# Passive Control of Base Pressure: A Review

^{*}

## Abstract

**:**

## 1. Introduction

_{1}M

_{1}d

_{1}) to a downstream state (P

_{2}M

_{2}d

_{2}). P

_{b}is the pressure at the base of the duct.

_{b}is the pressure at the base of the shell, and P

_{1}M

_{1}is the flow conditions. Figure 5B shows the schematic diagram of external flow over a blunt base. Figure 5C shows the schematic diagram of coherent vortex structures.

## 2. Various Types of Passive Controls

#### 2.1. Passive Control in the Form of Cavity

#### 2.2. Passive Control with Rib

#### 2.3. Passive Control with Dimple

^{3}. From this analysis, it is clear that an optimal L/D ratio can be found for a given nozzle pressure ratio, which results in a maximum increase/decrease in base pressure, and the passive controller can be efficient in controlling the base pressure.

#### 2.4. Passive Control with Static Cylinder

#### 2.5. Passive Control in the Form of Spikes

#### 2.6. Passive Control in the Form of Splitter Plate

_{pb}− {C

_{pb(without splitter plate)}}/(C

_{pb})

_{without splitter plate}) continuously decreases with the increment in l/h value. For l/h = 1, the C has a minimum value of −0.55. C then increases slightly with changes in l/h to a maximum value of −0.52 at l/h = 2, and above l/h = 2, C decreases somewhat at higher l/h, and therefore for l/h = 4, a constant value of −0.58 is maintained. Simultaneously, Bearman [27] and Nash et al. [28] show some differences when the present data are compared.

^{6}and 1.6 × 10

^{6}using a splitter plate at its front or rear a simplified car geometry to reduce drag. Utility vehicles or MPV vehicles are considered by representing them in the form of simplified geometry. A reduction in drag of around 28% is achieved by placing the model’s front splitter plate. This research demonstrates the advantage of position adaptation and orientation of passive control in the presence of lateral wind.

_{Dnet}is 0.1028. The resulting net base drag coefficients were C

_{Dnet}is 0.1033, 0.1071, and 0.1051, respectively, for the one-half, one-third, and one-fourth-cylinder configurations. Compared to the non-control geometries, the splitter plates generated drag coefficient changes of 0.5, 4.2, and 2.2 percent, which is within or too near to the usual measurement uncertainty.

#### 2.7. Other Types of Passive Control Technique

_{f}. The total mean drag coefficient is more than that of the plain duct for the attachment angle 40 and 60 degrees at Reynolds numbers 20 and 40. The results are due to the plates’ viscous effect, which is significant in the flow field’s steady regime.

## 3. Findings Discussion

- All the passive control methods to regulate base pressure are useful in creating a favourable pressure gradient. These techniques are also inadequately effective in the presence of an adverse pressure gradient (i.e., when the jets are over-expanded). In passive control, the level of expansion (i.e., P
_{e}/P_{a}) plays a vital role in fixing the base pressure values. It is seen that whenever the area ratio is five and above, the control effectiveness is minimal/not useful even though the flow from the nozzles is under the influence of a favourable pressure gradient. The physics behind this trend maybe when the relief effect due to an area ratio increase is beyond some limit. The flow from the converging or converging-diverging nozzle discharged into the enlarged duct tends to attach with reattachment length other than the optimum for a strong vortex at the base. This process makes the NPR effect on base pressure become insignificant after a critical area ratio. The review shows that when the jets are under-expanded for a lower area ratio, the passive control is significant, and base pressure is equal to the atmospheric pressure, or is more than the ambient pressure. Results indicate that for certain combinations of the parameters, an under-expansion level of 1.5 (i.e., P_{e}/P_{a}= 1.5) is the optimum value resulting in a maximum increase in the base pressure. - A new passive control device was considered for a form-drag reduction in the flow over a two-dimensional bluff body with a blunt trailing edge. The system consists of small tabs on the top and bottom edges of a bluff trail to effectively interrupt a two-dimensional wake. A wind tunnel experiment and a large-scale simulation were conducted to test its drag reduction efficiency. Extensive parametrical research is conducted experimentally by changing the passive control’s height and width in the form of a tab and the spacing along the span between the adjacent tabs. The Reynolds numbers considered for the study are 20,000, 40,000, and 80,000. The base pressure increases for a wide range of parameters (i.e., drag reduces) at all three Reynolds numbers.
- Similarly, the splitter plate’s effect at various length locations is useful in the base drag reduction at various NPR, Mach numbers, area ratios, and length-to-diameter ratios. The passive control in the form of a splitter plate is significant, resulting in reducing the drag. Drag is reduced from 9% to 57% by attaching the splitter plate to the cylinder. With vertical splitter plates positioned downstream of a straight base, drag reductions of nearly 12% were obtained. Finally, the results presented herein confirm the advantage of splitter plates in reducing aerodynamic drag and demonstrate the need to develop systems capable of adapting their position and angular orientation to external conditions. Triangular splitters that divide the near wake into one-half, one-third, and one-fourth cylinder regions were designed to exploit this flow’s specific stability characteristics. The impact of the immediate wake flow changes the base pressure and eventually affects the base drag. A base drag reduction of as high as 39% is achieved by employing the splitter plate, whereas, with passive control with spike, the base pressure starts to increase right from the beginning and becomes more than atmospheric pressure at L/W = 6 to 10, and acquired base pressure values are 5% more than atmospheric pressure. The effect of spike and grooved spikes play an essential role in fixing the base pressure values. The impact of cavities is to reduce the oscillations in the enlarged duct.
- A computational fluid dynamics simulation over a payload fairing of the satellite launch vehicle with aerospike presence is carried out. The payload fairing significantly modifies its flow field and reduces the aerodynamic drag at transonic and supersonic speeds. The simulations were done by solving time-dependent compressible turbulent axisymmetric Navier-Stokes equations. The closure of the system of equations is achieved using an algebraic turbulence model. The numerical simulation is performed on a single-block structured computational domain. The flow field over the aerospike depends on the freestream Mach number. The effects of the aerospike attached to payload fairing are studied with velocity and density plots. The schlieren pictures, oil flow, and the pressure measurements on an aerospike attached to the payload fairing are analyzed and compared with the present numerical results with the Mach number in the range of 0.8 ≤ M ≤ 3.0 and freestream Reynolds number range 33.35 × 10
^{6}/m ≤ Re_{∞}≤ 46.75 × 10^{6}/m. The Mach number range covers the maximum drag and dynamic conditions during the typical satellite launch vehicle’s ascent flight. A distinct flow field is found for M_{∞}< 1 and M_{∞}> 1 with and without the aerospike attached to the payload fairing. The Flow separation is found at all the freestream Mach numbers over the aerospike, with the recirculation zone being Mach number dependent. As the freestream Mach number increases, the separation zone becomes steeper. It is found that the aerospike attached to the payload fairing leads to drag decline.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

X | Axial distance along the duct |

D | Diameter of the duct |

L | Length of the duct |

G | Distance between the rear base point of the cylinder and the leading edge of the splitter plates |

d | Cylinder diameter. |

NPR | Nozzle Pressure Ratio |

x | Mean velocity field in the plane |

c | Adjustable distance to the ground called ground clearance |

BFS | Backward Facing Step |

CDnet | Net drag coefficient |

Cpb | Base pressure coefficient |

BB | Blunt Base Model |

SVC | Small Length Ventilated Model |

SC | Solid Model |

L/D | Length-to-Diameter Ratio of the enlarged duct (pipe) |

PIV | Particle Image Velocimetry |

L/W | Length-to-Width Ratio |

PCD | Pitch Circle Diameter |

St | Strouhal Number |

f | Vortex shedding frequency |

D | Height of the backward-facing step |

U | Freestream velocity |

P | Pressure |

M | Mach number |

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**Figure 1.**Sudden Expansion Phenomenon [2].

**Figure 5.**Schematic diagram of external flow. (

**A**) External flow over an artillery shell; (

**B**) Flow over a blunt base; (

**C**) Coherent Vortex structures of in the instantaneous flow (

**a**) Visualization (

**b**) Streamlines with velocity contour [3].

**Figure 6.**Dimensions of the nozzle and the duct [6].

**Figure 7.**Square nozzle and grooved control plate [7].

**Figure 9.**Base pressure changes when NPR is increased from 1.5 to 5, and the aspect ratio is changed from 3:1 to 3:3 [18].

**Figure 10.**Dimensions of nozzle and duct [19].

**Figure 11.**Experimental setup [20].

**Figure 12.**Control plates with aerospike [21].

**Figure 13.**Square nozzle with threaded spikes control plate [23].

**Figure 14.**Ahmed body with 35° slant angle detailed view with rectangular flap (dimensions in mm) [38].

Type of Passive Control | Effect on Flow Field/Effect on Base Pressure Control |
---|---|

For Internal Flow Conditions | |

Rectangular shaped cavity | Shear layer development & increase in vorticity thickness increases the base pressure. |

Semi-circular grooves | Reduces the base drag |

Rectangular Rib | Reverse flow creates a low-pressure zone by the vortex |

Dimples | Passive control highly effective at higher NPR |

Static cylinder | Increases base pressure up to 59% |

Aerospikes | Reduces the suction at the base and increases base pressure up to 5% more than atmospheric pressure.When the aerospikes are located at the nose, they decrease the fore-body drag. |

Threaded spikes | Due to the threads, it develops vortices and manipulates the flow field & ultimately increases base pressure. |

For External Flow Conditions | |

Base Cavity | Increases the recirculation region size |

Ventilated cavity | Increases base pressure by a natural bleeding process |

Transverse cavity | Reduces pressure drag |

Boattailing | Reduces the base drag depends on the ratio of D_{b}/D. Where D_{b} is the boattail base diameter and D is the maximum diameter of the projectile. |

Baseline and shallow cavity | Creates viscous vortex flow, which is a source of low pressure. |

Forward-facing Aerospike | Reduces fore-body aerodynamic drag by dividing the stagnation region of the nose area along the length of the projectile and modifying the flow field. |

Splitter plate | A splitter plate is also used to divide the stagnation region in front of the nose along the width. With an increase in Reynolds number, the drag reduction increases up to 6.7% |

Triangular splitter plate | Total drag reduction up to 57% |

Thin slit at the base region | Increases vortex shedding & results in increased wake rotational speed |

Symmetric plates attached to the rear surface | Maximum drag reduction achieved at attachment angle 40 to 50 degrees |

Semi-circular lobes | The semi-circular lobes Improve turbulent mixing & the creation of the shear layer. It also reduces the reattachment length significantly by 75%. |

Tabs | Optimal tab configuration gives 30% increases in base pressure. |

Rectangular flap | Up to 14% drag reduction is achieved. |

Horizontal and vertical deflectors | They Reduce drag due to the decline in the wake. |

Triangular and elliptical flap | 11.1% drag reduction in oval shape whereas 6% drag reduction in other shapes. |

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Khan, A.; Rajendran, P.; Sidhu, J.S.S.
Passive Control of Base Pressure: A Review. *Appl. Sci.* **2021**, *11*, 1334.
https://doi.org/10.3390/app11031334

**AMA Style**

Khan A, Rajendran P, Sidhu JSS.
Passive Control of Base Pressure: A Review. *Applied Sciences*. 2021; 11(3):1334.
https://doi.org/10.3390/app11031334

**Chicago/Turabian Style**

Khan, Ambareen, Parvathy Rajendran, and Junior Sarjit Singh Sidhu.
2021. "Passive Control of Base Pressure: A Review" *Applied Sciences* 11, no. 3: 1334.
https://doi.org/10.3390/app11031334