rough models.The drag forces encountered by the new designs and the baseline model at various vehicle speeds are compared in table 4. The analysis shows a clear reduction in drag, with the total drag force falling from 656.2 N to 349.28 N at 80 kmph for Model 1, 656.2 N to 342.66 N at 80 kmph for Model 2 with the diffuser angle at 25°, 656.32 N to 335.06 N at 80 kmph for Model 2 with the diffuser angle at 30°, and 656.2 N to 332.85 N at 80 kmph for Model 3.These improvements represent respective gains of 46.77%, 47.7%, 48.94%, and 49.28%.The modified models' total drag force rapidly decreases in comparison to the baseline model.Drag is decreased and crosswind stability is increased with the new model's variable diffuser angle and roof strip.

Table 4 .
Drag coefficient and drag force.

Table 5 .
Lift coefficient and lift force.

Table 7 .
Power and fuel saved in litter per hour.