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The correct OPTION is (b) Equation of state

Explanation: In the COMPRESSIBLE flows, the DENSITY TERMS of the continuity equation do not CANCEL out. So, density can be determined using the continuity equation. Using this density value and the equation of state, we can get the pressure values.

Right choice is (c) PRESSURE IMPLICIT with Splitting of Operators

Explanation: The PISO ALGORITHM is expanded as Pressure Implicit with Splitting of Operators. It was introduced by Issa in the year 1986. This is ALSO an extension of the SIMPLE algorithm with some changes in it.

Right choice is (b) Revised

The best I can explain: The SIMPLER ALGORITHM stands for SIMPLE – Revised algorithm. This was INTRODUCED by Patankar who had worked for building the SIMPLE algorithm also. This was introduced in the YEAR 1980.

Right choice is (c) implicit time-dependent method

To explain I would say: The pressure correction method is based on time. It uses time steps to move towards a steady SOLUTION for steady PROBLEMS. If the problem is transient it uses time steps to move to the desired interval of time. It is an implicit method as it solves all the equations SIMULTANEOUSLY.

Correct ANSWER is (d) Rate of CHANGE TERM

For explanation I would say: The rate of change term represents the change in momentum in the momentum equations. This change is affected by any changes in the SURFACE fluxes, surface forces and body forces acting on the element.

The correct option is (b) finite VOLUME method

To explain I WOULD say: The conservative and non-conservative approaches gives rise to a considerable difference only in the finite volume method. In the finite difference APPROACH, they do not result in any VARIATION.

The correct CHOICE is (b) PARTIALLY staggered grid arrangements

The BEST explanation: The Arbitrary Lagrangian-Eulerian method is a partially staggered grid arrangement. It uses different locations to STORE the velocity and pressure fields but the arrangement varies from the COMPLETELY staggered arrangement.

Correct choice is (c) Prediction-correction is USED for the VELOCITY field

To explain: Though the pressure field in the SIMPLER algorithm does not need any GUESS and correction, the velocity field still NEEDS a prediction-correction method. It is found in a similar way as in the SIMPLE algorithm.

Right answer is (c) Pressure is directly calculated

To explain I would say: The SIMPLE algorithm uses a correction factor for CORRECTING the initial guessed pressure. But, this SIMPLER algorithm does not INVOLVE any GUESS and correction of pressure. It has an equation which can be SOLVED to directly get the pressure VALUES.

Correct option is (c) linear interpolation in a collocated grid

For explanation I WOULD say: The decoupling between the PRESSURE and velocity values at the CELL level happens due to linear interpolation USED in the collocated grid. This gives rise to the CHECKERBOARD problem in the collocated grids.

Correct option is (a) Velocities are STORED in the face centres

Best explanation: In the Arbitrary Lagrangian-Eulerian method, the scalar QUANTITIES are all stored at the cell centres LIKE the completely staggered arrangement. All the VELOCITY components are stored at the same point which are the vertices.

Correct CHOICE is (a) face centres

Easy EXPLANATION: In the staggered grid ARRANGEMENT, the velocities are STORES in the face centres. This is why there will not be any need for interpolation to get the velocity field for the CONTINUITY equation.

Correct answer is (d) Wrong PRESSURE FIELD will influence the velocity field

The explanation is: The effect of the pressure field on the velocity field in the SIMPLEC ALGORITHM is the same as the SIMPLE algorithm. A wrong pressure field will RESULT in a bad velocity field too.

Right option is (C) OMITS less SIGNIFICANT TERMS

Best explanation: The SIMPLEC algorithm omits some less significant terms in the SIMPLE algorithm. So, the velocity CORRECTION equations of the SIMPLEC model in all the three directions has fewer terms than the SIMPLE algorithm.

Correct CHOICE is (d) Continuity is ENFORCED before at each step moving to the next step

Explanation: The divergence of the velocity field at the current step should be MADE zero. For this, the divergence of the velocity field at the previous step must be zero. So, continuity is zero at each step before moving to the next step.

Correct answer is (c) LAPLACIAN operator

Explanation: The POISSON’s EQUATION which is formulated for FINDING the pressure values has a Laplace operator. This is the product of the divergence operator in the continuity equation and the gradient operator in the momentum equation.

Right choice is (b) velocity

Explanation: In general,

\(\DOT{m}=\rho UA\)

A correction in MASS FLOW rate cannot be the correction in density as density is constant in the incompressible flows. It cannot be a correction in area also as it is geometrically defined by the GRIDS. So, it must be a correction in velocity.

Correct CHOICE is (a) Non-conservative error

For explanation: Without USING the Gauss-Divergence theorem, the pressure FORCE can be treated as a volume integral itself. But, this will LEAD to a non-conservative form of EQUATIONS which, in turn, will result in non-conservative errors.

Right choice is (b) Finite volume method – conservative approach

For EXPLANATION: In the GENERAL integral form of the conservation equations, the PRESSURE force is taken as a volume integral. While using the finite volume method, this is changed into a SURFACE force by using the Gauss-Divergence theorem.

The CORRECT choice is (c) Bulk viscosity

To EXPLAIN: A PART of the viscous TERMS in the momentum equation is present in the diffusive term. Among these COMES the bulk viscosity terms. These terms will be non-zero only for the compressible flows.

The correct ANSWER is (b) viscous dissipation term

Explanation: The viscous dissipation term is an ADDITIONAL term in the energy conservation equation of the COMPRESSIBLE flows like the BULK viscosity term of the momentum equation. The discretization PROCEDURE is the same as that of the bulk viscosity term.

The correct answer is (a) PRESSURE-correction equation

The best explanation: In the SIMPLER algorithm, the VELOCITY FIELD should be corrected. For this correction and updating purpose, the pressure correction equation is used as in the SIMPLE algorithm. Therefore, the momentum EQUATIONS are also satisfied.

Right CHOICE is (a) Neighbouring correction terms

Easy explanation: The discretized momentum equation is rewritten for the INITIAL GUESSES. Now, the correction is INTRODUCED into this equation and the correction equations are formed. In these correction equations, the corrections for the neighbouring terms are omitted. This is applicable as it does not make any changes globally.

Correct ANSWER is (d) ONE predictor and two corrector steps

The explanation is: The SIMPLE algorithm has one predictor and one corrector steps. But, the PISO algorithm has an extra corrector STEP. Therefore, it can be CALLED an extension of the SIMPLE algorithm.

Correct CHOICE is (d) Consistent

The BEST explanation: SIMPLEC expands as SIMPLE-Consistent ALGORITHM. It was BUILT by Von Doormal and Raithby in the year 1984. It is advantageous over both the SIMPLE and SIMPLER algorithms.

The CORRECT answer is (B) An under-relaxation factor is USED to avoid divergence

Easiest explanation: The pressure correction equation may DIVERGE if an under-relaxation factor is not used. So, an under-relaxation factor is used with the correction term which is added to the guessed term to get the correct value.

Right answer is (d) The gradient of pressure correction

Explanation: There are two TERMS involved in the MASS flow RATE correction. When the MACH number is low, the gradient of pressure correction term dominates the flow and makes the equation elliptic.

Correct choice is (b) UPWIND difference

The explanation: The central difference SCHEME (or linear interpolation profile) produces OSCILLATIONS at high speeds. So, a bounded upwind FIRST or higher-order equation is used to get the density VALUES at the interfaces.

Correct ANSWER is (c) Under-relaxation factor

The EXPLANATION is: The PISO algorithm uses the under-relaxation procedure followed in the SIMPLE algorithm. This is the only algorithm that is MODIFIED from the SIMPLE algorithm which uses this under-relaxation factor.

The CORRECT option is (d) Momentum equation

Easiest explanation: The initial PRESSURE guesses are obtained from the momentum equation. This pressure field is used to get the VELOCITY field approximations. This is corrected in the first CORRECTOR step USING the pressure-correction equation. It is again corrected using the momentum equation in the second corrector step.

Correct choice is (d) The velocity field does not satisfy the MOMENTUM equation

The best I can explain: In the SIMPLE ALGORITHM, the velocity field is INITIALLY guessed USING the momentum equation. Then, corrections are made using the continuity equation. But, once corrected, the velocity field does not satisfy the momentum EQUATIONS.

Correct answer is (b) pressure gradient term

The explanation: The body force in the staggered grid term has the exact STENCIL of the pressure GRADIENTS. THEREFORE, a redistribution of the body force term in the Rhie-Chow interpolation is NEEDED to match the staggered grids.

The correct answer is (a) When the mass flow RATE reaches an exact solution, the CORRECTION field becomes zero

Easiest explanation: The correction equation obtained for the mass flow rate is

\(\dot{m}_{e}^{‘}+\dot{m}_{w}^{‘}=-\dot{m_e}*-\dot{m}_{w}^{*}\)

When the solution reaches the exact ANSWERS,

\(-\dot{m}_{e}^{*}-\dot{m}_{w}^{*}=\dot{m_e}*+\dot{m}_{w}^{*}=0\)

THEREFORE, the correction field

\(\dot{m}_{e}^{‘}+\dot{m}_{w}^{‘}=0\).

Correct answer is (a) VISCOUS terms

The explanation is: Pressure forces and BODY forces are not PRESENT as the flow is incompressible and has no body forces. The flux terms are usually treated with the Gauss-Divergence theorem and converted into SURFACE integrals. Therefore, the viscous terms remain as volume integrals here.

The correct answer is (d) PSEUDO-velocities

To EXPLAIN I WOULD say: The discretized pressure equation of the SIMPLER algorithm is the same as the pressure correction equation OBTAINED for the SIMPLE algorithm. The only difference is that the source term here is obtained from the pseudo velocities.

Right answer is (d) It is simultaneous

For explanation: The SIMPLE algorithm is sequential. The final SOLUTION of each iteration satisfies both the CONTINUITY and the momentum EQUATIONS. Only when these TWO are SATISFIED, the algorithm moves forward for the next iteration.

Right OPTION is (d) SIMPLE algorithm

For explanation: Rhie-Chow interpolation is used in the collocated GRID without leading to the uncoupled PRESSURE and velocity FIELDS. Rhie-Chow interpolation leads to the formulation of the SIMPLE algorithm.

Correct choice is (b) get a VELOCITY field that satisfies the continuity EQUATION

The best explanation: The first corrector step of the PISO algorithm results in a velocity field which will SATISFY the continuity equation. The EQUATIONS resulting from this step is the same as the equations used in the SIMPLE algorithm.

Correct ANSWER is (b) Faster convergence

Best explanation: As some of the terms in the MOMENTUM equation are omitted in the SIMPLEC ALGORITHM, the velocity CORRECTION suits the momentum equations more. THEREFORE, the rate of convergence increases in this algorithm.

The CORRECT choice is (B) pressure-velocity coupling of the staggered grid arrangement

Easiest explanation: The pressure gradients in the Rhie-Chow interpolation are calculated USING small grid stencil with two different stencils. This resembles the pressure-velocity coupling of the staggered grid arrangement.

The CORRECT OPTION is (d) Poisson EQUATION

The explanation is: The RESULTANT equation obtained by modifying the existing governing equations to get the pressure values is a Poisson equation for pressure. A Poisson equation is a partial differential equation of elliptic type.