Hypersonics - Viscous Flow Flashcards
Covers the 6th chapter of John Andersons Hypersonic and High-Temperature gas dynamics.
What are similarity parameters?
Similarity parameters are useful constants that help determine the characteristics of a given flow.
They are obtained by non-dimensionalizing the governing equations and noting the constants that appear in front of the derivative terms.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 278
True or False
The assumption that ∂p/∂n = 0 in hypersonic flows is not always valid.
True.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 283
Define “self-similar solutions.”
Self-similar solutions occur when the coordinate system of the governing equations is transformed yet the solution gives the same profiles at different spatial locations in the transformed coordinate system.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 287
For hypersonic boundary layers, at large Mach numbers, the boundary layer thickness becomes ________.
Large.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 302
The effect of a cold wall is to ______ the boundary layer thickness.
reduce.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 303
The Eckert Number (E) is defined as ____ .
E = u^2 / h
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 748
The Lewis Number as defined by Anderson for chemically reacting flows is Le = __________.
Le = \rho_e D_{12}e cp{f,e} / k_e
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 748
What is the physical significance of the Eckert number?
It describes the ratio of kinetic flow energy to thermal energy.
E = u^2/h
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 748
What is the physical meaning of the Lewis Number?
It describes the ratio of energy transport caused by diffusion to thermal energy.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 748
True or False:
The Mach number and the ratio of specific heats are not similarity parameters for high speed chemically reacting flows.
True.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 748
For a gas in equilibrium, _____ thermodynamic variables uniquely define the thermodynamic state of the gas.
two
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 518
The translational mode has how many thermal degrees of freedom?
Three.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 521
What are the two contributions to the rotational mode?
- The rotational kinetic energy
- The moment of inertia.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 521
A diatomic molecule has how many geometric and thermal degrees of freedom with respect to the rotational mode?
Two
Extra Notes: The internuclear axis has negligible rotational kinetic energy and moment of inertia so it is usually ignored.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 521
A linear polyatomic molecule has how many geometric and thermal degrees of freedom with respect to the rotational mode?
Two
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 521
How many rotational degrees of freedom (geometric and thermal) does a non-linear polyatomic molecule have?
Three.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 521
What are the two energy contributions with vibrational energy?
- The kinetic energy of the linear motion of the atoms as they vibration back and forth
- The potential energy of the intermolecular force (symbolized as a spring).
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 521
How many geometric degrees of freedom are involved in the vibrational mode of a diatomic molecule?
One. The molecule only vibrates along the internuclear axis.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 521
For a polyatomic molecule, how many thermal degrees of freedom are there with respect to the vibrational mode?
Explain the physical contributions to each mode.
Two.
The contributions come from the kinetic energy of linear motion of the atoms as they vibrate back and forth, and the potential energy stored in the molecular bonds (symbolized as a spring).
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 521
True or False:
For polyatomic molecules, the vibrational modes are complex and there can be a large number of them.
True.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 521
For a single atom, only the ______ and ____modes exist.
translational, and electronic.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 522
The spacing for the vibrational modes _____ for higher energy levels?
decreases.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 522
The spacing for the rotational energy levels _________ with increasing energy levels?
increases
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 522
The rotational zero point energy is _____ at 0K.
zero.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 523
The energy spacings on the electronic mode ladder get _____ with increasing energy.
Smaller.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 522
True or False:
The zero point energies for translational, vibrational, and electronic energy modes are non-zero.
True.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 523
Explain why the zero point energy for the electronic mode is not zero.
Because if it were the electrons would fall into the nucleus and the atom would colapse.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 523
For a given energy level, there can be a number of different states with the same energy. This is called ________.
Degeneracy.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 525
Define “Population of an Energy Level.”
The number of atoms/molecules that are at a particular energy level(e.g., 20 molecules at 100 Joules).
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 525
Define “Population Distribution.”
A set of numbers that shows how many molecules are in each energy state. For example, 50 molecules at 1J, 100 molecules at 20 J, etc.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 525
The most probable macrostate is the one which has the maximum number of _____________.
microstates.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 527Wh
Define microstate?
A given population distribution. See the definition of population distribution.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 525
What distribution gives the most probable distribution of molecules over all the available energy levels of the system.
The Boltzmann distribution.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 534
What is the equation for e_trans for three degrees of freedom for a single species gas?
e_{trans} = (3/2)RT
Equation 11.57a
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 545
What is the equation for e_rot for a single species gas?
e_{rot} = RT := J/(kg)
Equation (11.59) in the reference.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 545
What is the equation for the vibration energy e_{vib}?
e_{vib} = ((hv/kbT)/(exp(hv/kbT) - 1)) * RT
Eq. (11.61) in the reference.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 545
What is the definition of c_v in terms of partial derivatives for atoms.
cv = (3/2)R + ∂e_{el}/∂T
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 547
For a gas with only tranlational and rotational energy for atoms, the equation for cv = ______.
cv = (3/2)R
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 547
For a pure gas with diatomic molecules, the equation for cv is __________.
cv = (5/2)R
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 5547
What is the equation for cp in terms of the specific gas constant and cv?
cp = cv + R := J/(kg-K)
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 547
An O2 molecule must experience approximately ______ collisions before it becomes vibrationally excited.
20,000
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 597
Molecules have their vibrational energy changed by ____________.
Collisions.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 595
Chemical reactions take place through ___________.
Collisions.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 595
The collision frequency Z is proportional to what two thermodynamic state variables?
Pressure and temperature (see equation below).
Z \propto p/sqrt{T}
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 596
The vibrational rate equation describes _______.
The time rate of change of vibrational energy of a gas as a result of molecular collisions.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 597
With regard to vibrational states, describe the principle of detailed balancing.
In equilibrium, each vibrational transition from one direction to another is exactly balanced by it’s couterpart in the opposite direction.
Extra Notes: From ChatGPT - For a system in equilibrium, in every process occurring in a system, there is a corresponding reverse process happening at the same rate, ensuring that the system is in a state of detailed equilibrium.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 598
If a gas is excited such that the vibrational mode goes above its equilibrium value, the excited particles will exchange vibrational energy with the _________ and ________ modes of the gas.
translational, rotational
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 602
As vibrational energy in excess gradually disperses towards the equilibrium value, it then reappears in part as an increase in the _______ energy.
translational
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 602
Explain Translation-Vibration (TV) transfers?
A molecule upon collision with another will gain or lose vibrational energy which then reappears as a decrease or increase in the translational kinetic energy of the molecules.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 603
Explain vibration-vibration (VV) transfers.
Upon a collision, the vibrational quantum lost by one molecule is gained by its collision partner.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 604
What is Anharmonic pumping?
During an expansion process (decreasing temperature), the V-V transfers among anharmonic molecules, result in a higher population in the higher energy levels than would be the case for a harmonic oscillator.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 605
During chemical non-equilibrium, chemical reactions take place at a _________ rate.
definite net (finite)
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 605
True or False:
For a non-equilibrium reaction, the individual chemical reactions that make up the reaction mechanism do not have to be independent.
True.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 610
True or False:
The chemical kinetic rates for dissociation are going to be slower if the gas is already highly excited vibrationally.
False. It will be faster.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 613
Define “thermodynamic equilibrium” wrt/ a local flowfield.
A local Boltzmann distribution exists at each point in the flow at the local temperature T.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 620
Define “local chemical equilibrium.”
The local chemical composition at each point in the flow is the same as that determined by the chemical equilibrium calculations at the local value of temperature and pressure.
ExtraNotes from ChatGPT: This refers to a state where the rates of the forward and reverse chemical reactions are equal, leading to constant concentrations of the reactants and products over time. Chemical equilibrium can be achieved in a closed system where no external forces or flows are acting to change the composition. In such a state, the concentrations of different species are determined by the equilibrium constants of the reactions, which depend on conditions like temperature and pressure but not on the concentrations of reactants and products themselves.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 620
What is the relationship between the chemical and vibrational rates for an equilibrium flow?
The chemical and vibraitonal rates are infinite for an equilibrium flow.
d[X]/dt = ∞
de_{vib} /dt = ∞
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 644
What is the relationship between the chemical and vibrational rates for a frozen flow?
The rates for both chemical and vibrational reactions/changes is zero for a frozen flow.
d[X]/dt = 0
de_{vib}/dt = 0
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 644
For a vibrationally frozen flow, the vibrational energy remains _______ throughout the flow.
Constant.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 645
What is the vibrational relaxation time for a frozen flow?
Infinite.
For a frozen flow, kf = kb = 0 and tau = infinity.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 672
What is the vibrational relaxation time for an equilibrium flow?
Zero.
Additional explanation: The vibrational relaxation time for an equilibrium flow is considered zero because, by definition, equilibrium implies that all processes, including vibrational relaxation, have reached a state where their rates are balanced.
See GoodNotes for a more detailed explanation.
Anderson, Hypersonic and High-Temperature Gas Dynamics, Pg. 672
What are the four similarity parameters for a hypersonic, viscous, chemically reacting flow?
- Reynolds Number
- Prandtl Number
- Lewis Number
- Eckert Number
Anderon, Hypersonic and High Temperature Gas Dynamics, Pg. 148
For a calorically perfect gas, what are the equations for e and h?
e = cvT
h = cpT
Fundamentals of Aerodynamics, Anderson, Pg. 531 (physical text version).
For a calorically perfect gas, what are the equations for cv and cp in terms of γ and R?
cp = γR / (γ - 1)
cv = R/(γ - 1)
Fundamentals of Aerodynamics, Anderson, Pg. 532 (physical text version).
