Here's the Nemo of the society - trying to join the dots - Bharat's successful Shakti (ASAT) mission and the recent decision of Mauritius satellite tracking centre...

Sabkuch dikhta nahi hai ... Not everything is visible... As an avid reader, we must try to join the dots...

So... here we go...

Remember, Modi sir's speech in 2019 after successful Mission Shakti?

watch here...

Key Facts

1. Mission Shakti (India’s ASAT test, 2019):

   • On 27 March 2019, India (DRDO) destroyed one of its own satellites in low Earth orbit via a kinetic interceptor. 

   • It was done at a relatively low altitude (~282 km) to limit long‐lived debris.

   • The test had both technical and strategic significance: demonstrating capability, signaling deterrence, and making clearer India’s interest in space situational awareness (SSA) and satellite security.

2. India‑Mauritius Satellite Tracking / Telemetry, Tracking, and Telecommand (TT&C) Station:

   • Very recently, India and Mauritius signed a Memorandum of Understanding to set up a satellite tracking station in Mauritius, covering telemetry, tracking, and telecommand for satellites and launch vehicles. 

   • The purpose is non‑military (on paper), for space research, science, applications, etc. But it will improve India’s ability to monitor and manage its satellite assets, especially those in the Indian Ocean region. 

   • The facility will help receive data, send commands, monitor satellite health, track orbit, etc. 

How They Are Connected...

The connection between the ASAT test and the tracking station shows up in a few dimensions:

1. Need for Space Situational Awareness (SSA):

   • After carrying out ASAT, or in a strategic environment where anti‑satellite threats exist (whether from others or potential escalation), being able to see, track, monitor, and predict what satellites—including potentially hostile or damaged ones—are doing becomes very important. The ASAT test showed that space is contested, or at least that India wants to position itself as having deterrent capabilities. To make deterrence credible, you need monitoring/observation infrastructure.

   • A ground station in Mauritius helps India cover parts of the sky (especially over the Indian Ocean) that otherwise might have gaps in tracking or coverage from ground stations in India. Better coverage means better SSA, which in turn sharpens both defensive and deterrent capabilities (e.g. detect unusual or hostile satellite behavior; respond, etc.).

2. Operational Support for Satellite Control / Responsiveness:

   • Satellites (and launch vehicles) need ground stations for tracking, telemetry, commands. A closer or more distributed network of TT&C facilities allows more timely response in case of anomaly, damage, or threat.

   • In military terms, when one has ASAT capability, the other side might try to degrade or interfere with one’s satellites. Being able to quickly detect, diagnose, restore or re‑route around those effects depends on having resilient command, tracking and telemetry infrastructure.

3. Geopolitical / Strategic Depth in the Indian Ocean Region (IOR):

   • The Indian Ocean has become a focus region for strategic competition. Having infrastructure in Mauritius gives India strategic depth in the IOR—not only for "civil" satellites but also with dual‑use implications (i.e. facilities may help track foreign satellites or space debris of concern, or respond to threats).

   • It also aligns with India’s maritime/security/diplomatic goals in the region. Cooperation with Mauritius strengthens India’s presence and ability to project or monitor in the region. India’s “Mahāsāgar” vision, “Neighbourhood First” etc. policies tie into these strategic ambitions.

4. Deterrence Credibility:

   • Showing that one has ASAT means being able to threaten or counter adversaries in space. But that threat is more persuasive if the adversary knows you can detect their satellites (or threats), know their orbital path, see when something anomalous happens, etc. A good SSA network undercuts surprise, supports attribution, and thus enhances deterrence.

   • Also, if something happens to India’s satellite (say an attack or collision, etc.), having the tracking station means India can better document and assess the damage or cause, which can matter diplomatically or for escalation decisions.

What Is Not (Yet) Clear...

While the above linkages are logical, some matters are not yet fully known or confirmed; they rest on inference rather than public statements.

1. Extent of Military Use / Dual‑Use:

   • The TT&C station is officially for civil and scientific use, but such infrastructure is inherently dual‑use (civil/military). There is no public confirmation yet that it will be explicitly used for tracking adversarial satellites, missile warning, or counterspace operations.

   • How closely this facility will be integrated into India’s defence or space security architecture (e.g. with its SSA networks, Defence Space Agency, etc.) is not yet confirmed.

2. Technical Capabilities:

   • We don’t (publicly) have full details of the antenna sizes, sensitivities, coverage, whether the station can do optical, radar, or only radio telemetry/tracking, whether it will help track small debris, etc. This limits how capable the facility will be in supporting advanced SSA.

   • Also, how continuous will be its coverage; how much overlap with other Indian stations is there; what latencies; what secure communication; etc.

3. Policy / Doctrine Links:

   • Whether this specific station is explicitly tied into doctrine developed post‑ASAT (for example, specific roles in deterrence, threat detection, response, attribution) isn’t clear in open sources.

   • The legal, diplomatic, and strategic rules around India using such stations in case of conflict or threat are likely still being worked out behind the scenes.

4. Reaction by Other Powers / Risks of Countermeasures:

   • Building more tracking stations increases capabilities but could also be seen by others (e.g. China, maybe even the US or others) as increasing India’s space control / surveillance capacity. That can raise tensions. But so far, these concerns seem known and factored in diplomatically.

   • There might be diplomatic / diplomatic/security trade‑offs (e.g., sovereignty, data sharing, security of the infrastructure, vulnerability of the facility itself, etc.).

Overall Assessment

Putting it all together, the Mauritius satellite tracking station is very likely part of India's broader strategy post‑ASAT to build a more resilient, distributed, capable space infrastructure. It helps in bolstering space situational awareness, improving command and control of satellites, enhancing early warning or tracking of threats or anomalies, and thus reinforcing deterrence.

In short, ASAT was a capability demonstration; the new tracking station is part of the enabling infrastructure: it's less flashy, but essential, if India wants to make its deterrence credible, protect its own space assets, and possibly deter or counter hostile space operations in the Indian Ocean / North Hemisphere region.

My journey in exploration of CFD - verifying Couette flow using OpenFoam and ParaView - when theory meets computer analysis...

Have you ever wondered how fluids behave when they're dragged by a moving surface? Or how a thin layer of oil lubricates machinery? These phenomena, and many more, can be understood through a fundamental concept in fluid mechanics called Couette Flow.

Today, we're going to explore Couette flow, not just theoretically, but also through the lens of Computational Fluid Dynamics (CFD) using a simulation result visualized in ParaView.

What is Couette Flow?

Imagine two parallel plates. One plate is stationary, and the other is moving at a constant speed, dragging a viscous fluid between them. This is the essence of Couette flow. It's one of the simplest forms of fluid motion, driven purely by the shear stress exerted by the moving plate on the fluid.

Key Characteristics:

• Steady-state: The flow doesn't change with time.

• Laminar: The fluid moves in smooth, parallel layers, without turbulence.

• Incompressible: The fluid density remains constant.

• Constant Viscosity: The fluid's resistance to flow doesn't change.

• No Pressure Gradient: The flow is solely driven by the moving plate, not by a pressure difference.

Under these conditions, the velocity of the fluid varies linearly from zero at the stationary plate to the speed of the moving plate at its surface. This linear velocity profile is the hallmark of Couette flow.

Bringing it to Life with CFD

While analytical solutions for Couette flow exist, using CFD allows us to simulate and visualize these principles, even for more complex scenarios. Our image showcases the results of a CFD simulation for a Couette flow case.

Let's break down what we see in the ParaView visualization:

The image shows a fluid between two plates, with the top plate moving and the bottom one stationary. This setup creates a shear flow, where the fluid velocity varies linearly between the plates.

The smaller plot on the right, labeled "LineChartView1," is the most telling part. It shows the velocity profile along the vertical axis (Y-axis). The X-axis of this plot represents the velocity component U_X, and the Y-axis represents the vertical position.

The plot starts at zero velocity at the bottom (Y = 0).

It increases linearly with height.

It reaches a maximum velocity at the top of the domain.

This straight, diagonal line is the signature linear velocity profile of a simple, incompressible Couette flow.

I am happy to analyse a completely new subject - the Fluid Mechanics...

Jai hind... 

So...

Here I am...

Verifying Poiseuille Flow Using OpenFOAM and ParaView - the engineer in me is still alive...

Introduction

In computational fluid dynamics (CFD), verifying the solution of known analytical problems helps build confidence in simulation tools and numerical schemes. One such classical benchmark is Poiseuille flow — a pressure-driven, fully developed laminar flow through a channel.

This blog post shows how I recreated and verified the parabolic velocity profile of Poiseuille flow using OpenFOAM and visualized it using ParaView.

What Is Poiseuille Flow?

Poiseuille flow describes steady, incompressible, laminar flow of a Newtonian fluid in a long, straight channel driven by a pressure gradient. For a 2D rectangular channel, the flow is unidirectional along the channel length and exhibits a parabolic velocity profile in the transverse direction.

Governing Equations

We start with the Navier-Stokes equations simplified under assumptions:

• Incompressible, steady-state

• No-slip walls

• Pressure-driven

• Fully developed (no dependence on streamwise direction)

For flow in the x-direction, the reduced equation becomes:

$$\mu \frac{d^2 u}{dy^2} = \frac{dp}{dx}$$

Where:

• $u(y)$ is the velocity in x-direction

• $\mu$ is dynamic viscosity

• $\frac{dp}{dx}$ is the imposed pressure gradient

Analytical Solution

Solving the second-order ODE gives:

$$u(y) = \frac{1}{2\mu} \left( -\frac{dp}{dx} \right) y(H - y)$$

Where:

• $H$ is the channel height

• $y$ varies from 0 (bottom wall) to $H$ (top wall)

This is a parabola with maximum velocity at the centerline $y = H/2$ and zero velocity at the walls (due to no-slip boundary condition).

CFD Experiment Setup in OpenFOAM

I set up a simple 2D channel geometry using blockMeshDict, and simulated the flow using icoFoam, which is suitable for transient incompressible laminar flows.

📁 Boundary Conditions

• Inlet: Pressure fixed at 1 unit

• Outlet: Pressure fixed at 0 unit

• Walls: No-slip condition (U = (0 0 0))

• Initial Velocity: (0 0 0) throughout

🧱 Mesh

A rectangular domain:

• Length = 1 m

• Height = 0.1 m

• Depth = very thin (or empty to treat as 2D)

Result: Parabolic Profile in ParaView

Using ParaView, I plotted the x-component of velocity (U_X) along a vertical line from the bottom wall to the top wall at the center of the channel (x = 0.5).

📸 Here's the result:

As expected, the profile is:

• Zero at both walls (due to no-slip condition)

• Maximum at the center

• Symmetric about the mid-height

✅ This matches the theoretical prediction of Poiseuille's parabolic velocity profile.

Key Learnings

• CFD tools like OpenFOAM can accurately reproduce classical flow profiles

• Setting appropriate boundary conditions is crucial

• Post-processing in ParaView enables quantitative verification

• This benchmark builds confidence before moving to more complex simulations (e.g., turbulence, heat transfer)

Conclusion

Poiseuille flow is more than a textbook example — it's a fundamental test of our CFD setup. Successfully simulating it validates:

• Solver setup

• Boundary conditions

• Mesh quality

• Visualization pipeline

✅ And as shown, OpenFOAM + ParaView handles it elegantly.

So.... here I am...

The engineer in me is still thriving - verifying the no-slip boundary condition of Fluid Mechanics using OpenFOAM and ParaView...

 

Here i am doing proper CFD post-processing to experimentally verify the no-slip boundary condition using ParaView and the OpenFOAM elbow case. Let’s now interpret the screenshot from a CFD physics point of view.

Setup Summary

• Case: OpenFOAM elbow (steady incompressible internal flow)

• Tool: ParaView

• Filter: Plot Over Line

• Quantity: U_Magnitude (velocity magnitude)

• X-axis: arc_length along the line (from one point inside the fluid to the wall)

• Output: Velocity profile graph

What the Plot Shows

The graph on the right side shows:

• X-axis: Distance along the probing line (arc_length)

• Y-axis: Velocity magnitude (U_Magnitude)

The curve rises from a lower value, reaches a plateau around ~1.0, and then drops sharply to near 0 at the right end of the line.

CFD Interpretation of the Image

1. Velocity Profile Inside the Fluid

• The flat region (plateau around ~1.0) in the middle of the curve indicates uniform flow in the bulk of the fluid (away from walls).

• This is expected in fully developed or near-uniform flow in a pipe elbow.

2. Sharp Drop in Velocity Near the Wall

• On both ends (especially the right), the velocity drops rapidly to nearly 0.

• This is exactly what we expect from the no-slip boundary condition:

  Velocity must be zero at the wall due to the viscous adhesion of the fluid.

This confirms that my line probe passed from:

• Inside the fluid,

• Through the boundary layer,

• Up to the wall.

The no-slip condition is numerically satisfied in simulation.

3. Boundary Layer Visualization

• The sharp decline in the graph represents the boundary layer — the thin region near the wall where velocity transitions from free-stream to 0.🔹 

4. Numerical Observations

• The velocity doesn't drop instantly to zero, but over a few sample points — this is due to:

  • Finite resolution of the mesh,

  • Interpolation used in Plot Over Line,

  • Numerical diffusion (small artificial smearing due to discretization).

This is normal and expected in CFD.

CFD Physics Conclusion

Observation	CFD Interpretation
Velocity ~0 at wall	✔ No-slip boundary condition is respected
Plateau in middle	✔ Uniform flow in the bulk
Sharp gradient near wall	✔ Boundary layer captured
Small non-zero near-wall velocity	Acceptable due to mesh + numerical limits

From Software to Simulations: My Journey into Fluid Mechanics and the Navier-Stokes Theorem in Plain English...

As a software engineer, I’m used to breaking complex systems into components — loops, states, memory, and flow.

But when I stepped into the world of fluid mechanics, I found something just as elegant: the Navier-Stokes theorem, the core of Computational Fluid Dynamics (CFD).

Here’s how I made sense of this “fluid algorithm” using the tools I already know — abstraction, flow logic, and interpretation.

Software Meets Physics

I began to see fluid particles as objects in motion, and the forces acting on them as functions that change their velocity over time.

Like in physics engines or game loops, the core question remains:
What makes a particle move the way it does?

Breaking Down the Navier-Stokes Equation

Here’s the Navier-Stokes equation, often feared for its complexity, but actually a beautiful balance of terms:

In Plain English:

$$\text{Mass per unit volume} \times (\text{Local acceleration} + \text{Convective acceleration}) =$$ $$-\text{Pressure per unit volume} + \mu \times \text{Laplacian of velocity} + \text{Weight per unit volume}$$

Term-by-Term Interpretation

Term	Meaning
🧊 Mass per unit volume	Represents how much inertia the fluid has
⏱ Local acceleration	How fast the velocity is changing at a point
🧭 Convective acceleration	How fluid carries velocity changes through space
💨 − Pressure per unit volume	Push from surrounding particles (inward force)
🌀 μ × Laplacian of velocity	Viscous spreading — like internal friction
🌍 Weight per unit volume	Gravity or other body forces acting on fluid

Thinking Like a Programmer

Imagine you’re writing a simulator. For each fluid particle:

mass_density = ...
acceleration = local_acceleration + convective_acceleration

net_force = -pressure_gradient + viscosity_diffusion + body_force

acceleration = net_force / mass_density

It’s just Newton’s law applied to a fluid, per unit volume, using partial derivatives.

What I Learned

• Fluid motion is a dynamic balance of pressure, viscosity, and momentum.

• The Navier-Stokes equation is an algorithm for nature’s fluid engine.

• My software mindset helped me break it down, understand it, and even simulate it.

Conclusion

If you're coming from a programming or systems background, don't fear the math.
Look for the patterns, forces, and balances — the equation is just a logic tree waiting to be read.

For the engineering students, do you remember the free body diagrams used to solve engineering mechanics problems?

The Navier-Stoke theorem is just like that - only the logic of balance is applied to an infinitesimal small grid within a fluid.

"Yatha pinde tatha brahmande"- a Sanskrit phrase from the Yajurveda that means "As is the microcosm, so is the macrocosm," or "As the individual, so the universe" is...

Does not it sound like Calculus?

Enjoy...

In the search of WHY Computational Fluid Dynamics....

I am of the opinion that when we plan to delve into a subject, we must have a clear cut purpose - why we are doing it. This is what I say - first What - then Why - and then only How.

Purpose of learning a subject is essential to fall in love with the subject.

So here we go...

My exploration continues.

Why We Need CFD (Computational Fluid Dynamics)

We need CFD because the governing equations of fluid motion — such as the Navier-Stokes equations — are continuous, nonlinear partial differential equations (PDEs) that describe how fluid velocity, pressure, temperature, and density evolve over time and space.

These equations are derived based on:

- Conservation of mass (Continuity equation)

- Conservation of momentum (Newton’s second law → Navier-Stokes equations)

- Conservation of energy (First law of thermodynamics)

The Core Challenge...

These governing equations are defined in a continuous domain — meaning:

They assume infinitely small control volumes,

Variables like velocity and pressure change smoothly and continuously,

Solutions require solving PDEs over an infinite number of points in space and time.

But this is not possible to compute directly on a computer because:

GComputers can only work with discrete data — finite points and numbers.

How CFD Helps...

CFD bridges the gap by:

Discretizing the continuous equations into a finite form (e.g., using finite volume, finite difference, or finite element methods),

Breaking the domain into small control volumes or grid cells (called meshing),

Approximating the continuous functions and derivatives using numerical methods,

Solving the resulting algebraic equations using iterative solvers.

We need CFD because the fundamental equations governing fluid flow, like the Navier-Stokes equations, are defined in continuous form and cannot be solved analytically for most real-world problems. CFD allows us to discretize these equations, making them solvable using numerical methods on computers.

CFD exists because real fluids follow continuous laws, but computers need discrete data. CFD translates the language of calculus into the language of algorithms.